[Question]
  [
Similar to the images on [allrgb.com](http://allrgb.com/), make images where each pixel is a unique color (no color is used twice and no color is missing).
Give a program that generates such an image, along with a screenshot or file of the output (upload as PNG).
* Create the image purely algorithmically.
* Image must be 256×128 (or grid that can be screenshot and saved at 256×128)
* Use all 15-bit colors\*
* No external input allowed (also no web queries, URLs or databases)
* No embedded images allowed (source code which is an image is fine, *e.g.* [Piet](http://esolangs.org/wiki/Piet))
* Dithering is allowed
* This is not a short code contest, although it might win you votes.
* If you're really up for a challenge, do 512×512, 2048×1024 or 4096×4096 (in increments of 3 bits).
**Scoring is by vote.** Vote for the most beautiful images made by the most elegant code and/or interesting algorithm.
Two-step algorithms, where you first generate a nice image and then fit all pixels to one of the available colors, are of course allowed, but won't win you elegance points.
\* 15-bit colors are the 32768 colors that can be made by mixing 32 reds, 32 greens, and 32 blues, all in equidistant steps and equal ranges. Example: in 24 bits images (8 bit per channel), the range per channel is 0..255 (or 0..224), so divide it up into 32 equally spaced shades.
To be very clear, the array of image pixels should be a permutation, because all possible images have the same colors, just at different pixels locations. I'll give a trivial permutation here, which isn't beautiful at all:
## Java 7
```
import java.awt.image.BufferedImage;
import java.io.BufferedOutputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.OutputStream;
import javax.imageio.ImageIO;
public class FifteenBitColors {
    public static void main(String[] args) {
        BufferedImage img = new BufferedImage(256, 128, BufferedImage.TYPE_INT_RGB);
        // Generate algorithmically.
        for (int i = 0; i < 32768; i++) {
            int x = i & 255;
            int y = i / 256;
            int r = i << 3 & 0xF8;
            int g = i >> 2 & 0xF8;
            int b = i >> 7 & 0xF8;
            img.setRGB(x, y, (r << 8 | g) << 8 | b);
        }
        // Save.
        try (OutputStream out = new BufferedOutputStream(new FileOutputStream("RGB15.png"))) {
            ImageIO.write(img, "png", out);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}
```
![enter image description here](https://i.stack.imgur.com/B4e5u.png)
## Winner
Because the 7 days are over, I'm declaring a winner
However, by no means, think this is over. I, and all readers, always welcome more awesome designs. Don't stop creating.
Winner: **fejesjoco** with 231 votes
  
[Answer]
# C#
I put a random pixel in the middle, and then start putting random pixels in a neighborhood that most resembles them. Two modes are supported: with minimum selection, only one neighboring pixel is considered at a time; with average selection, all (1..8) are averaged. Minimum selection is somewhat noisy, average selection is of course more blurred, but both look like paintings actually. After some editing, here is the current, somewhat optimized version (it even uses parallel processing!):
```
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Drawing;
using System.Drawing.Imaging;
using System.Diagnostics;
using System.IO;
class Program
{
    // algorithm settings, feel free to mess with it
    const bool AVERAGE = false;
    const int NUMCOLORS = 32;
    const int WIDTH = 256;
    const int HEIGHT = 128;
    const int STARTX = 128;
    const int STARTY = 64;
    // represent a coordinate
    struct XY
    {
        public int x, y;
        public XY(int x, int y)
        {
            this.x = x;
            this.y = y;
        }
        public override int GetHashCode()
        {
            return x ^ y;
        }
        public override bool Equals(object obj)
        {
            var that = (XY)obj;
            return this.x == that.x && this.y == that.y;
        }
    }
    // gets the difference between two colors
    static int coldiff(Color c1, Color c2)
    {
        var r = c1.R - c2.R;
        var g = c1.G - c2.G;
        var b = c1.B - c2.B;
        return r * r + g * g + b * b;
    }
    // gets the neighbors (3..8) of the given coordinate
    static List<XY> getneighbors(XY xy)
    {
        var ret = new List<XY>(8);
        for (var dy = -1; dy <= 1; dy++)
        {
            if (xy.y + dy == -1 || xy.y + dy == HEIGHT)
                continue;
            for (var dx = -1; dx <= 1; dx++)
            {
                if (xy.x + dx == -1 || xy.x + dx == WIDTH)
                    continue;
                ret.Add(new XY(xy.x + dx, xy.y + dy));
            }
        }
        return ret;
    }
    // calculates how well a color fits at the given coordinates
    static int calcdiff(Color[,] pixels, XY xy, Color c)
    {
        // get the diffs for each neighbor separately
        var diffs = new List<int>(8);
        foreach (var nxy in getneighbors(xy))
        {
            var nc = pixels[nxy.y, nxy.x];
            if (!nc.IsEmpty)
                diffs.Add(coldiff(nc, c));
        }
        // average or minimum selection
        if (AVERAGE)
            return (int)diffs.Average();
        else
            return diffs.Min();
    }
    static void Main(string[] args)
    {
        // create every color once and randomize the order
        var colors = new List<Color>();
        for (var r = 0; r < NUMCOLORS; r++)
            for (var g = 0; g < NUMCOLORS; g++)
                for (var b = 0; b < NUMCOLORS; b++)
                    colors.Add(Color.FromArgb(r * 255 / (NUMCOLORS - 1), g * 255 / (NUMCOLORS - 1), b * 255 / (NUMCOLORS - 1)));
        var rnd = new Random();
        colors.Sort(new Comparison<Color>((c1, c2) => rnd.Next(3) - 1));
        // temporary place where we work (faster than all that many GetPixel calls)
        var pixels = new Color[HEIGHT, WIDTH];
        Trace.Assert(pixels.Length == colors.Count);
        // constantly changing list of available coordinates (empty pixels which have non-empty neighbors)
        var available = new HashSet<XY>();
        // calculate the checkpoints in advance
        var checkpoints = Enumerable.Range(1, 10).ToDictionary(i => i * colors.Count / 10 - 1, i => i - 1);
        // loop through all colors that we want to place
        for (var i = 0; i < colors.Count; i++)
        {
            if (i % 256 == 0)
                Console.WriteLine("{0:P}, queue size {1}", (double)i / WIDTH / HEIGHT, available.Count);
            XY bestxy;
            if (available.Count == 0)
            {
                // use the starting point
                bestxy = new XY(STARTX, STARTY);
            }
            else
            {
                // find the best place from the list of available coordinates
                // uses parallel processing, this is the most expensive step
                bestxy = available.AsParallel().OrderBy(xy => calcdiff(pixels, xy, colors[i])).First();
            }
            // put the pixel where it belongs
            Trace.Assert(pixels[bestxy.y, bestxy.x].IsEmpty);
            pixels[bestxy.y, bestxy.x] = colors[i];
            // adjust the available list
            available.Remove(bestxy);
            foreach (var nxy in getneighbors(bestxy))
                if (pixels[nxy.y, nxy.x].IsEmpty)
                    available.Add(nxy);
            // save a checkpoint
            int chkidx;
            if (checkpoints.TryGetValue(i, out chkidx))
            {
                var img = new Bitmap(WIDTH, HEIGHT, PixelFormat.Format24bppRgb);
                for (var y = 0; y < HEIGHT; y++)
                {
                    for (var x = 0; x < WIDTH; x++)
                    {
                        img.SetPixel(x, y, pixels[y, x]);
                    }
                }
                img.Save("result" + chkidx + ".png");
            }
        }
        Trace.Assert(available.Count == 0);
    }
}
```
256x128 pixels, starting in the middle, minimum selection:
![](https://i.stack.imgur.com/huHP9.png)
![](https://i.stack.imgur.com/uB9cK.png)
256x128 pixels, starting in the top left corner, minimum selection:
![](https://i.stack.imgur.com/QFZgD.png)
256x128 pixels, starting in the middle, average selection:
![](https://i.stack.imgur.com/EB9xk.png)
![](https://i.stack.imgur.com/IqPnN.png)
Here are two 10-frame animgifs that show how minimum and average selection works (kudos to the gif format for being able to display it with 256 colors only):
![](https://i.stack.imgur.com/uuQ4z.gif)
![](https://i.stack.imgur.com/fSLeC.gif)
The mimimum selection mode grows with a small wavefront, like a blob, filling all pixels as it goes. In the average mode, however, when two different colored branches start growing next to each other, there will be a small black gap because nothing will be close enough to two different colors. Because of those gaps, the wavefront will be an order of magnitude larger, therefore the algorithm will be so much slower. But it's nice because it looks like a growing coral. If I would drop the average mode, it could be made a bit faster because each new color is compared to each existing pixel about 2-3 times. I see no other ways to optimize it, I think it's good enough as it is.
And the big attraction, here's an 512x512 pixels rendering, middle start, minimum selection:
![](https://i.stack.imgur.com/MlIL8.png)
I just can't stop playing with this! In the above code, the colors are sorted randomly. If we don't sort at all, or sort by hue (`(c1, c2) => c1.GetHue().CompareTo(c2.GetHue())`), we get these, respectively (both middle start and minimum selection):
![](https://i.stack.imgur.com/tVeGg.png)
![](https://i.stack.imgur.com/kBbUv.png)
Another combination, where the coral form is kept until the end: hue ordered with average selection, with a 30-frame animgif:
![](https://i.stack.imgur.com/8XrOG.png)
![](https://i.stack.imgur.com/GE6Ut.gif)
# UPDATE: IT IS READY!!!
You wanted hi-res, I wanted hi-res, you were impatient, I barely slept. Now I'm excited to announce that it's finally ready, production quality. And I am releasing it with a big bang, an awesome 1080p YouTube video! [Click here for the video](https://www.youtube.com/watch?v=OuvFsB4SLhA), let's make it viral to promote the geek style. I'm also posting stuff on my blog at <http://joco.name/>, there will be a technical post about all the interesting details, the optimizations, how I made the video, etc. And finally, I am [sharing the source code](https://code.google.com/archive/p/joco-tools/source) under GPL. It's become huge so a proper hosting is the best place for this, I will not edit the above part of my answer anymore. Be sure to compile in release mode! The program scales well to many CPU cores. A 4Kx4K render requires about 2-3 GB RAM.
I can now render huge images in 5-10 hours. I already have some 4Kx4K renders, I will post them later. The program has advanced a lot, there have been countless optimizations. I also made it user friendly so that anyone can easily use it, it has a nice command line. The program is also deterministically random, which means, you can use a random seed and it will generate the same image every time.
Here are some big renders.
My favorite 512:
[![](https://i.stack.imgur.com/M6mB8.png)](http://joco.name/wp-content/uploads/2014/03/rgb_512_3.png)  
(source: [joco.name](http://joco.name/wp-content/uploads/2014/03/rgb_512_3-150x150.png)) 
The 2048's which appear in my [video](https://www.youtube.com/watch?v=OuvFsB4SLhA):
[![](https://i.stack.imgur.com/2J5fZ.png)](http://joco.name/wp-content/uploads/2014/03/rgb_2048_1.png)  
(source: [joco.name](http://joco.name/wp-content/uploads/2014/03/rgb_2048_1-150x75.png)) 
[![](https://i.stack.imgur.com/IcqRp.png)](http://joco.name/wp-content/uploads/2014/03/rgb_2048_2.png)  
(source: [joco.name](http://joco.name/wp-content/uploads/2014/03/rgb_2048_2-150x75.png)) 
[![](https://i.stack.imgur.com/oY4YF.png)](http://joco.name/wp-content/uploads/2014/03/rgb_2048_3.png)  
(source: [joco.name](http://joco.name/wp-content/uploads/2014/03/rgb_2048_3-150x75.png)) 
[![](https://i.stack.imgur.com/pRlWt.png)](http://joco.name/wp-content/uploads/2014/03/rgb_2048_4.png)  
(source: [joco.name](http://joco.name/wp-content/uploads/2014/03/rgb_2048_4-150x75.png)) 
The first 4096 renders (TODO: they are being uploaded, and my website cannot handle the big traffic, so they are temporarily relocated):
[![](https://i.stack.imgur.com/xEoPV.png)](https://i.stack.imgur.com/xEoPV.png)  
(source: [joco.name](http://joco.name/wp-content/uploads/2014/03/rgb_4096_1-150x150.png)) 
[![](https://i.stack.imgur.com/bjax5.png)](https://i.stack.imgur.com/bjax5.png)  
(source: [joco.name](http://joco.name/wp-content/uploads/2014/03/rgb_4096_2-150x150.png)) 
[![](https://i.stack.imgur.com/0n8bv.png)](https://i.stack.imgur.com/0n8bv.png)  
(source: [joco.name](http://joco.name/wp-content/uploads/2014/03/rgb_4096_3-150x150.png)) 
[![](https://i.stack.imgur.com/hZIGS.png)](https://i.stack.imgur.com/hZIGS.png)  
(source: [joco.name](http://joco.name/wp-content/uploads/2014/03/rgb_4096_4-150x150.png)) 
[Answer]
# Processing
**Update!** 4096x4096 images!
I've merged my second post into this one by combining the two programs together.
**A full collection of selected images can be found [here, on Dropbox](https://www.dropbox.com/sh/hza6e3m77b0bedc/fL9B6o_NV4).** (Note: DropBox can't generate previews for the 4096x4096 images; just click them then click "Download").
If you only look at one [look at this one](https://www.dropbox.com/s/j5a9d4v1zkqgyn5/bigtile_128.png) (tileable)! Here it is scaled down (and many more below), original 2048x1024:
![enter image description here](https://i.stack.imgur.com/er15O.jpg)
This program works by walking paths from randomly selected points in the color cube, then drawing them into randomly selected paths in the image. There are a lot of possibilities. Configurable options are:
* Maximum length of color cube path.
* Maximum step to take through color cube (larger values cause larger variance but minimize the number of small paths towards the end when things get tight).
* Tiling the image.
* There are currently two image path modes:
	+ Mode 1 (the mode of this original post): Finds a block of unused pixels in the image and renders to that block. Blocks can be either randomly located, or ordered from left to right.
	+ Mode 2 (the mode of my second post that I merged into this one): Picks a random start point in the image and walks along a path through unused pixels; can walk around used pixels. Options for this mode:
		- Set of directions to walk in (orthogonal, diagonal, or both).
		- Whether or not to change the direction (currently clockwise but code is flexible) after each step, or to only change direction upon encountering an occupied pixel..
		- Option to shuffle order of direction changes (instead of clockwise).
It works for all sizes up to 4096x4096.
The complete Processing sketch can be found here: [Tracer.zip](https://www.dropbox.com/s/62bllk1ye63aob9/Tracer.zip) 
I've pasted all the files in the same code block below just to save space (even all in one file, it is still a valid sketch). If you want to use one of the presets, change the index in the `gPreset` assignment. If you run this in Processing you can press `r` while it is running to generate a new image.
* *Update 1: Optimized code to track first unused color/pixel and not search over known-used pixels; reduced 2048x1024 generation time from 10-30 minutes down to about 15 seconds, and 4096x4096 from 1-3 hours to about 1 minute. Drop box source and source below updated.*
* *Update 2: Fixed bug that was preventing 4096x4096 images from being generated.*
```
final int BITS = 5; // Set to 5, 6, 7, or 8!
// Preset (String name, int colorBits, int maxCubePath, int maxCubeStep, int imageMode, int imageOpts)
final Preset[] PRESETS = new Preset[] {
  // 0
  new Preset("flowers",      BITS, 8*32*32, 2, ImageRect.MODE2, ImageRect.ALL_CW | ImageRect.CHANGE_DIRS),
  new Preset("diamonds",     BITS, 2*32*32, 2, ImageRect.MODE2, ImageRect.ORTHO_CW | ImageRect.CHANGE_DIRS),
  new Preset("diamondtile",  BITS, 2*32*32, 2, ImageRect.MODE2, ImageRect.ORTHO_CW | ImageRect.CHANGE_DIRS | ImageRect.WRAP),
  new Preset("shards",       BITS, 2*32*32, 2, ImageRect.MODE2, ImageRect.ALL_CW | ImageRect.CHANGE_DIRS | ImageRect.SHUFFLE_DIRS),
  new Preset("bigdiamonds",  BITS,  100000, 6, ImageRect.MODE2, ImageRect.ORTHO_CW | ImageRect.CHANGE_DIRS),
  // 5
  new Preset("bigtile",      BITS,  100000, 6, ImageRect.MODE2, ImageRect.ORTHO_CW | ImageRect.CHANGE_DIRS | ImageRect.WRAP),
  new Preset("boxes",        BITS,   32*32, 2, ImageRect.MODE2, ImageRect.ORTHO_CW),
  new Preset("giftwrap",     BITS,   32*32, 2, ImageRect.MODE2, ImageRect.ORTHO_CW | ImageRect.WRAP),
  new Preset("diagover",     BITS,   32*32, 2, ImageRect.MODE2, ImageRect.DIAG_CW),
  new Preset("boxfade",      BITS,   32*32, 2, ImageRect.MODE2, ImageRect.DIAG_CW | ImageRect.CHANGE_DIRS),
  // 10
  new Preset("randlimit",    BITS,     512, 2, ImageRect.MODE1, ImageRect.RANDOM_BLOCKS),
  new Preset("ordlimit",     BITS,      64, 2, ImageRect.MODE1, 0),
  new Preset("randtile",     BITS,    2048, 3, ImageRect.MODE1, ImageRect.RANDOM_BLOCKS | ImageRect.WRAP),
  new Preset("randnolimit",  BITS, 1000000, 1, ImageRect.MODE1, ImageRect.RANDOM_BLOCKS),
  new Preset("ordnolimit",   BITS, 1000000, 1, ImageRect.MODE1, 0)
};
PGraphics gFrameBuffer;
Preset gPreset = PRESETS[2];
void generate () {
  ColorCube cube = gPreset.createCube();
  ImageRect image = gPreset.createImage();
  gFrameBuffer = createGraphics(gPreset.getWidth(), gPreset.getHeight(), JAVA2D);
  gFrameBuffer.noSmooth();
  gFrameBuffer.beginDraw();
  while (!cube.isExhausted())
    image.drawPath(cube.nextPath(), gFrameBuffer);
  gFrameBuffer.endDraw();
  if (gPreset.getName() != null)
    gFrameBuffer.save(gPreset.getName() + "_" + gPreset.getCubeSize() + ".png");
  //image.verifyExhausted();
  //cube.verifyExhausted();
}
void setup () {
  size(gPreset.getDisplayWidth(), gPreset.getDisplayHeight());
  noSmooth();
  generate();
}
void keyPressed () {
  if (key == 'r' || key == 'R')
    generate();
}
boolean autogen = false;
int autop = 0;
int autob = 5;
void draw () {
  if (autogen) {
    gPreset = new Preset(PRESETS[autop], autob);
    generate();
    if ((++ autop) >= PRESETS.length) {
      autop = 0;
      if ((++ autob) > 8)
        autogen = false;
    }
  }
  if (gPreset.isWrapped()) {
    int hw = width/2;
    int hh = height/2;
    image(gFrameBuffer, 0, 0, hw, hh);
    image(gFrameBuffer, hw, 0, hw, hh);
    image(gFrameBuffer, 0, hh, hw, hh);
    image(gFrameBuffer, hw, hh, hw, hh);
  } else {
    image(gFrameBuffer, 0, 0, width, height);
  }
}
static class ColorStep {
  final int r, g, b;
  ColorStep (int rr, int gg, int bb) { r=rr; g=gg; b=bb; }
}
class ColorCube {
  final boolean[] used;
  final int size; 
  final int maxPathLength;
  final ArrayList<ColorStep> allowedSteps = new ArrayList<ColorStep>();
  int remaining;
  int pathr = -1, pathg, pathb;
  int firstUnused = 0;
  ColorCube (int size, int maxPathLength, int maxStep) {
    this.used = new boolean[size*size*size];
    this.remaining = size * size * size;
    this.size = size;
    this.maxPathLength = maxPathLength;
    for (int r = -maxStep; r <= maxStep; ++ r)
      for (int g = -maxStep; g <= maxStep; ++ g)
        for (int b = -maxStep; b <= maxStep; ++ b)
          if (r != 0 && g != 0 && b != 0)
            allowedSteps.add(new ColorStep(r, g, b));
  }
  boolean isExhausted () {
    println(remaining);
    return remaining <= 0;
  }
  boolean isUsed (int r, int g, int b) {
    if (r < 0 || r >= size || g < 0 || g >= size || b < 0 || b >= size)
      return true;
    else
      return used[(r*size+g)*size+b];
  }
  void setUsed (int r, int g, int b) {
    used[(r*size+g)*size+b] = true;
  }
  int nextColor () {
    if (pathr == -1) { // Need to start a new path.
      // Limit to 50 attempts at random picks; things get tight near end.
      for (int n = 0; n < 50 && pathr == -1; ++ n) {
        int r = (int)random(size);
        int g = (int)random(size);
        int b = (int)random(size);
        if (!isUsed(r, g, b)) {
          pathr = r;
          pathg = g;
          pathb = b;
        }
      }
      // If we didn't find one randomly, just search for one.
      if (pathr == -1) {
        final int sizesq = size*size;
        final int sizemask = size - 1;
        for (int rgb = firstUnused; rgb < size*size*size; ++ rgb) {
          pathr = (rgb/sizesq)&sizemask;//(rgb >> 10) & 31;
          pathg = (rgb/size)&sizemask;//(rgb >> 5) & 31;
          pathb = rgb&sizemask;//rgb & 31;
          if (!used[rgb]) {
            firstUnused = rgb;
            break;
          }
        }
      }
      assert(pathr != -1);
    } else { // Continue moving on existing path.
      // Find valid next path steps.
      ArrayList<ColorStep> possibleSteps = new ArrayList<ColorStep>();
      for (ColorStep step:allowedSteps)
        if (!isUsed(pathr+step.r, pathg+step.g, pathb+step.b))
          possibleSteps.add(step);
      // If there are none end this path.
      if (possibleSteps.isEmpty()) {
        pathr = -1;
        return -1;
      }
      // Otherwise pick a random step and move there.
      ColorStep s = possibleSteps.get((int)random(possibleSteps.size()));
      pathr += s.r;
      pathg += s.g;
      pathb += s.b;
    }
    setUsed(pathr, pathg, pathb);  
    return 0x00FFFFFF & color(pathr * (256/size), pathg * (256/size), pathb * (256/size));
  } 
  ArrayList<Integer> nextPath () {
    ArrayList<Integer> path = new ArrayList<Integer>(); 
    int rgb;
    while ((rgb = nextColor()) != -1) {
      path.add(0xFF000000 | rgb);
      if (path.size() >= maxPathLength) {
        pathr = -1;
        break;
      }
    }
    remaining -= path.size();
    //assert(!path.isEmpty());
    if (path.isEmpty()) {
      println("ERROR: empty path.");
      verifyExhausted();
    }
    return path;
  }
  void verifyExhausted () {
    final int sizesq = size*size;
    final int sizemask = size - 1;
    for (int rgb = 0; rgb < size*size*size; ++ rgb) {
      if (!used[rgb]) {
        int r = (rgb/sizesq)&sizemask;
        int g = (rgb/size)&sizemask;
        int b = rgb&sizemask;
        println("UNUSED COLOR: " + r + " " + g + " " + b);
      }
    }
    if (remaining != 0)
      println("REMAINING COLOR COUNT IS OFF: " + remaining);
  }
}
static class ImageStep {
  final int x;
  final int y;
  ImageStep (int xx, int yy) { x=xx; y=yy; }
}
static int nmod (int a, int b) {
  return (a % b + b) % b;
}
class ImageRect {
  // for mode 1:
  //   one of ORTHO_CW, DIAG_CW, ALL_CW
  //   or'd with flags CHANGE_DIRS
  static final int ORTHO_CW = 0;
  static final int DIAG_CW = 1;
  static final int ALL_CW = 2;
  static final int DIR_MASK = 0x03;
  static final int CHANGE_DIRS = (1<<5);
  static final int SHUFFLE_DIRS = (1<<6);
  // for mode 2:
  static final int RANDOM_BLOCKS = (1<<0);
  // for both modes:
  static final int WRAP = (1<<16);
  static final int MODE1 = 0;
  static final int MODE2 = 1;
  final boolean[] used;
  final int width;
  final int height;
  final boolean changeDir;
  final int drawMode;
  final boolean randomBlocks;
  final boolean wrap;
  final ArrayList<ImageStep> allowedSteps = new ArrayList<ImageStep>();
  // X/Y are tracked instead of index to preserve original unoptimized mode 1 behavior
  // which does column-major searches instead of row-major.
  int firstUnusedX = 0;
  int firstUnusedY = 0;
  ImageRect (int width, int height, int drawMode, int drawOpts) {
    boolean myRandomBlocks = false, myChangeDir = false;
    this.used = new boolean[width*height];
    this.width = width;
    this.height = height;
    this.drawMode = drawMode;
    this.wrap = (drawOpts & WRAP) != 0;
    if (drawMode == MODE1) {
      myRandomBlocks = (drawOpts & RANDOM_BLOCKS) != 0;
    } else if (drawMode == MODE2) {
      myChangeDir = (drawOpts & CHANGE_DIRS) != 0;
      switch (drawOpts & DIR_MASK) {
      case ORTHO_CW:
        allowedSteps.add(new ImageStep(1, 0));
        allowedSteps.add(new ImageStep(0, -1));
        allowedSteps.add(new ImageStep(-1, 0));
        allowedSteps.add(new ImageStep(0, 1));
        break;
      case DIAG_CW:
        allowedSteps.add(new ImageStep(1, -1));
        allowedSteps.add(new ImageStep(-1, -1));
        allowedSteps.add(new ImageStep(-1, 1));
        allowedSteps.add(new ImageStep(1, 1));
        break;
      case ALL_CW:
        allowedSteps.add(new ImageStep(1, 0));
        allowedSteps.add(new ImageStep(1, -1));
        allowedSteps.add(new ImageStep(0, -1));
        allowedSteps.add(new ImageStep(-1, -1));
        allowedSteps.add(new ImageStep(-1, 0));
        allowedSteps.add(new ImageStep(-1, 1));
        allowedSteps.add(new ImageStep(0, 1));
        allowedSteps.add(new ImageStep(1, 1));
        break;
      }
      if ((drawOpts & SHUFFLE_DIRS) != 0)
        java.util.Collections.shuffle(allowedSteps);
    }
    this.randomBlocks = myRandomBlocks;
    this.changeDir = myChangeDir;
  }
  boolean isUsed (int x, int y) {
    if (wrap) {
      x = nmod(x, width);
      y = nmod(y, height);
    }
    if (x < 0 || x >= width || y < 0 || y >= height)
      return true;
    else
      return used[y*width+x];
  }
  boolean isUsed (int x, int y, ImageStep d) {
    return isUsed(x + d.x, y + d.y);
  }
  void setUsed (int x, int y) {
    if (wrap) {
      x = nmod(x, width);
      y = nmod(y, height);
    }
    used[y*width+x] = true;
  }
  boolean isBlockFree (int x, int y, int w, int h) {
    for (int yy = y; yy < y + h; ++ yy)
      for (int xx = x; xx < x + w; ++ xx)
        if (isUsed(xx, yy))
          return false;
    return true;
  }
  void drawPath (ArrayList<Integer> path, PGraphics buffer) {
    if (drawMode == MODE1)
      drawPath1(path, buffer);
    else if (drawMode == MODE2)
      drawPath2(path, buffer);
  }
  void drawPath1 (ArrayList<Integer> path, PGraphics buffer) {
    int w = (int)(sqrt(path.size()) + 0.5);
    if (w < 1) w = 1; else if (w > width) w = width;
    int h = (path.size() + w - 1) / w; 
    int x = -1, y = -1;
    int woff = wrap ? 0 : (1 - w);
    int hoff = wrap ? 0 : (1 - h);
    // Try up to 50 times to find a random location for block.
    if (randomBlocks) {
      for (int n = 0; n < 50 && x == -1; ++ n) {
        int xx = (int)random(width + woff);
        int yy = (int)random(height + hoff);
        if (isBlockFree(xx, yy, w, h)) {
          x = xx;
          y = yy;
        }
      }
    }
    // If random choice failed just search for one.
    int starty = firstUnusedY;
    for (int xx = firstUnusedX; xx < width + woff && x == -1; ++ xx) {
      for (int yy = starty; yy < height + hoff && x == -1; ++ yy) {
        if (isBlockFree(xx, yy, w, h)) {
          firstUnusedX = x = xx;
          firstUnusedY = y = yy;
        }  
      }
      starty = 0;
    }
    if (x != -1) {
      for (int xx = x, pathn = 0; xx < x + w && pathn < path.size(); ++ xx)
        for (int yy = y; yy < y + h && pathn < path.size(); ++ yy, ++ pathn) {
          buffer.set(nmod(xx, width), nmod(yy, height), path.get(pathn));
          setUsed(xx, yy);
        }
    } else {
      for (int yy = 0, pathn = 0; yy < height && pathn < path.size(); ++ yy)
        for (int xx = 0; xx < width && pathn < path.size(); ++ xx)
          if (!isUsed(xx, yy)) {
            buffer.set(nmod(xx, width), nmod(yy, height), path.get(pathn));
            setUsed(xx, yy);
            ++ pathn;
          }
    }
  }
  void drawPath2 (ArrayList<Integer> path, PGraphics buffer) {
    int pathn = 0;
    while (pathn < path.size()) {
      int x = -1, y = -1;
      // pick a random location in the image (try up to 100 times before falling back on search)
      for (int n = 0; n < 100 && x == -1; ++ n) {
        int xx = (int)random(width);
        int yy = (int)random(height);
        if (!isUsed(xx, yy)) {
          x = xx;
          y = yy;
        }
      }  
      // original:
      //for (int yy = 0; yy < height && x == -1; ++ yy)
      //  for (int xx = 0; xx < width && x == -1; ++ xx)
      //    if (!isUsed(xx, yy)) {
      //      x = xx;
      //      y = yy;
      //    }
      // optimized:
      if (x == -1) {
        for (int n = firstUnusedY * width + firstUnusedX; n < used.length; ++ n) {
          if (!used[n]) {
            firstUnusedX = x = (n % width);
            firstUnusedY = y = (n / width);
            break;
          }     
        }
      }
      // start drawing
      int dir = 0;
      while (pathn < path.size()) {
        buffer.set(nmod(x, width), nmod(y, height), path.get(pathn ++));
        setUsed(x, y);
        int diro;
        for (diro = 0; diro < allowedSteps.size(); ++ diro) {
          int diri = (dir + diro) % allowedSteps.size();
          ImageStep step = allowedSteps.get(diri);
          if (!isUsed(x, y, step)) {
            dir = diri;
            x += step.x;
            y += step.y;
            break;
          }
        }
        if (diro == allowedSteps.size())
          break;
        if (changeDir) 
          ++ dir;
      }    
    }
  }
  void verifyExhausted () {
    for (int n = 0; n < used.length; ++ n)
      if (!used[n])
        println("UNUSED IMAGE PIXEL: " + (n%width) + " " + (n/width));
  }
}
class Preset {
  final String name;
  final int cubeSize;
  final int maxCubePath;
  final int maxCubeStep;
  final int imageWidth;
  final int imageHeight;
  final int imageMode;
  final int imageOpts;
  final int displayScale;
  Preset (Preset p, int colorBits) {
    this(p.name, colorBits, p.maxCubePath, p.maxCubeStep, p.imageMode, p.imageOpts);
  }
  Preset (String name, int colorBits, int maxCubePath, int maxCubeStep, int imageMode, int imageOpts) {
    final int csize[] = new int[]{ 32, 64, 128, 256 };
    final int iwidth[] = new int[]{ 256, 512, 2048, 4096 };
    final int iheight[] = new int[]{ 128, 512, 1024, 4096 };
    final int dscale[] = new int[]{ 2, 1, 1, 1 };
    this.name = name; 
    this.cubeSize = csize[colorBits - 5];
    this.maxCubePath = maxCubePath;
    this.maxCubeStep = maxCubeStep;
    this.imageWidth = iwidth[colorBits - 5];
    this.imageHeight = iheight[colorBits - 5];
    this.imageMode = imageMode;
    this.imageOpts = imageOpts;
    this.displayScale = dscale[colorBits - 5];
  }
  ColorCube createCube () {
    return new ColorCube(cubeSize, maxCubePath, maxCubeStep);
  }
  ImageRect createImage () {
    return new ImageRect(imageWidth, imageHeight, imageMode, imageOpts);
  }
  int getWidth () {
    return imageWidth;
  }
  int getHeight () {
    return imageHeight;
  }
  int getDisplayWidth () {
    return imageWidth * displayScale * (isWrapped() ? 2 : 1);
  }
  int getDisplayHeight () {
    return imageHeight * displayScale * (isWrapped() ? 2 : 1);
  }
  String getName () {
    return name;
  }
  int getCubeSize () {
    return cubeSize;
  }
  boolean isWrapped () {
    return (imageOpts & ImageRect.WRAP) != 0;
  }
}
```
Here is a full set of 256x128 images that I like:
**Mode 1:**
My favorite from original set (max\_path\_length=512, path\_step=2, random, displayed 2x, link [256x128](http://s30.postimg.org/gqtujx71t/image.png)):
![enter image description here](https://i.stack.imgur.com/LAjNW.png)
Others (left two ordered, right two random, top two path length limited, bottom two unlimitted):
![ordlimit](https://i.stack.imgur.com/HOCNW.png)
![randlimit](https://i.stack.imgur.com/oYDGY.png)
![ordnolimit](https://i.stack.imgur.com/xnEm2.png)
![randnolimit](https://i.stack.imgur.com/Sydy3.png)
This one can be tiled:
![randtile](https://i.stack.imgur.com/Z7kEn.png)
**Mode 2:**
![diamonds](https://i.stack.imgur.com/cdrpA.png)
![flowers](https://i.stack.imgur.com/mxgiZ.png)
![boxfade](https://i.stack.imgur.com/RKIEf.png)
![diagover](https://i.stack.imgur.com/aMJQZ.png)
![bigdiamonds](https://i.stack.imgur.com/6IMsA.png)
![boxes2](https://i.stack.imgur.com/wox5T.png)
![shards](https://i.stack.imgur.com/Q1LkH.png)
These ones can be tiled:
![bigtile](https://i.stack.imgur.com/50ElU.png)
![diamondtile](https://i.stack.imgur.com/v0eMH.png)
![giftwrap](https://i.stack.imgur.com/p50cs.png)
**512x512 selections:**
Tileable diamonds, my favorite from mode 2; you can see in this one how the paths walk around existing objects:
![enter image description here](https://i.stack.imgur.com/1msnf.png)
Larger path step and max path length, tileable:
![enter image description here](https://i.stack.imgur.com/iLEnX.png)
Random mode 1, tileable:
![enter image description here](https://i.stack.imgur.com/ts1HA.png)
More selections:
![enter image description here](https://i.stack.imgur.com/imq0M.png)
![enter image description here](https://i.stack.imgur.com/mTqh6.png)
![enter image description here](https://i.stack.imgur.com/oHOvJ.png)
All of the 512x512 renderings can be found in the dropbox folder (\*\_64.png).
**2048x1024 and 4096x4096:**
These are too large to embed and all the image hosts I found drop them down to 1600x1200. I'm currently rendering a set of 4096x4096 images so more will be available soon. Instead of including all the links here, just go check them out in the dropbox folder (\*\_128.png and \*\_256.png, note: the 4096x4096 ones are too big for the dropbox previewer, just click "download"). Here are some of my favorites, though:
[2048x1024 big tileable diamonds](https://www.dropbox.com/s/j5a9d4v1zkqgyn5/bigtile_128.png) (same one I linked to at start of this post)
[2048x1024 diamonds](https://www.dropbox.com/s/vn7sxdthkg5k131/diamonds_128.png) (I love this one!), scaled down:
![enter image description here](https://i.stack.imgur.com/pFDhp.jpg)
[4096x4096 big tileable diamonds](https://www.dropbox.com/s/t2jvkxgvcz122r7/bigtile_256.png) (Finally! Click 'download' in Dropbox link; it's too large for their previewer), scaled way down:
[![4096x4096 big tileable diamonds](https://i.stack.imgur.com/SPQdz.jpg)](https://dl.dropboxusercontent.com/s/t2jvkxgvcz122r7/bigtile_256.png)
[4096x4096 random mode 1](https://www.dropbox.com/s/3g3bavtgjl7339r/randlimit_256.png):
![enter image description here](https://i.stack.imgur.com/WSBOV.jpg)
[4096x4096 another cool one](https://www.dropbox.com/s/eu93netbkedx2g8/roughtdiamondstile_256.png)
Update: The 2048x1024 preset image set is finished and in the dropbox. The 4096x4096 set should be done within the hour.
There's tons of good ones, I'm having a really hard time picking which ones to post, so please check out the folder link!
[Answer]
## Python w/ [PIL](http://www.pythonware.com/products/pil/)
This is based on a [Newtonian Fractal](http://en.wikipedia.org/wiki/Newton_fractal), specifically for *z → z5 - 1*. Because there are five roots, and thus five convergence points, the available color space is split into five regions, based on Hue. The individual points are sorted first by number of iterations required to reach their convergence point, ~~and then by distance to that point~~, with earlier values being assigned a more luminous color.
**Update:** 4096x4096 big renders, hosted on [allrgb.com](https://allrgb.com/).
**Update 2:** Because Newton's iteration converges quadratically, it's possible to compute non-integer convergence numbers, by adjusting by the log of the distance to the convergence point, divided by the log of the threshold. This creates a smooth gradient, without any noticeable rings.
![](https://i.stack.imgur.com/woj1Q.png)
[Original](https://allrgb.com/newtonian-fractal-1-redux) (44.2 MB)
A close-up of the very center (actual size):
![](https://i.stack.imgur.com/xehCm.png)
A different vantage point using these values:
```
xstart = 0
ystart = 0
xd = 1 / dim[0]
yd = 1 / dim[1]
```
![](https://i.stack.imgur.com/dPcxv.png)
[Original](https://allrgb.com/newtonian-fractal-2-redux) (42.7 MB)
And another using these:
```
xstart = 0.5
ystart = 0.5
xd = 0.001 / dim[0]
yd = 0.001 / dim[1]
```
![](https://i.stack.imgur.com/VKngr.png)
[Original](https://allrgb.com/newtonian-fractal-3-redux) (43.1 MB)
---
**Animation**
By request, I've compiled a zoom animation.
Focal Point: (*0.50051*, *-0.50051*)  
Zoom factor: *21/5*
The focal point is a slightly odd value, because I didn't want to zoom in on a black dot. The zoom factor is chosen such that it doubles every 5 frames.
A 32x32 teaser:
![](https://i.stack.imgur.com/EM2nP.gif)
A 256x256 version can be seen here:  
<http://www.pictureshack.org/images/66172_frac.gif> (5.4MB)
There may be points that mathematically zoom in "onto themselves," which would allow for an infinite animation. If I can identify any, I'll add them here.
---
**Source**
```
from __future__ import division
from PIL import Image, ImageDraw
from cmath import phase
from sys import maxint
from math import log10
dim  = (4096, 4096)
bits = 8
def RGBtoHSV(R, G, B):
  R /= 255
  G /= 255
  B /= 255
  cmin = min(R, G, B)
  cmax = max(R, G, B)
  dmax = cmax - cmin
  V = cmax
  if dmax == 0:
    H = 0
    S = 0
  else:
    S = dmax/cmax
    dR = ((cmax - R)/6 + dmax/2)/dmax
    dG = ((cmax - G)/6 + dmax/2)/dmax
    dB = ((cmax - B)/6 + dmax/2)/dmax
    if   R == cmax: H = (dB - dG)%1
    elif G == cmax: H = (1/3 + dR - dB)%1
    elif B == cmax: H = (2/3 + dG - dR)%1
  return (H, S, V)
cmax = (1<<bits)-1
cfac = 255/cmax
img  = Image.new('RGB', dim)
draw = ImageDraw.Draw(img)
xstart = -2
ystart = -2
xd = 4 / dim[0]
yd = 4 / dim[1]
tol = 1e-6
a = [[], [], [], [], []]
for x in range(dim[0]):
  print x, "\r",
  for y in range(dim[1]):
    z = d = complex(xstart + x*xd, ystart + y*yd)
    c = 0.0
    l = 1
    while abs(l-z) > tol and abs(z) > tol:
      l = z
      z -= (z**5-1)/(5*z**4)
      c += 1.0
    if z == 0: c = maxint
    p = int(phase(z))
    if abs(l-z) > 0.0:
      c += log10(abs(l-z)) / 6
    a[p] += (c, x, y),
for i in range(5):
  a[i].sort(reverse = False)
pnum = [len(a[i]) for i in range(5)]
ptot = dim[0]*dim[1]
bounds = []
lbound = 0
for i in range(4):
  nbound = lbound + pnum[i]/ptot
  bounds += nbound,
  lbound = nbound
t = [[], [], [], [], []]
for i in range(ptot-1, -1, -1):
  r = (i>>bits*2)*cfac
  g = (cmax&i>>bits)*cfac
  b = (cmax&i)*cfac
  (h, s, v) = RGBtoHSV(r, g, b)
  h = (h+0.1)%1
  if   h < bounds[0] and len(t[0]) < pnum[0]: p=0
  elif h < bounds[1] and len(t[1]) < pnum[1]: p=1
  elif h < bounds[2] and len(t[2]) < pnum[2]: p=2
  elif h < bounds[3] and len(t[3]) < pnum[3]: p=3
  else: p=4
  t[p] += (int(r), int(g), int(b)),
for i in range(5):
  t[i].sort(key = lambda c: c[0]*2126 + c[1]*7152 + c[2]*722, reverse = True)
r = [0, 0, 0, 0, 0]
for p in range(5):
  for c,x,y in a[p]:
    draw.point((x,y), t[p][r[p]])
    r[p] += 1
img.save("out.png")
```
[Answer]
I got this idea from user fejesjoco's algorithm and wanted to play a bit, so I started to write my own algorithm from scratch.
I'm posting this because I feel that if I can make something better\* than the best out of you guys, I don't think this challenge is finished yet. To compare, there are some stunning designs on allRGB that I consider way beyond the level reached here and I have no idea how they did it.
\*) will still be decided by votes
This algorithm:
1. Start with a (few) seed(s), with colors as close as possible to black.
2. Keep a list of all pixels that are unvisited and 8-connected to a visited point.
3. Select a random\*\* point from that list
4. Calculate the average color of all calculated pixels [Edit ...in a 9x9 square using a Gaussian kernel] ~~8-connected to it (this is the reason why it looks so smooth)~~ If none are found, take black.
5. in a 3x3x3 cube around this color, search for an unused color.
* When multple colors are found, take the darkest one.
* When multple equally dark colors are found, take a random one out of those.
* When nothing is found, update the search range to 5x5x5, 7x7x7, etc. Repeat from 5.
1. Plot pixel, update list and repeat from 3
I also experimented with different probabilities of choosing candidate points based on counting how many visited neighbors the selected pixel has, but it only slowed down the algorithm without making it prettier. The current algorithm doesn't use probabilities and chooses a random point from the list. This causes points with lots of neighbors to quickly fill up, making it just a growing solid ball with a fuzzy edge. This also prevents unavailability of neighboring colors if the crevices were to be filled up later in the process.
The image is toroidal.
## Java
Download: [`com.digitalmodular` library](https://web.archive.org/web/20160313202909/https://dl.dropboxusercontent.com/u/13260068/com.digitalmodular.zip)
```
package demos;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.io.IOException;
import java.util.Arrays;
import com.digitalmodular.utilities.RandomFunctions;
import com.digitalmodular.utilities.gui.ImageFunctions;
import com.digitalmodular.utilities.swing.window.PixelImage;
import com.digitalmodular.utilities.swing.window.PixelWindow;
/**
 * @author jeronimus
 */
// Date 2014-02-28
public class AllColorDiffusion extends PixelWindow implements Runnable {
    private static final int    CHANNEL_BITS    = 7;
    public static void main(String[] args) {
        int bits = CHANNEL_BITS * 3;
        int heightBits = bits / 2;
        int widthBits = bits - heightBits;
        new AllColorDiffusion(CHANNEL_BITS, 1 << widthBits, 1 << heightBits);
    }
    private final int           width;
    private final int           height;
    private final int           channelBits;
    private final int           channelSize;
    private PixelImage          img;
    private javax.swing.Timer   timer;
    private boolean[]           colorCube;
    private long[]              foundColors;
    private boolean[]           queued;
    private int[]               queue;
    private int                 queuePointer    = 0;
    private int                 remaining;
    public AllColorDiffusion(int channelBits, int width, int height) {
        super(1024, 1024 * height / width);
        RandomFunctions.RND.setSeed(0);
        this.width = width;
        this.height = height;
        this.channelBits = channelBits;
        channelSize = 1 << channelBits;
    }
    @Override
    public void initialized() {
        img = new PixelImage(width, height);
        colorCube = new boolean[channelSize * channelSize * channelSize];
        foundColors = new long[channelSize * channelSize * channelSize];
        queued = new boolean[width * height];
        queue = new int[width * height];
        for (int i = 0; i < queue.length; i++)
            queue[i] = i;
        new Thread(this).start();
    }
    @Override
    public void resized() {}
    @Override
    public void run() {
        timer = new javax.swing.Timer(500, new ActionListener() {
            @Override
            public void actionPerformed(ActionEvent e) {
                draw();
            }
        });
        while (true) {
            img.clear(0);
            init();
            render();
        }
        // System.exit(0);
    }
    private void init() {
        RandomFunctions.RND.setSeed(0);
        Arrays.fill(colorCube, false);
        Arrays.fill(queued, false);
        remaining = width * height;
        // Initial seeds (need to be the darkest colors, because of the darkest
        // neighbor color search algorithm.)
        setPixel(width / 2 + height / 2 * width, 0);
        remaining--;
    }
    private void render() {
        timer.start();
        for (; remaining > 0; remaining--) {
            int point = findPoint();
            int color = findColor(point);
            setPixel(point, color);
        }
        timer.stop();
        draw();
        try {
            ImageFunctions.savePNG(System.currentTimeMillis() + ".png", img.image);
        }
        catch (IOException e1) {
            e1.printStackTrace();
        }
    }
    void draw() {
        g.drawImage(img.image, 0, 0, getWidth(), getHeight(), 0, 0, width, height, null);
        repaintNow();
    }
    private int findPoint() {
        while (true) {
            // Time to reshuffle?
            if (queuePointer == 0) {
                for (int i = queue.length - 1; i > 0; i--) {
                    int j = RandomFunctions.RND.nextInt(i);
                    int temp = queue[i];
                    queue[i] = queue[j];
                    queue[j] = temp;
                    queuePointer = queue.length;
                }
            }
            if (queued[queue[--queuePointer]])
                return queue[queuePointer];
        }
    }
    private int findColor(int point) {
        int x = point & width - 1;
        int y = point / width;
        // Calculate the reference color as the average of all 8-connected
        // colors.
        int r = 0;
        int g = 0;
        int b = 0;
        int n = 0;
        for (int j = -1; j <= 1; j++) {
            for (int i = -1; i <= 1; i++) {
                point = (x + i & width - 1) + width * (y + j & height - 1);
                if (img.pixels[point] != 0) {
                    int pixel = img.pixels[point];
                    r += pixel >> 24 - channelBits & channelSize - 1;
                    g += pixel >> 16 - channelBits & channelSize - 1;
                    b += pixel >> 8 - channelBits & channelSize - 1;
                    n++;
                }
            }
        }
        r /= n;
        g /= n;
        b /= n;
        // Find a color that is preferably darker but not too far from the
        // original. This algorithm might fail to take some darker colors at the
        // start, and when the image is almost done the size will become really
        // huge because only bright reference pixels are being searched for.
        // This happens with a probability of 50% with 6 channelBits, and more
        // with higher channelBits values.
        //
        // Try incrementally larger distances from reference color.
        for (int size = 2; size <= channelSize; size *= 2) {
            n = 0;
            // Find all colors in a neighborhood from the reference color (-1 if
            // already taken).
            for (int ri = r - size; ri <= r + size; ri++) {
                if (ri < 0 || ri >= channelSize)
                    continue;
                int plane = ri * channelSize * channelSize;
                int dr = Math.abs(ri - r);
                for (int gi = g - size; gi <= g + size; gi++) {
                    if (gi < 0 || gi >= channelSize)
                        continue;
                    int slice = plane + gi * channelSize;
                    int drg = Math.max(dr, Math.abs(gi - g));
                    int mrg = Math.min(ri, gi);
                    for (int bi = b - size; bi <= b + size; bi++) {
                        if (bi < 0 || bi >= channelSize)
                            continue;
                        if (Math.max(drg, Math.abs(bi - b)) > size)
                            continue;
                        if (!colorCube[slice + bi])
                            foundColors[n++] = Math.min(mrg, bi) << channelBits * 3 | slice + bi;
                    }
                }
            }
            if (n > 0) {
                // Sort by distance from origin.
                Arrays.sort(foundColors, 0, n);
                // Find a random color amongst all colors equally distant from
                // the origin.
                int lowest = (int)(foundColors[0] >> channelBits * 3);
                for (int i = 1; i < n; i++) {
                    if (foundColors[i] >> channelBits * 3 > lowest) {
                        n = i;
                        break;
                    }
                }
                int nextInt = RandomFunctions.RND.nextInt(n);
                return (int)(foundColors[nextInt] & (1 << channelBits * 3) - 1);
            }
        }
        return -1;
    }
    private void setPixel(int point, int color) {
        int b = color & channelSize - 1;
        int g = color >> channelBits & channelSize - 1;
        int r = color >> channelBits * 2 & channelSize - 1;
        img.pixels[point] = 0xFF000000 | ((r << 8 | g) << 8 | b) << 8 - channelBits;
        colorCube[color] = true;
        int x = point & width - 1;
        int y = point / width;
        queued[point] = false;
        for (int j = -1; j <= 1; j++) {
            for (int i = -1; i <= 1; i++) {
                point = (x + i & width - 1) + width * (y + j & height - 1);
                if (img.pixels[point] == 0) {
                    queued[point] = true;
                }
            }
        }
    }
}
```
* 512×512
* original 1 seed
* 1 second
![enter image description here](https://i.stack.imgur.com/6fJbB.png)
* 2048×1024
* slightly tiled to 1920×1080 desktop
* 30 seconds
* negative in photoshop
[![enter image description here](https://i.stack.imgur.com/LmlTg.png)](https://www.dropbox.com/s/1iv69l81du7eb4e/1393627450209desktop.png)
* 2048×1024
* 8 seeds
* 27 seconds
[![enter image description here](https://i.stack.imgur.com/mIibM.png)](https://www.dropbox.com/s/cxjsqq23hkijh5n/1393632034224.png)
* 512×512
* 40 random seeds
* 6 seconds
![enter image description here](https://i.stack.imgur.com/LhBOK.png)
* 4096×4096
* 1 seed
* Streaks get significantly sharper (as in they look like they could chop a fish into sashimi)
* Looked like it finished in 20 minutes, but ... failed to finish for some reason, so now I'm running 7 instances in parallel overnight.
[See below]
[Edit]  
\*\* I discovered that my method of choosing pixels was not totally random at all. I thought having a random permutation of the search space would be random and faster than real random (because a point will not be chosen twice by chance. However somehow, replacing it with real random, I consistently get more noise speckles in my image.
[version 2 code removed because I was over the 30,000 character limit]
![enter image description here](https://i.stack.imgur.com/fQ9AN.png)
* Increased the initial search cube to 5x5x5
![enter image description here](https://i.stack.imgur.com/95gxQ.png)
* Even bigger, 9x9x9
![enter image description here](https://i.stack.imgur.com/THD6R.png)
* Accident 1. Disabled the permutation so the search space is always linear.
![enter image description here](https://i.stack.imgur.com/roVx3.png)
* Accident 2. Tried a new search technique using a fifo queue. Still have to analyze this but I thought it was worth sharing.
![enter image description here](https://i.stack.imgur.com/yTliq.png)
* Always choosing within X unused pixels from the center
* X ranges from 0 to 8192 in steps of 256
Image can't be uploaded: "Oops! Something Bad Happened! It’s not you, it’s us. This is our fault." Image is just too big for imgur. Trying elsewhere...
[![enter image description here](https://i.stack.imgur.com/dscwE.gif)](https://i.stack.imgur.com/dscwE.gif)  
(source: [gfycat.com](https://giant.gfycat.com/UnconsciousYawningArcticwolf.gif))
Experimenting with a scheduler package I found in the `digitalmodular` library to determine the order in which the pixels are handled (instead of diffusion).
```
package demos;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.io.IOException;
import java.util.Arrays;
import com.digitalmodular.utilities.RandomFunctions;
import com.digitalmodular.utilities.gui.ImageFunctions;
import com.digitalmodular.utilities.gui.schedulers.ScheduledPoint;
import com.digitalmodular.utilities.gui.schedulers.Scheduler;
import com.digitalmodular.utilities.gui.schedulers.XorScheduler;
import com.digitalmodular.utilities.swing.window.PixelImage;
import com.digitalmodular.utilities.swing.window.PixelWindow;
/**
 * @author jeronimus
 */
// Date 2014-02-28
public class AllColorDiffusion3 extends PixelWindow implements Runnable {
    private static final int    CHANNEL_BITS    = 7;
    public static void main(String[] args) {
        int bits = CHANNEL_BITS * 3;
        int heightBits = bits / 2;
        int widthBits = bits - heightBits;
        new AllColorDiffusion3(CHANNEL_BITS, 1 << widthBits, 1 << heightBits);
    }
    private final int           width;
    private final int           height;
    private final int           channelBits;
    private final int           channelSize;
    private PixelImage          img;
    private javax.swing.Timer   timer;
    private Scheduler           scheduler   = new XorScheduler();
    private boolean[]           colorCube;
    private long[]              foundColors;
    public AllColorDiffusion3(int channelBits, int width, int height) {
        super(1024, 1024 * height / width);
        this.width = width;
        this.height = height;
        this.channelBits = channelBits;
        channelSize = 1 << channelBits;
    }
    @Override
    public void initialized() {
        img = new PixelImage(width, height);
        colorCube = new boolean[channelSize * channelSize * channelSize];
        foundColors = new long[channelSize * channelSize * channelSize];
        new Thread(this).start();
    }
    @Override
    public void resized() {}
    @Override
    public void run() {
        timer = new javax.swing.Timer(500, new ActionListener() {
            @Override
            public void actionPerformed(ActionEvent e) {
                draw();
            }
        });
        // for (double d = 0.2; d < 200; d *= 1.2)
        {
            img.clear(0);
            init(0);
            render();
        }
        // System.exit(0);
    }
    private void init(double param) {
        // RandomFunctions.RND.setSeed(0);
        Arrays.fill(colorCube, false);
        // scheduler = new SpiralScheduler(param);
        scheduler.init(width, height);
    }
    private void render() {
        timer.start();
        while (scheduler.getProgress() != 1) {
            int point = findPoint();
            int color = findColor(point);
            setPixel(point, color);
        }
        timer.stop();
        draw();
        try {
            ImageFunctions.savePNG(System.currentTimeMillis() + ".png", img.image);
        }
        catch (IOException e1) {
            e1.printStackTrace();
        }
    }
    void draw() {
        g.drawImage(img.image, 0, 0, getWidth(), getHeight(), 0, 0, width, height, null);
        repaintNow();
        setTitle(Double.toString(scheduler.getProgress()));
    }
    private int findPoint() {
        ScheduledPoint p = scheduler.poll();
        // try {
        // Thread.sleep(1);
        // }
        // catch (InterruptedException e) {
        // }
        return p.x + width * p.y;
    }
    private int findColor(int point) {
        // int z = 0;
        // for (int i = 0; i < colorCube.length; i++)
        // if (!colorCube[i])
        // System.out.println(i);
        int x = point & width - 1;
        int y = point / width;
        // Calculate the reference color as the average of all 8-connected
        // colors.
        int r = 0;
        int g = 0;
        int b = 0;
        int n = 0;
        for (int j = -3; j <= 3; j++) {
            for (int i = -3; i <= 3; i++) {
                point = (x + i & width - 1) + width * (y + j & height - 1);
                int f = (int)Math.round(10000 * Math.exp((i * i + j * j) * -0.4));
                if (img.pixels[point] != 0) {
                    int pixel = img.pixels[point];
                    r += (pixel >> 24 - channelBits & channelSize - 1) * f;
                    g += (pixel >> 16 - channelBits & channelSize - 1) * f;
                    b += (pixel >> 8 - channelBits & channelSize - 1) * f;
                    n += f;
                }
                // System.out.print(f + "\t");
            }
            // System.out.println();
        }
        if (n > 0) {
            r /= n;
            g /= n;
            b /= n;
        }
        // Find a color that is preferably darker but not too far from the
        // original. This algorithm might fail to take some darker colors at the
        // start, and when the image is almost done the size will become really
        // huge because only bright reference pixels are being searched for.
        // This happens with a probability of 50% with 6 channelBits, and more
        // with higher channelBits values.
        //
        // Try incrementally larger distances from reference color.
        for (int size = 2; size <= channelSize; size *= 2) {
            n = 0;
            // Find all colors in a neighborhood from the reference color (-1 if
            // already taken).
            for (int ri = r - size; ri <= r + size; ri++) {
                if (ri < 0 || ri >= channelSize)
                    continue;
                int plane = ri * channelSize * channelSize;
                int dr = Math.abs(ri - r);
                for (int gi = g - size; gi <= g + size; gi++) {
                    if (gi < 0 || gi >= channelSize)
                        continue;
                    int slice = plane + gi * channelSize;
                    int drg = Math.max(dr, Math.abs(gi - g));
                    // int mrg = Math.min(ri, gi);
                    long srg = ri * 299L + gi * 436L;
                    for (int bi = b - size; bi <= b + size; bi++) {
                        if (bi < 0 || bi >= channelSize)
                            continue;
                        if (Math.max(drg, Math.abs(bi - b)) > size)
                            continue;
                        if (!colorCube[slice + bi])
                            // foundColors[n++] = Math.min(mrg, bi) <<
                            // channelBits * 3 | slice + bi;
                            foundColors[n++] = srg + bi * 114L << channelBits * 3 | slice + bi;
                    }
                }
            }
            if (n > 0) {
                // Sort by distance from origin.
                Arrays.sort(foundColors, 0, n);
                // Find a random color amongst all colors equally distant from
                // the origin.
                int lowest = (int)(foundColors[0] >> channelBits * 3);
                for (int i = 1; i < n; i++) {
                    if (foundColors[i] >> channelBits * 3 > lowest) {
                        n = i;
                        break;
                    }
                }
                int nextInt = RandomFunctions.RND.nextInt(n);
                return (int)(foundColors[nextInt] & (1 << channelBits * 3) - 1);
            }
        }
        return -1;
    }
    private void setPixel(int point, int color) {
        int b = color & channelSize - 1;
        int g = color >> channelBits & channelSize - 1;
        int r = color >> channelBits * 2 & channelSize - 1;
        img.pixels[point] = 0xFF000000 | ((r << 8 | g) << 8 | b) << 8 - channelBits;
        colorCube[color] = true;
    }
}
```
* Angular(8)
![enter image description here](https://i.stack.imgur.com/A1xCe.png)
* Angular(64)
![enter image description here](https://i.stack.imgur.com/YzXDS.png)
* CRT
![enter image description here](https://i.stack.imgur.com/uOpPO.png)
* Dither
![enter image description here](https://i.stack.imgur.com/w1CDK.png)
* Flower(5, X), where X ranges from 0.5 to 20 in steps of X=X×1.2
[![enter image description here](https://web.archive.org/web/20200427233053/https://giant.gfycat.com/DeficientRegularDalmatian.gif)](https://web.archive.org/web/20200427233053/https://giant.gfycat.com/DeficientRegularDalmatian.gif)
* Mod
![enter image description here](https://i.stack.imgur.com/9HgIv.png)
* Pythagoras
![enter image description here](https://i.stack.imgur.com/gmTDd.png)
* Radial
![enter image description here](https://i.stack.imgur.com/zZMMX.png)
* Random
![enter image description here](https://i.stack.imgur.com/kJCnK.png)
* Scanline
![enter image description here](https://i.stack.imgur.com/nrquO.png)
* Spiral(X), where X ranges from 0.1 to 200 in steps of X=X×1.2
* You can see it ranges in between Radial to Angular(5)
![enter image description here](https://web.archive.org/web/20200427233038/https://giant.gfycat.com/GrandCorruptDogwoodtwigborer.gif)
* Split
![enter image description here](https://i.stack.imgur.com/XMmQ8.png)
* SquareSpiral
![enter image description here](https://i.stack.imgur.com/3zw5Q.png)
* XOR
![enter image description here](https://i.stack.imgur.com/hA9eB.png)
## New eye-food
* Effect of color selection by `max(r, g, b)`
[![enter image description here](https://i.stack.imgur.com/p0Hch.png)](https://www.dropbox.com/s/jewh7p1dlpr7gbq/1393880791834%20Max.png)
* Effect of color selection by `min(r, g, b)`
* Notice that this one has exactly the same features/details as the one above, only with different colors! (same random seed)
[![enter image description here](https://i.stack.imgur.com/zETcn.png)](https://www.dropbox.com/s/95liwa92026ld2z/1393880713852%20Min.png)
* Effect of color selection by `max(r, min(g, b))`
![enter image description here](https://i.stack.imgur.com/gfv8d.png)
* Effect of color selection by gray value `299*r + 436*g + 114*b`
[![enter image description here](https://i.stack.imgur.com/1cQ25.png)](https://www.dropbox.com/s/ha0dc86z12eiysc/1393880296207%20Min%20rg,%20Max%20b.png)
* Effect of color selection by `1*r + 10*g + 100*b`
![enter image description here](https://i.stack.imgur.com/Fa2Vo.png)
* Effect of color selection by `100*r + 10*g + 1*b`
![enter image description here](https://i.stack.imgur.com/eewr1.png)
* Happy accidents when `299*r + 436*g + 114*b` overflowed in a 32-bit integer
![enter image description here](https://i.stack.imgur.com/DeIAc.png)
![enter image description here](https://i.stack.imgur.com/77Oo3.png)
![enter image description here](https://i.stack.imgur.com/wrTqr.png)
* Variant 3, with gray value and Radial scheduler
![enter image description here](https://i.stack.imgur.com/I3fAd.png)
* I forgot how I created this
![enter image description here](https://i.stack.imgur.com/Sv4BC.png)
* The CRT Scheduler also had a happy integer overflow bug (updated the ZIP), this caused it to start half-way, with 512×512 images, instead of at the center. This is what it's supposed to look like:
![enter image description here](https://i.stack.imgur.com/N2QWv.png)
[![enter image description here](https://i.stack.imgur.com/8lFHq.png)](https://www.dropbox.com/s/w1w9im8zcpdj4fr/1393881350789.png)
* `InverseSpiralScheduler(64)` (new)
[![enter image description here](https://i.stack.imgur.com/0QqYS.png)](https://www.dropbox.com/s/agbvtlhnj2gw3qv/1393881704577%20Spiral%20inverse.png)
* Another XOR
[![enter image description here](https://i.stack.imgur.com/bW5Q7.png)](https://www.dropbox.com/s/ohdx7xb4r24pltj/1393882082161.png)
* First successful 4096 render after the bugfix. I think this was version 3 on `SpiralScheduler(1)` or something
[![enter image description here](https://i.stack.imgur.com/N9ND8.png)](https://www.dropbox.com/s/mbn22zbu2ngwban/1393878918242%204096.png) (50MB!!)
* Version 1 4096, but I accidentally left the color criteria on `max()`
[![enter image description here](https://i.stack.imgur.com/98OL3.png)](https://www.dropbox.com/s/tdadbkt5z64qdlz/1393884676911.png) (50MB!!)
* 4096, now with `min()`
* Notice that this one has exactly the same features/details as the one above, only with different colors! (same random seed)
* Time: forgot to record it but the file timestamp is 3 minutes after the image before
[![enter image description here](https://i.stack.imgur.com/IfPSF.png)](https://www.dropbox.com/s/uan1gli8hlqz9i3/1393915197270.png) (50MB!!)
[Answer]
## C++ w/ Qt
I see you version:
![enter image description here](https://i.stack.imgur.com/g0cEF.png)
using normal distribution for the colors:
![enter image description here](https://i.stack.imgur.com/vXIfR.png)
![enter image description here](https://i.stack.imgur.com/F2mab.png)
or first sorted by red / hue (with a smaller deviation):
![enter image description here](https://i.stack.imgur.com/WfldG.png)
![enter image description here](https://i.stack.imgur.com/hnQmr.png)
or some other distributions:
![enter image description here](https://i.stack.imgur.com/a746K.png)
![enter image description here](https://i.stack.imgur.com/AgYkE.png)
Cauchy distribution (hsl / red):
![enter image description here](https://i.stack.imgur.com/wIPX1.png)
![enter image description here](https://i.stack.imgur.com/NVfch.png)
sorted cols by lightness (hsl):
![enter image description here](https://i.stack.imgur.com/3zVel.png)
updated source code - produces 6th image:
```
int main() {
    const int c = 256*128;
    std::vector<QRgb> data(c);
    QImage image(256, 128, QImage::Format_RGB32);
    std::default_random_engine gen;
    std::normal_distribution<float> dx(0, 2);
    std::normal_distribution<float> dy(0, 1);
    for(int i = 0; i < c; ++i) {
        data[i] = qRgb(i << 3 & 0xF8, i >> 2 & 0xF8, i >> 7 & 0xF8);
    }
    std::sort(data.begin(), data.end(), [] (QRgb a, QRgb b) -> bool {
        return QColor(a).hsvHue() < QColor(b).hsvHue();
    });
    int i = 0;
    while(true) {
        if(i % 10 == 0) { //no need on every iteration
            dx = std::normal_distribution<float>(0, 8 + 3 * i/1000.f);
            dy = std::normal_distribution<float>(0, 4 + 3 * i/1000.f);
        }
        int x = (int) dx(gen);
        int y = (int) dy(gen);
        if(x < 256 && x >= 0 && y >= 0 && y < 128) {
            if(!image.pixel(x, y)) {
                image.setPixel(x, y, data[i]);
                if(i % (c/100) == 1) {
                    std::cout << (int) (100.f*i/c) << "%\n";
                }
                if(++i == c) break;
            }
        }
    }
    image.save("tmp.png");
    return 0;
}
```
[Answer]
# In Java:
```
import java.awt.Color;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.Collections;
import java.util.LinkedList;
import javax.imageio.ImageIO;
public class ImgColor {
    private static class Point {
        public int x, y;
        public color c;
        public Point(int x, int y, color c) {
            this.x = x;
            this.y = y;
            this.c = c;
        }
    }
    private static class color {
        char r, g, b;
        public color(int i, int j, int k) {
            r = (char) i;
            g = (char) j;
            b = (char) k;
        }
    }
    public static LinkedList<Point> listFromImg(String path) {
        LinkedList<Point> ret = new LinkedList<>();
        BufferedImage bi = null;
        try {
            bi = ImageIO.read(new File(path));
        } catch (IOException e) {
            e.printStackTrace();
        }
        for (int x = 0; x < 4096; x++) {
            for (int y = 0; y < 4096; y++) {
                Color c = new Color(bi.getRGB(x, y));
                ret.add(new Point(x, y, new color(c.getRed(), c.getGreen(), c.getBlue())));
            }
        }
        Collections.shuffle(ret);
        return ret;
    }
    public static LinkedList<color> allColors() {
        LinkedList<color> colors = new LinkedList<>();
        for (int r = 0; r < 256; r++) {
            for (int g = 0; g < 256; g++) {
                for (int b = 0; b < 256; b++) {
                    colors.add(new color(r, g, b));
                }
            }
        }
        Collections.shuffle(colors);
        return colors;
    }
    public static Double cDelta(color a, color b) {
        return Math.pow(a.r - b.r, 2) + Math.pow(a.g - b.g, 2) + Math.pow(a.b - b.b, 2);
    }
    public static void main(String[] args) {
        BufferedImage img = new BufferedImage(4096, 4096, BufferedImage.TYPE_INT_RGB);
        LinkedList<Point> orig = listFromImg(args[0]);
        LinkedList<color> toDo = allColors();
        Point p = null;
        while (orig.size() > 0 && (p = orig.pop()) != null) {
            color chosen = toDo.pop();
            for (int i = 0; i < Math.min(100, toDo.size()); i++) {
                color c = toDo.pop();
                if (cDelta(c, p.c) < cDelta(chosen, p.c)) {
                    toDo.add(chosen);
                    chosen = c;
                } else {
                    toDo.add(c);
                }
            }
            img.setRGB(p.x, p.y, new Color(chosen.r, chosen.g, chosen.b).getRGB());
        }
        try {
            ImageIO.write(img, "PNG", new File(args[1]));
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}
```
and an input image:
![lemur](https://i.stack.imgur.com/gxg6C.jpg)
I generate something like this:
![acidLemur](https://i.stack.imgur.com/cec0B.jpg)
uncompressed version here: <https://www.mediafire.com/?7g3fetvaqhoqgh8>
It takes my computer roughly 30 minutes to do a 4096^2 image, which is a huge improvement over the 32 days my first implementation would have taken.
[Answer]
## Java
Variations of a color picker in 512x512. *Elegant code it is not*, but I do like the pretty pictures:
```
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.Random;
import javax.imageio.ImageIO;
public class EighteenBitColors {
    static boolean shuffle_block = false;
    static int shuffle_radius = 0;
    
    public static void main(String[] args) {
        BufferedImage img = new BufferedImage(512, 512, BufferedImage.TYPE_INT_RGB);
        for(int r=0;r<64;r++)
            for(int g=0;g<64;g++)
                for(int b=0;b<64;b++)
                    img.setRGB((r * 8) + (b / 8), (g * 8) + (b % 8), ((r * 4) << 8 | (g * 4)) << 8 | (b * 4));
        
        if(shuffle_block)
            blockShuffle(img);
        else
            shuffle(img, shuffle_radius);
        
        try {           
            ImageIO.write(img, "png", new File(getFileName()));
        } catch(IOException e){
            System.out.println("suck it");
        }
    }
    
    public static void shuffle(BufferedImage img, int radius){
        if(radius < 1)
            return;
        int width = img.getWidth();
        int height = img.getHeight();
        Random rand = new Random();
        for(int x=0;x<512;x++){
            for(int y=0;y<512;y++){
                int xx = -1;
                int yy = -1;
                while(xx < 0 || xx >= width){
                    xx = x + rand.nextInt(radius*2+1) - radius;
                }
                while(yy < 0 || yy >= height){
                    yy = y + rand.nextInt(radius*2+1) - radius;
                }
                int tmp = img.getRGB(xx, yy);
                img.setRGB(xx, yy, img.getRGB(x, y));
                img.setRGB(x,y,tmp);
            }
        }
    }
    
    public static void blockShuffle(BufferedImage img){
        int tmp;
        Random rand = new Random();
        for(int bx=0;bx<8;bx++){
            for(int by=0;by<8;by++){
                for(int x=0;x<64;x++){
                    for(int y=0;y<64;y++){
                        int xx = bx*64+x;
                        int yy = by*64+y;
                        int xxx = bx*64+rand.nextInt(64);
                        int yyy = by*64+rand.nextInt(64);
                        tmp = img.getRGB(xxx, yyy);
                        img.setRGB(xxx, yyy, img.getRGB(xx, yy));
                        img.setRGB(xx,yy,tmp);
                    }
                }
            }
        }
    }
    
    public static String getFileName(){
        String fileName = "allrgb_";
        if(shuffle_block){
            fileName += "block";
        } else if(shuffle_radius > 0){
            fileName += "radius_" + shuffle_radius;
        } else {
            fileName += "no_shuffle";
        }
        return fileName + ".png";
    }
}
```
As written, it outputs:
![no shuffle](https://i.stack.imgur.com/4NN4a.png)
If you run it with `shuffle_block = true`, it shuffles the colors in each 64x64 block:
![block shuffle](https://i.stack.imgur.com/TeQm8.png)
Else, if you run it with `shuffle_radius > 0`, it shuffles each pixel with a random pixel within `shuffle_radius` in x/y. After playing with various sizes, I like a 32 pixel radius, as it blurs the lines without moving stuff around too much:
![enter image description here](https://i.stack.imgur.com/1EbkO.png)
[Answer]
# Java with BubbleSort
(usually Bubblesort isnt liked that much but for this challenge it finally had a use :)
generated a line with all elements in 4096 steps apart then shuffled it;
the sorting went thru and each like got 1 added to their value while being sorted so as result you got the values sorted and all colors
Updated the Sourcecode to get those big stripes removed  
(needed some bitwise magic :P)
```
class Pix
{
    public static void main(String[] devnull) throws Exception
    {
        int chbits=8;
        int colorsperchannel=1<<chbits;
        int xsize=4096,ysize=4096;
        System.out.println(colorsperchannel);
        int[] x = new int[xsize*ysize];//colorstream
        BufferedImage i = new BufferedImage(xsize,ysize, BufferedImage.TYPE_INT_RGB);
        List<Integer> temp = new ArrayList<>();
        for (int j = 0; j < 4096; j++)
        {
            temp.add(4096*j);
        }
        int[] temp2=new int[4096];
        
        Collections.shuffle(temp,new Random(9263));//intended :P looked for good one
        for (int j = 0; j < temp.size(); j++)
        {
            temp2[j]=(int)(temp.get(j));
        }
        x = spezbubblesort(temp2, 4096);
        int b=-1;
        int b2=-1;
        for (int j = 0; j < x.length; j++)
        {
            if(j%(4096*16)==0)b++;
            if(j%(4096)==0)b2++;
            int h=j/xsize;
            int w=j%xsize;
            i.setRGB(w, h, x[j]&0xFFF000|(b|(b2%16)<<8));
            x[j]=x[j]&0xFFF000|(b|(b2%16)<<8);
        }  
        
        //validator sorting and checking that all values only have 1 difference
        Arrays.sort(x);
        int diff=0;
        for (int j = 1; j < x.length; j++)
        {
            int ndiff=x[j]-x[j-1];
            if(ndiff!=diff)
            {
                System.out.println(ndiff);
            }
            diff=ndiff;
            
        }
        OutputStream out = new BufferedOutputStream(new FileOutputStream("RGB24.bmp"));
        ImageIO.write(i, "bmp", out);
    }
    public static int[] spezbubblesort(int[] vals,int lines)
    {
        int[] retval=new int[vals.length*lines];
        for (int i = 0; i < lines; i++)
        {
            retval[(i<<12)]=vals[0];
            for (int j = 1; j < vals.length; j++)
            {
                retval[(i<<12)+j]=vals[j];
                if(vals[j]<vals[j-1])
                {
                    
                    int temp=vals[j-1];
                    vals[j-1]=vals[j];
                    vals[j]=temp;
                }
                vals[j-1]=vals[j-1]+1;
            }
            vals[lines-1]=vals[lines-1]+1;
        }
        return retval;
    }
}
```
![Result:](https://i.stack.imgur.com/qfvwr.jpg)
Old version
```
class Pix
{
    public static void main(String[] devnull) throws Exception
    {
        int[] x = new int[4096*4096];//colorstream
        int idx=0;
        BufferedImage i = new BufferedImage(4096, 4096, BufferedImage.TYPE_INT_RGB);
        //GENCODE
        List<Integer> temp = new ArrayList<>();
        for (int j = 0; j < 4096; j++)
        {
            temp.add(4096*j);
        }
        int[] temp2=new int[4096];
        
        Collections.shuffle(temp,new Random(9263));//intended :P looked for good one
        for (int j = 0; j < temp.size(); j++)
        {
            temp2[j]=(int)(temp.get(j));
        }
        x = spezbubblesort(temp2, 4096);
        for (int j = 0; j < x.length; j++)
        {
            int h=j/4096;
            int w=j%4096;
            i.setRGB(w, h, x[j]);
        }
        //validator sorting and checking that all values only have 1 difference
        Arrays.sort(x);
        int diff=0;
        for (int j = 1; j < x.length; j++)
        {
            int ndiff=x[j]-x[j-1];
            if(ndiff!=diff)
            {
                System.out.println(ndiff);
            }
            diff=ndiff;
            
        }
        OutputStream out = new BufferedOutputStream(new FileOutputStream("RGB24.bmp"));
        ImageIO.write(i, "bmp", out);
    }
    public static int[] spezbubblesort(int[] vals,int lines)
    {
        int[] retval=new int[vals.length*lines];
        for (int i = 0; i < lines; i++)
        {
            retval[(i<<12)]=vals[0];
            for (int j = 1; j < vals.length; j++)
            {
                retval[(i<<12)+j]=vals[j];
                if(vals[j]<vals[j-1])
                {
                    
                    int temp=vals[j-1];
                    vals[j-1]=vals[j];
                    vals[j]=temp;
                }
                vals[j-1]=vals[j-1]+1;
            }
            vals[lines-1]=vals[lines-1]+1;
        }
        return retval;
    }
}
```
![output preview](https://i.stack.imgur.com/kqatz.jpg)
[Answer]
# C
Creates a vortex, for reasons I don't understand, with even and odd frames containing completely different vortices.
This a preview of the first 50 odd frames:
![vortex preview](https://i.stack.imgur.com/BEyPY.gif)
Sample image converted from PPM to demo complete color coverage:
![sample image](https://i.stack.imgur.com/3GnAW.png)
Later on, when it's all blended into grey, you can still see it spinning: [longer sequence](http://www.mediafire.com/convkey/c01a/lz56znlgsre8cddfg.jpg).
Code as follows. To run, include the frame number, e.g.:
```
./vortex 35 > 35.ppm
```
I used this to get an animated GIF:
```
convert -delay 10 `ls *.ppm | sort -n | xargs` -loop 0 vortex.gif
```
```
#include <stdlib.h>
#include <stdio.h>
#define W 256
#define H 128
typedef struct {unsigned char r, g, b;} RGB;
int S1(const void *a, const void *b)
{
    const RGB *p = a, *q = b;
    int result = 0;
    if (!result)
        result = (p->b + p->g * 6 + p->r * 3) - (q->b + q->g * 6 + q->r * 3);
    return result;
}
int S2(const void *a, const void *b)
{
    const RGB *p = a, *q = b;
    int result = 0;
    if (!result)
        result = p->b * 6 - p->g;
    if (!result)
        result = p->r - q->r;
    if (!result)
        result = p->g - q->b * 6;
    return result;
}
int main(int argc, char *argv[])
{
    int i, j, n;
    RGB *rgb = malloc(sizeof(RGB) * W * H);
    RGB c[H];
    for (i = 0; i < W * H; i++)
    {
        rgb[i].b = (i & 0x1f) << 3;
        rgb[i].g = ((i >> 5) & 0x1f) << 3;
        rgb[i].r = ((i >> 10) & 0x1f) << 3;
    }
    qsort(rgb, H * W, sizeof(RGB), S1);
    for (n = 0; n < atoi(argv[1]); n++)
    {
        for (i = 0; i < W; i++)
        {
            for (j = 0; j < H; j++)
                c[j] = rgb[j * W + i];
            qsort(c, H, sizeof(RGB), S2);
            for (j = 0; j < H; j++)
                rgb[j * W + i] = c[j];
        }
        for (i = 0; i < W * H; i += W)
            qsort(rgb + i, W, sizeof(RGB), S2);
    }
    printf("P6 %d %d 255\n", W, H);
    fwrite(rgb, sizeof(RGB), W * H, stdout);
    free(rgb);
    return 0;
}
```
[Answer]
# Processing
I'm just getting started with C (having programmed in other languages) but found the graphics in Visual C tough to follow, so I downloaded this Processing program used by @ace.
Here's my code and my algorithm.
```
void setup(){
  size(256,128);
  background(0);
  frameRate(1000000000);
  noLoop();
 }
int x,y,r,g,b,c;
void draw() {
  for(y=0;y<128;y++)for(x=0;x<128;x++){
    r=(x&3)+(y&3)*4;
    g=x>>2;
    b=y>>2;
    c=0;
    //c=x*x+y*y<10000? 1:0; 
    stroke((r^16*c)<<3,g<<3,b<<3);
    point(x,y);
    stroke((r^16*(1-c))<<3,g<<3,b<<3);
    point(255-x,y);  
  } 
}
```
**Algorithm**
Start with 4x4 squares of all possible combinations of 32 values of green and blue, in x,y. format, making a 128x128 square Each 4x4 square has 16 pixels, so make a mirror image beside it to give 32 pixels of each possible combination of green and blue, per image below.
(bizarrely the full green looks brighter than the full cyan. ~~This must be an optical illusion.~~ clarified in comments)
In the lefthand square, add in the red values 0-15. For the righthand square, XOR these values with 16, to make the values 16-31.
![enter image description here](https://i.stack.imgur.com/ZP40E.png)
**Output 256x128**
This gives the output in the top image below.
However, every pixel differs from its mirror image only in the most significant bit of the red value. So, I can apply a condition with the variable `c`, to reverse the XOR, which has the same effect as exchanging these two pixels.
An example of this is given in the bottom image below (if we uncomment the line of code which is currently commented out.)
![enter image description here](https://i.stack.imgur.com/GW1gg.png)
**512 x 512 - A tribute to Andy Warhol's Marylin**
Inspired by Quincunx's answer to this question with an "evil grin" in freehand red circles, here is my version of the famous picture. The original actually had 25 coloured Marylins and 25 black & white Marylins and was Warhol's tribute to Marylin after her untimely death. See <http://en.wikipedia.org/wiki/Marilyn_Diptych>
I changed to different functions after discovering that Processing renders the ones I used in 256x128 as semitransparent. The new ones are opaque.
And although the image isn't completely algorithmic, I rather like it.
```
int x,y,r,g,b,c;
PImage img;
color p;
void setup(){
  size(512,512);
  background(0);
  img = loadImage("marylin256.png");
  frameRate(1000000000);
  noLoop();
 }
void draw() {
   
   image(img,0,0);
  
   for(y=0;y<256;y++)for(x=0;x<256;x++){
      // Note the multiplication by 0 in the next line. 
      // Replace the 0 with an 8 and the reds are blended checkerboard style
      // This reduces the grain size, but on balance I decided I like the grain.
      r=((x&3)+(y&3)*4)^0*((x&1)^(y&1));
      g=x>>2;
      b=y>>2; 
      c=brightness(get(x,y))>100? 32:0;
      p=color((r^c)<<2,g<<2,b<<2);
      set(x,y,p);
      p=color((r^16^c)<<2,g<<2,b<<2);
      set(256+x,y,p);  
      p=color((r^32^c)<<2,g<<2,b<<2);
      set(x,256+y,p);
      p=color((r^48^c)<<2,g<<2,b<<2);
      set(256+x,256+y,p);  
 } 
 save("warholmarylin.png");
```
}
![enter image description here](https://i.stack.imgur.com/0w2DZ.png)
**512x512 Twilight over a lake with mountains in the distance**
Here, a fully algorithmic picture. I've played around with changing which colour I modulate with the condition, but I just come back to the conclusion that red works best. Similar to the Marylin picture, I draw the mountains first, then pick the brightness from that picture to overwrite the positive RGB image, while copying to the negative half. A slight difference is that the bottom of many of the mountains (because they are all drawn the same size) extends below the read area, so this area is simply cropped during the reading process (which therefore gives the desired impression of different size mountains.)
In this one I use an 8x4 cell of 32 reds for the positive, and the remaining 32 reds for the negative.
Note the expicit command frameRate(1) at the end of my code. I discovered that without this command, Processing would use 100% of one core of my CPU, even though it had finished drawing. As far as I can tell there is no Sleep function, all you can do is reduce the frequency of polling.
```
int i,j,x,y,r,g,b,c;
PImage img;
color p;
void setup(){
  size(512,512);
  background(255,255,255);
  frameRate(1000000000);
  noLoop();
 }
void draw() {
  for(i=0; i<40; i++){
    x=round(random(512));
    y=round(random(64,256));
    for(j=-256; j<256; j+=12) line(x,y,x+j,y+256);  
  }
  for(y=0;y<256;y++)for(x=0;x<512;x++){
    r=(x&7)+(y&3)*8;
    b=x>>3;
    g=(255-y)>>2;
    c=brightness(get(x,y))>100? 32:0;
    p=color((r^c)<<2,g<<2,b<<2);
    set(x,y,p);
    p=color((r^32^c)<<2,g<<2,b<<2);
    set(x,511-y,p);  
  }
  save("mountainK.png");
  frameRate(1);
}
```
![enter image description here](https://i.stack.imgur.com/ezbmA.png)
[Answer]
I just arranged all 16-bit colors (5r,6g,5b) on a [Hilbert curve](http://en.wikipedia.org/wiki/Hilbert_curve) in JavaScript.
![hilbert curve colors](https://i.stack.imgur.com/BWYc4.png)
Previous, (not Hilbert curve) image:
![hilbert curve](https://i.stack.imgur.com/9pRO2.png)
JSfiddle: [jsfiddle.net/LCsLQ/3](http://jsfiddle.net/LCsLQ/3/)
# JavaScript
```
// ported code from http://en.wikipedia.org/wiki/Hilbert_curve
function xy2d (n, p) {
    p = {x: p.x, y: p.y};
    var r = {x: 0, y: 0},
        s,
        d=0;
    for (s=(n/2)|0; s>0; s=(s/2)|0) {
        r.x = (p.x & s) > 0 ? 1 : 0;
        r.y = (p.y & s) > 0 ? 1 : 0;
        d += s * s * ((3 * r.x) ^ r.y);
        rot(s, p, r);
    }
    return d;
}
//convert d to (x,y)
function d2xy(n, d) {
    var r = {x: 0, y: 0},
        p = {x: 0, y: 0},
        s,
        t=d;
    for (s=1; s<n; s*=2) {
        r.x = 1 & (t/2);
        r.y = 1 & (t ^ rx);
        rot(s, p, r);
        p.x += s * r.x;
        p.y += s * r.y;
        t /= 4;
    }
    return p;
}
//rotate/flip a quadrant appropriately
function rot(n, p, r) {
    if (r.y === 0) {
        if (r.x === 1) {
            p.x = n-1 - p.x;
            p.y = n-1 - p.y;
        }
        //Swap x and y
        var t  = p.x;
        p.x = p.y;
        p.y = t;
    }
}
function v2rgb(v) {
    return ((v & 0xf800) << 8) | ((v & 0x7e0) << 5) | ((v & 0x1f) << 3); 
}
function putData(arr, size, coord, v) {
    var pos = (coord.x + size * coord.y) * 4,
        rgb = v2rgb(v);
    arr[pos] = (rgb & 0xff0000) >> 16;
    arr[pos + 1] = (rgb & 0xff00) >> 8;
    arr[pos + 2] = rgb & 0xff;
    arr[pos + 3] = 0xff;
}
var size = 256,
    context = a.getContext('2d'),
    data = context.getImageData(0, 0, size, size);
for (var i = 0; i < size; i++) {
    for (var j = 0; j < size; j++) {
        var p = {x: j, y: i};
        putData(data.data, size, p, xy2d(size, p));
    }
}
context.putImageData(data, 0, 0);
```
*Edit*: It turns out that there was a bug in my function to calculate Hilbert curve and it was incorrect; namely, `r.x = (p.x & s) > 0; r.y = (p.y & s) > 0;` changed to `r.x = (p.x & s) > 0 ? 1 : 0; r.y = (p.y & s) > 0 ? 1 : 0;`
*Edit 2:* Another fractal:
![sierpinsky](https://i.stack.imgur.com/sfjQw.png)
<http://jsfiddle.net/jej2d/5/>
[Answer]
## C#: Iterative local similarity optimization
```
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Drawing;
using System.Drawing.Imaging;
namespace AllColors
{
    class Program
    {
        static Random _random = new Random();
        const int ImageWidth = 256;
        const int ImageHeight = 128;
        const int PixelCount = ImageWidth * ImageHeight;
        const int ValuesPerChannel = 32;
        const int ChannelValueDelta = 256 / ValuesPerChannel;
        static readonly int[,] Kernel;
        static readonly int KernelWidth;
        static readonly int KernelHeight;
        static Program()
        {
            // Version 1
            Kernel = new int[,] { { 0, 1, 0, },
                                  { 1, 0, 1, },
                                  { 0, 1, 0, } };
            // Version 2
            //Kernel = new int[,] { { 0, 0, 1, 0, 0 },
            //                      { 0, 2, 3, 2, 0 },
            //                      { 1, 3, 0, 3, 1 },
            //                      { 0, 2, 3, 2, 0 },
            //                      { 0, 0, 1, 0, 0 } };
            // Version 3
            //Kernel = new int[,] { { 3, 0, 0, 0, 3 },
            //                      { 0, 1, 0, 1, 0 },
            //                      { 0, 0, 0, 0, 0 },
            //                      { 0, 1, 0, 1, 0 },
            //                      { 3, 0, 0, 0, 3 } };
            // Version 4
            //Kernel = new int[,] { { -9, -9, -9, -9, -9 },
            //                      {  1,  2,  3,  2,  1 },
            //                      {  2,  3,  0,  3,  2 },
            //                      {  1,  2,  3,  2,  1 },
            //                      {  0,  0,  0,  0,  0 } };
            // Version 5
            //Kernel = new int[,] { { 0, 0, 1, 0, 0, 0, 0 },
            //                      { 0, 1, 2, 1, 0, 0, 0 },
            //                      { 1, 2, 3, 0, 1, 0, 0 },
            //                      { 0, 1, 2, 0, 0, 0, 0 },
            //                      { 0, 0, 1, 0, 0, 0, 0 } };
            KernelWidth = Kernel.GetLength(1);
            KernelHeight = Kernel.GetLength(0);
            if (KernelWidth % 2 == 0 || KernelHeight % 2 == 0)
            {
                throw new InvalidOperationException("Invalid kernel size");
            }
        }
        private static Color[] CreateAllColors()
        {
            int i = 0;
            Color[] colors = new Color[PixelCount];
            for (int r = 0; r < ValuesPerChannel; r++)
            {
                for (int g = 0; g < ValuesPerChannel; g++)
                {
                    for (int b = 0; b < ValuesPerChannel; b++)
                    {
                        colors[i] = Color.FromArgb(255, r * ChannelValueDelta, g * ChannelValueDelta, b * ChannelValueDelta);
                        i++;
                    }
                }
            }
            return colors;
        }
        private static void Shuffle(Color[] colors)
        {
            // Knuth-Fisher-Yates shuffle
            for (int i = colors.Length - 1; i > 0; i--)
            {
                int n = _random.Next(i + 1);
                Swap(colors, i, n);
            }
        }
        private static void Swap(Color[] colors, int index1, int index2)
        {
            var temp = colors[index1];
            colors[index1] = colors[index2];
            colors[index2] = temp;
        }
        private static Bitmap ToBitmap(Color[] pixels)
        {
            Bitmap bitmap = new Bitmap(ImageWidth, ImageHeight);
            int x = 0;
            int y = 0;
            for (int i = 0; i < PixelCount; i++)
            {
                bitmap.SetPixel(x, y, pixels[i]);
                x++;
                if (x == ImageWidth)
                {
                    x = 0;
                    y++;
                }
            }
            return bitmap;
        }
        private static int GetNeighborDelta(Color[] pixels, int index1, int index2)
        {
            return GetNeighborDelta(pixels, index1) + GetNeighborDelta(pixels, index2);
        }
        private static int GetNeighborDelta(Color[] pixels, int index)
        {
            Color center = pixels[index];
            int sum = 0;
            for (int x = 0; x < KernelWidth; x++)
            {
                for (int y = 0; y < KernelHeight; y++)
                {
                    int weight = Kernel[y, x];
                    if (weight == 0)
                    {
                        continue;
                    }
                    int xOffset = x - (KernelWidth / 2);
                    int yOffset = y - (KernelHeight / 2);
                    int i = index + xOffset + yOffset * ImageWidth;
                    if (i >= 0 && i < PixelCount)
                    {
                        sum += GetDelta(pixels[i], center) * weight;
                    }
                }
            }
            return sum;
        }
        private static int GetDelta(Color c1, Color c2)
        {
            int sum = 0;
            sum += Math.Abs(c1.R - c2.R);
            sum += Math.Abs(c1.G - c2.G);
            sum += Math.Abs(c1.B - c2.B);
            return sum;
        }
        private static bool TryRandomSwap(Color[] pixels)
        {
            int index1 = _random.Next(PixelCount);
            int index2 = _random.Next(PixelCount);
            int delta = GetNeighborDelta(pixels, index1, index2);
            Swap(pixels, index1, index2);
            int newDelta = GetNeighborDelta(pixels, index1, index2);
            if (newDelta < delta)
            {
                return true;
            }
            else
            {
                // Swap back
                Swap(pixels, index1, index2);
                return false;
            }
        }
        static void Main(string[] args)
        {
            string fileNameFormat = "{0:D10}.png";
            var image = CreateAllColors();
            ToBitmap(image).Save("start.png");
            Shuffle(image);
            ToBitmap(image).Save(string.Format(fileNameFormat, 0));
            long generation = 0;
            while (true)
            {
                bool swapped = TryRandomSwap(image);
                if (swapped)
                {
                    generation++;
                    if (generation % 1000 == 0)
                    {
                        ToBitmap(image).Save(string.Format(fileNameFormat, generation));
                    }
                }
            }
        }
    }
}
```
### Idea
First we start with a random shuffle:
![enter image description here](https://i.stack.imgur.com/ciYlp.png)
Then we randomly select two pixels and swap them. If this does not increase the similarity of the pixels to their neighbors, we swap back and try again. We repeat this process over and over again.
After just a few generations (5000) the differences are not that obvious...
![enter image description here](https://i.stack.imgur.com/mBOg6.png)
But the longer it runs (25000), ...
![enter image description here](https://i.stack.imgur.com/5N2ow.png)
...the more certain patterns start to emerge (100000).
![enter image description here](https://i.stack.imgur.com/QzPtR.png)
Using different definitions for *neighborhood*, we can influence these patterns and whether they are stable or not. The `Kernel` is a matrix similar to the [ones used for filters in image processing](http://en.wikipedia.org/wiki/Kernel_%28image_processing%29). It specifies the weights of each neighbor used for the RGB delta calculation.
### Results
Here are some of the results I created. The videos show the iterative process (1 frame == 1000 generations), but sadly the quality is not the best (vimeo, YouTube etc. do not properly support such small dimensions). I may later try to create videos of better quality.
```
0 1 0
1 X 1
0 1 0
```
185000 generations:
![enter image description here](https://i.stack.imgur.com/6QAYk.png) [Video (00:06)](https://vimeo.com/87981881)
---
```
0 0 1 0 0
0 2 3 2 0
1 3 X 3 1
0 2 3 2 0
0 0 1 0 0
```
243000 generations:
![enter image description here](https://i.stack.imgur.com/r1bAL.png) [Video (00:07)](https://vimeo.com/87982854)
---
```
3 0 0 0 3
0 1 0 1 0
0 0 X 0 0
0 1 0 1 0
3 0 0 0 3
```
230000 generations:
![enter image description here](https://i.stack.imgur.com/U9cJh.png) [Video (00:07)](https://vimeo.com/87982856)
---
```
0 0 1 0 0 0 0
0 1 2 1 0 0 0
1 2 3 X 1 0 0
0 1 2 0 0 0 0
0 0 1 0 0 0 0
```
This kernel is interesting because due to its asymmetry the patterns are not stable and the whole image moves to the right as the generations go by.
2331000 generations:
![enter image description here](https://i.stack.imgur.com/iD2lS.png) [Video (01:10)](https://vimeo.com/87982857)
---
### Large Results (512x512)
Using the kernels above with a larger image dimension creates the same local patterns, spaning a larger total area. A 512x512 image takes between 1 and 2 million generations to stabilize.
![enter image description here](https://i.stack.imgur.com/Fh0QV.png)
![enter image description here](https://i.stack.imgur.com/KMZ2A.png)
![enter image description here](https://i.stack.imgur.com/jslCA.png)
---
OK, now let's get serious and create larger, less local patterns with a 15x15 radial kernel:
```
0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
0 0 0 1 1 2 2 2 2 2 1 1 0 0 0
0 0 1 2 2 3 3 3 3 3 2 2 1 0 0
0 1 2 2 3 4 4 4 4 4 3 2 2 1 0
0 1 2 3 4 4 5 5 5 4 4 3 2 1 0
1 2 3 4 4 5 6 6 6 5 4 4 3 2 1
1 2 3 4 5 6 7 7 7 6 5 4 3 2 1
1 2 3 4 5 6 7 X 7 6 5 4 3 2 1
1 2 3 4 5 6 7 7 7 6 5 4 3 2 1
1 2 3 4 4 5 6 6 6 5 4 4 3 2 1
0 1 2 3 4 4 5 5 5 4 4 3 2 1 0
0 1 2 2 3 4 4 4 4 4 3 2 2 1 0
0 0 1 2 2 3 3 3 3 3 2 2 1 0 0
0 0 0 1 1 2 2 2 2 2 1 1 0 0 0
0 0 0 0 0 1 1 1 1 1 0 0 0 0 0
```
This drastically increases the computation time per generation. 1.71 million generations and 20 hours later:
![enter image description here](https://i.stack.imgur.com/95wif.png)
[Answer]
# Java
I wasn't actually sure how to create 15- or 18-bit colors, so I just left off the least significant bit of each channel's byte to make 2^18 different 24-bit colors. Most of the noise is removed by sorting, but effective noise removal looks like it would require comparison of more than just two elements at a time the way Comparator does. I'll try manipulation using larger kernels, but in the mean time, this is about the best I've been able to do.
![enter image description here](https://i.stack.imgur.com/lfoub.png)
[Click for HD image #2](https://SSend.it/hj4ovh)
![Low resolution image #2](https://i.stack.imgur.com/25TtG.png)
```
import java.awt.*;
import java.awt.image.*;
import javax.swing.*;
import java.util.*;
public class ColorSpan extends JFrame{
    private int h, w = h = 512;
    private BufferedImage image = 
            new BufferedImage(w,h,BufferedImage.TYPE_INT_RGB);
    private WritableRaster raster = image.getRaster();
    private DataBufferInt dbInt = (DataBufferInt) 
            (raster.getDataBuffer());
    private int[] data = dbInt.getData();
    private JLabel imageLabel = new JLabel(new ImageIcon(image));
    private JPanel bordered = new JPanel(new BorderLayout());
    public <T> void transpose(ArrayList<T> objects){
        for(int i = 0; i < w; i++){
            for(int j = 0; j < i; j++){
                Collections.swap(objects,i+j*w,j+i*h);
            }
        }
    }
    public <T> void sortByLine(ArrayList<T> objects, Comparator<T> comp){
        for(int i = 0; i < h; i++){
            Collections.sort(objects.subList(i*w, (i+1)*w), comp);
        }
    }
    public void init(){
        ArrayList<Integer> colors = new ArrayList<Integer>();
        for(int i = 0, max = 1<<18; i < max; i++){
            int r = i>>12, g = (i>>6)&63, b = i&63;
            colors.add(((r<<16)+(g<<8)+b)<<2);
        }
        Comparator<Integer> comp1 = new Comparator<Integer>(){
            public int compare(Integer left, Integer right){
                int a = left.intValue(), b = right.intValue();
                int rA = a>>16, rB = b>>16,
                    gA = (a>>8)&255, gB = (b>>8)&255;
                /*double thA = Math.acos(gA*2d/255-1),
                        thB = Math.acos(gB*2d/255-1);*/
                double thA = Math.atan2(rA/255d-.5,gA/255d-.5),
                        thB = Math.atan2(rB/255d-.5,gB/255d-.5);
                return -Double.compare(thA,thB);
            }
        }, comp2 = new Comparator<Integer>(){
            public int compare(Integer left, Integer right){
                int a = left.intValue(), b = right.intValue();
                int rA = a>>16, rB = b>>16,
                    gA = (a>>8)&255, gB = (b>>8)&255,
                    bA = a&255, bB = b&255;
                double dA = Math.hypot(gA-rA,bA-rA),
                        dB = Math.hypot(gB-rB,bB-rB);
                return Double.compare(dA,dB);
            }
        }, comp3 = new Comparator<Integer>(){
            public int compare(Integer left, Integer right){
                int a = left.intValue(), b = right.intValue();
                int rA = a>>16, rB = b>>16,
                    gA = (a>>8)&255, gB = (b>>8)&255,
                    bA = a&255, bB = b&255;
                    return Integer.compare(rA+gA+bA,rB+gB+bB);
            }
        };
        /* Start: Image 1 */
        Collections.sort(colors, comp2);
        transpose(colors);
        sortByLine(colors,comp2);
        transpose(colors);
        sortByLine(colors,comp1);
        transpose(colors);
        sortByLine(colors,comp2);
        sortByLine(colors,comp3);
        /* End: Image 1 */
        /* Start: Image 2 */
        Collections.sort(colors, comp1);
        sortByLine(colors,comp2);
        transpose(colors);
        sortByLine(colors,comp2);
        transpose(colors);
        sortByLine(colors,comp1);
        transpose(colors);
        sortByLine(colors,comp1);
        /* End: Image 2 */
        int index = 0;
        for(Integer color : colors){
            int cInt = color.intValue();
            data[index] = cInt;
            index++;
        }
    }
    public ColorSpan(){
        super("512x512 Unique Colors");
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        init();
        bordered.setBorder(BorderFactory.createEmptyBorder(2,2,2,2));
        bordered.add(imageLabel,BorderLayout.CENTER);
        add(bordered,BorderLayout.CENTER);
        pack();
    }
    public static void main(String[] args){
        new ColorSpan().setVisible(true);
    }
}
```
[Answer]
# Java
With a few variations on my other answer, we can get some very interesting outputs.
```
import java.awt.Point;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.Random;
import java.util.logging.Level;
import java.util.logging.Logger;
import javax.imageio.ImageIO;
/**
 *
 * @author Quincunx
 */
public class AllColorImage {
    public static void main(String[] args) {
        BufferedImage img = new BufferedImage(4096, 4096, BufferedImage.TYPE_INT_RGB);
        int num = 0;
        ArrayList<Point> points = new ArrayList<>();
        for (int y = 0; y < 4096; y++) {
            for (int x = 0; x < 4096; x++) {
                points.add(new Point(x, y));
            }
        }
        Collections.sort(points, new Comparator<Point>() {
            @Override
            public int compare(Point t, Point t1) {
                int compareVal = (Integer.bitCount(t.x) + Integer.bitCount(t.y))
                        - (Integer.bitCount(t1.x) + Integer.bitCount(t1.y));
                return compareVal < 0 ? -1 : compareVal == 0 ? 0 : 1;
            }
        });
        for (Point p : points) {
            int x = p.x;
            int y = p.y;
            img.setRGB(x, y, num);
            num++;
        }
        try {
            ImageIO.write(img, "png", new File("Filepath"));
        } catch (IOException ex) {
            Logger.getLogger(AllColorImage.class.getName()).log(Level.SEVERE, null, ex);
        }
    }
}
```
The important code is here:
```
Collections.sort(points, new Comparator<Point>() {
    @Override
    public int compare(Point t, Point t1) {
        int compareVal = (Integer.bitCount(t.x) + Integer.bitCount(t.y))
                - (Integer.bitCount(t1.x) + Integer.bitCount(t1.y));
        return compareVal < 0 ? -1 : compareVal == 0 ? 0 : 1;
    }
});
```
Output (screenshot):
![enter image description here](https://i.stack.imgur.com/YV9Mw.jpg)
Change the comparator to this:
```
public int compare(Point t, Point t1) {
    int compareVal = (Integer.bitCount(t.x + t.y))
            - (Integer.bitCount(t1.x + t1.y));
    return compareVal < 0 ? -1 : compareVal == 0 ? 0 : 1;
}
```
And we get this:
![enter image description here](https://i.stack.imgur.com/tybmG.jpg)
Another variation:
```
public int compare(Point t, Point t1) {
    int compareVal = (t.x + t.y)
            - (t1.x + t1.y);
    return compareVal < 0 ? -1 : compareVal == 0 ? 0 : 1;
}
```
![enter image description here](https://i.stack.imgur.com/dNhGq.jpg)
Yet another variation (reminds me of cellular automata):
```
public int compare(Point t, Point t1) {
    int compareVal = (t1.x - t.y)
            + (t.x - t1.y);
    return compareVal < 0 ? -1 : compareVal == 0 ? 0 : 1;
}
```
![enter image description here](https://i.stack.imgur.com/HFaS9.png)
Yet another another variation (new personal favorite):
```
public int compare(Point t, Point t1) {
    int compareVal = (Integer.bitCount(t.x ^ t.y))
            - (Integer.bitCount(t1.x ^ t1.y));
    return compareVal < 0 ? -1 : compareVal == 0 ? 0 : 1;
}
```
![enter image description here](https://i.stack.imgur.com/ZnxUo.jpg)
It looks so fractal-ly. XOR is so beautiful, especially closeup:
![enter image description here](https://i.stack.imgur.com/j3gkX.png)
Another closeup:
![enter image description here](https://i.stack.imgur.com/YuRdv.png)
And now the Sierpinski Triangle, tilted:
```
public int compare(Point t, Point t1) {
    int compareVal = (Integer.bitCount(t.x | t.y))
            - (Integer.bitCount(t1.x | t1.y));
    return compareVal < 0 ? -1 : compareVal == 0 ? 0 : 1;
}
```
![enter image description here](https://i.stack.imgur.com/xiDig.jpg)
[Answer]
# C#
Wow, really cool things in this challenge. I took a stab at this at in C# and generated a 4096x4096 image in about 3 minutes (i7 CPU) using every single color via Random Walk logic. 
Ok, so for the code. After being frustrated with hours of research and trying to generate every single HSL color using for loops in code, I settled for creating a flat file to read HSL colors from. What I did was create every single RGB color into a List, then I ordered by Hue, Luminosity, then Saturation. Then I saved the List to a text file. ColorData is just a small class I wrote that accepts an RGB color and also stores the HSL equivalent. This code is a HUGE RAM eater. Used about 4GB RAM lol.
```
public class RGB
{
    public double R = 0;
    public double G = 0;
    public double B = 0;
    public override string ToString()
    {
        return "RGB:{" + (int)R + "," + (int)G + "," + (int)B + "}";
    }
}
public class HSL
{
    public double H = 0;
    public double S = 0;
    public double L = 0;
    public override string ToString()
    {
        return "HSL:{" + H + "," + S + "," + L + "}";
    }
}
public class ColorData
{
    public RGB rgb;
    public HSL hsl;
    public ColorData(RGB _rgb)
    {
        rgb = _rgb;
        var _hsl = ColorHelper._color_rgb2hsl(new double[]{rgb.R,rgb.G,rgb.B});
        hsl = new HSL() { H = _hsl[0], S = _hsl[1], L = _hsl[2] };
    }
    public ColorData(double[] _rgb)
    {
        rgb = new RGB() { R = _rgb[0], G = _rgb[1], B = _rgb[2] };
        var _hsl = ColorHelper._color_rgb2hsl(_rgb);
        hsl = new HSL() { H = _hsl[0], S = _hsl[1], L = _hsl[2] };
    }
    public override string ToString()
    {
        return rgb.ToString() + "|" + hsl.ToString();
    }
    public int Compare(ColorData cd)
    {
        if (this.hsl.H > cd.hsl.H)
        {
            return 1;
        }
        if (this.hsl.H < cd.hsl.H)
        {
            return -1;
        }
        if (this.hsl.S > cd.hsl.S)
        {
            return 1;
        }
        if (this.hsl.S < cd.hsl.S)
        {
            return -1;
        }
        if (this.hsl.L > cd.hsl.L)
        {
            return 1;
        }
        if (this.hsl.L < cd.hsl.L)
        {
            return -1;
        }
        return 0;
    }
}
public static class ColorHelper
{
    public static void MakeColorFile(string savePath)
    {
        List<ColorData> Colors = new List<ColorData>();
        System.IO.File.Delete(savePath);
        for (int r = 0; r < 256; r++)
        {
            for (int g = 0; g < 256; g++)
            {
                for (int b = 0; b < 256; b++)
                {
                    double[] rgb = new double[] { r, g, b };
                    ColorData cd = new ColorData(rgb);
                    Colors.Add(cd);
                }
            }
        }
        Colors = Colors.OrderBy(x => x.hsl.H).ThenBy(x => x.hsl.L).ThenBy(x => x.hsl.S).ToList();
        string cS = "";
        using (System.IO.StreamWriter fs = new System.IO.StreamWriter(savePath))
        {
            foreach (var cd in Colors)
            {
                cS = cd.ToString();
                fs.WriteLine(cS);
            }
        }
    }
    public static IEnumerable<Color> NextColorHThenSThenL()
    {
        HashSet<string> used = new HashSet<string>();
        double rMax = 720;
        double gMax = 700;
        double bMax = 700;
        for (double r = 0; r <= rMax; r++)
        {
            for (double g = 0; g <= gMax; g++)
            {
                for (double b = 0; b <= bMax; b++)
                {
                    double h = (r / (double)rMax);
                    double s = (g / (double)gMax);
                    double l = (b / (double)bMax);
                    var c = _color_hsl2rgb(new double[] { h, s, l });
                    Color col = Color.FromArgb((int)c[0], (int)c[1], (int)c[2]);
                    string key = col.R + "-" + col.G + "-" + col.B;
                    if (!used.Contains(key))
                    {
                        used.Add(key);
                        yield return col;
                    }
                    else
                    {
                        continue;
                    }
                }
            }
        }
    }
    public static Color HSL2RGB(double h, double s, double l){
        double[] rgb= _color_hsl2rgb(new double[] { h, s, l });
        return Color.FromArgb((int)rgb[0], (int)rgb[1], (int)rgb[2]);
    }
    public static double[] _color_rgb2hsl(double[] rgb)
    {
        double r = rgb[0]; double g = rgb[1]; double b = rgb[2];
        double min = Math.Min(r, Math.Min(g, b));
        double max = Math.Max(r, Math.Max(g, b));
        double delta = max - min;
        double l = (min + max) / 2.0;
        double s = 0;
        if (l > 0 && l < 1)
        {
            s = delta / (l < 0.5 ? (2 * l) : (2 - 2 * l));
        }
        double h = 0;
        if (delta > 0)
        {
            if (max == r && max != g) h += (g - b) / delta;
            if (max == g && max != b) h += (2 + (b - r) / delta);
            if (max == b && max != r) h += (4 + (r - g) / delta);
            h /= 6;
        } return new double[] { h, s, l };
    }
    public static double[] _color_hsl2rgb(double[] hsl)
    {
        double h = hsl[0];
        double s = hsl[1];
        double l = hsl[2];
        double m2 = (l <= 0.5) ? l * (s + 1) : l + s - l * s;
        double m1 = l * 2 - m2;
        return new double[]{255*_color_hue2rgb(m1, m2, h + 0.33333),
           255*_color_hue2rgb(m1, m2, h),
           255*_color_hue2rgb(m1, m2, h - 0.33333)};
    }
    public static double _color_hue2rgb(double m1, double m2, double h)
    {
        h = (h < 0) ? h + 1 : ((h > 1) ? h - 1 : h);
        if (h * (double)6 < 1) return m1 + (m2 - m1) * h * (double)6;
        if (h * (double)2 < 1) return m2;
        if (h * (double)3 < 2) return m1 + (m2 - m1) * (0.66666 - h) * (double)6;
        return m1;
    }
}
```
With that out of the way. I wrote a class to get the next color from the generated file. It lets you set the hue start and hue end. In reality, that could and should probably be generalized to whichever dimension the file was sorted by first. Also I realize that for a performance boost here, I could have just put the RGB values into the file and kept each line at a fixed length. That way I could have easily specified the byte offset instead of looping through every line until I reached the line I wanted to start at. But it wasn't that much of a performance hit for me. But here's that class
```
public class HSLGenerator
{
    double hEnd = 1;
    double hStart = 0;
    double colCount = 256 * 256 * 256;
    public static Color ReadRGBColorFromLine(string line)
    {
        string sp1 = line.Split(new string[] { "RGB:{" }, StringSplitOptions.None)[1];
        string sp2 = sp1.Split('}')[0];
        string[] sp3 = sp2.Split(',');
        return Color.FromArgb(Convert.ToInt32(sp3[0]), Convert.ToInt32(sp3[1]), Convert.ToInt32(sp3[2]));
    }
    public IEnumerable<Color> GetNextFromFile(string colorFile)
    {
        int currentLine = -1;
        int startLine = Convert.ToInt32(hStart * colCount);
        int endLine = Convert.ToInt32(hEnd * colCount);
        string line = "";
        using(System.IO.StreamReader sr = new System.IO.StreamReader(colorFile))
        {
            while (!sr.EndOfStream)
            {
                line = sr.ReadLine();
                currentLine++;
                if (currentLine < startLine) //begin at correct offset
                {
                    continue;
                }
                yield return ReadRGBColorFromLine(line);
                if (currentLine > endLine) 
                {
                    break;
                }
            }
    }
    HashSet<string> used = new HashSet<string>();
    public void SetHueLimits(double hueStart, double hueEnd)
    {
        hEnd = hueEnd;
        hStart = hueStart;
    }
}
```
So now that we have the color file, and we have a way to read the file, we can now actually make the image. I used a class I found to boost performance of setting pixels in a bitmap, called LockBitmap. [LockBitmap source](http://www.codeproject.com/Tips/240428/Work-with-bitmap-faster-with-Csharp)
I created a small Vector2 class to store coordinate locations
```
public class Vector2
{
    public int X = 0;
    public int Y = 0;
    public Vector2(int x, int y)
    {
        X = x;
        Y = y;
    }
    public Vector2 Center()
    {
        return new Vector2(X / 2, Y / 2);
    }
    public override string ToString()
    {
        return X.ToString() + "-" + Y.ToString();
    }
}
```
And I also created a class called SearchArea, which was helpful for finding neighboring pixels. You specify the pixel you want to find neighbors for, the bounds to search within, and the size of the "neighbor square" to search. So if the size is 3, that means you're searching a 3x3 square, with the specified pixel right in the center.
```
public class SearchArea
{
    public int Size = 0;
    public Vector2 Center;
    public Rectangle Bounds;
    public SearchArea(int size, Vector2 center, Rectangle bounds)
    {
        Center = center;
        Size = size;
        Bounds = bounds;
    }
    public bool IsCoordinateInBounds(int x, int y)
    {
        if (!IsXValueInBounds(x)) { return false; }
        if (!IsYValueInBounds(y)) { return false; }
        return true;
    }
    public bool IsXValueInBounds(int x)
    {
        if (x < Bounds.Left || x >= Bounds.Right) { return false; }
        return true;
    }
    public bool IsYValueInBounds(int y)
    {
        if (y < Bounds.Top || y >= Bounds.Bottom) { return false; }
        return true;
    }
}
```
Here's the class that actually chooses the next neighbor. Basically there's 2 search modes. A) The full square, B) just the perimeter of the square. This was an optimization that I made to prevent searching the full square again after realizing the square was full. The DepthMap was a further optimization to prevent searching the same squares over and over again. However, I didn't fully optimize this. Every call to GetNeighbors will always do the full square search first. I know I could optimize this to only do the perimeter search after completing the initial full square. I just didn't get around to that optimization yet, and even without it the code is pretty fast. The commented out "lock" lines are because I was using Parallel.ForEach at one point, but realized I had to write more code than I wanted for that lol.
```
public class RandomWalkGenerator
{
    HashSet<string> Visited = new HashSet<string>();
    Dictionary<string, int> DepthMap = new Dictionary<string, int>();
    Rectangle Bounds;
    Random rnd = new Random();
    public int DefaultSearchSize = 3;
    public RandomWalkGenerator(Rectangle bounds)
    {
        Bounds = bounds;
    }
    private SearchArea GetSearchArea(Vector2 center, int size)
    {
        return new SearchArea(size, center, Bounds);
    }
    private List<Vector2> GetNeighborsFullSearch(SearchArea srchArea, Vector2 coord)
    {
        int radius = (int)Math.Floor((double)((double)srchArea.Size / (double)2));
        List<Vector2> pixels = new List<Vector2>();
        for (int rX = -radius; rX <= radius; rX++)
        {
            for (int rY = -radius; rY <= radius; rY++)
            {
                if (rX == 0 && rY == 0) { continue; } //not a new coordinate
                int x = rX + coord.X;
                int y = rY + coord.Y;
                if (!srchArea.IsCoordinateInBounds(x, y)) { continue; }
                var key = x + "-" + y;
                // lock (Visited)
                {
                    if (!Visited.Contains(key))
                    {
                        pixels.Add(new Vector2(x, y));
                    }
                }
            }
        }
        if (pixels.Count == 0)
        {
            int depth = 0;
            string vecKey = coord.ToString();
            if (!DepthMap.ContainsKey(vecKey))
            {
                DepthMap.Add(vecKey, depth);
            }
            else
            {
                depth = DepthMap[vecKey];
            }
            var size = DefaultSearchSize + 2 * depth;
            var sA = GetSearchArea(coord, size);
            pixels = GetNeighborsPerimeterSearch(sA, coord, depth);
        }
        return pixels;
    }
    private Rectangle GetBoundsForPerimeterSearch(SearchArea srchArea, Vector2 coord)
    {
        int radius = (int)Math.Floor((decimal)(srchArea.Size / 2));
        Rectangle r = new Rectangle(-radius + coord.X, -radius + coord.Y, srchArea.Size, srchArea.Size);
        return r;
    }
    private List<Vector2> GetNeighborsPerimeterSearch(SearchArea srchArea, Vector2 coord, int depth = 0)
    {
        string vecKey = coord.ToString();
        if (!DepthMap.ContainsKey(vecKey))
        {
            DepthMap.Add(vecKey, depth);
        }
        else
        {
            DepthMap[vecKey] = depth;
        }
        Rectangle bounds = GetBoundsForPerimeterSearch(srchArea, coord);
        List<Vector2> pixels = new List<Vector2>();
        int depthMax = 1500;
        if (depth > depthMax)
        {
            return pixels;
        }
        int yTop = bounds.Top;
        int yBot = bounds.Bottom;
        //left to right scan
        for (int x = bounds.Left; x < bounds.Right; x++)
        {
            if (srchArea.IsCoordinateInBounds(x, yTop))
            {
                var key = x + "-" + yTop;
                // lock (Visited)
                {
                    if (!Visited.Contains(key))
                    {
                        pixels.Add(new Vector2(x, yTop));
                    }
                }
            }
            if (srchArea.IsCoordinateInBounds(x, yBot))
            {
                var key = x + "-" + yBot;
                // lock (Visited)
                {
                    if (!Visited.Contains(key))
                    {
                        pixels.Add(new Vector2(x, yBot));
                    }
                }
            }
        }
        int xLeft = bounds.Left;
        int xRight = bounds.Right;
        int yMin = bounds.Top + 1;
        int yMax = bounds.Bottom - 1;
        //top to bottom scan
        for (int y = yMin; y < yMax; y++)
        {
            if (srchArea.IsCoordinateInBounds(xLeft, y))
            {
                var key = xLeft + "-" + y;
                // lock (Visited)
                {
                    if (!Visited.Contains(key))
                    {
                        pixels.Add(new Vector2(xLeft, y));
                    }
                }
            }
            if (srchArea.IsCoordinateInBounds(xRight, y))
            {
                var key = xRight + "-" + y;
                // lock (Visited)
                {
                    if (!Visited.Contains(key))
                    {
                        pixels.Add(new Vector2(xRight, y));
                    }
                }
            }
        }
        if (pixels.Count == 0)
        {
            var size = srchArea.Size + 2;
            var sA = GetSearchArea(coord, size);
            pixels = GetNeighborsPerimeterSearch(sA, coord, depth + 1);
        }
        return pixels;
    }
    private List<Vector2> GetNeighbors(SearchArea srchArea, Vector2 coord)
    {
        return GetNeighborsFullSearch(srchArea, coord);
    }
    public Vector2 ChooseNextNeighbor(Vector2 coord)
    {
        SearchArea sA = GetSearchArea(coord, DefaultSearchSize);
        List<Vector2> neighbors = GetNeighbors(sA, coord);
        if (neighbors.Count == 0)
        {
            return null;
        }
        int idx = rnd.Next(0, neighbors.Count);
        Vector2 elm = neighbors.ElementAt(idx);
        string key = elm.ToString();
        // lock (Visited)
        {
            Visited.Add(key);
        }
        return elm;
    }
}
```
Ok great, so now here's the class that creates the image
```
public class RandomWalk
{
    Rectangle Bounds;
    Vector2 StartPath = new Vector2(0, 0);
    LockBitmap LockMap;
    RandomWalkGenerator rwg;
    public int RandomWalkSegments = 1;
    string colorFile = "";
    public RandomWalk(int size, string _colorFile)
    {
        colorFile = _colorFile;
        Bounds = new Rectangle(0, 0, size, size);
        rwg = new RandomWalkGenerator(Bounds);
    }
    private void Reset()
    {
        rwg = new RandomWalkGenerator(Bounds);
    }
    public void CreateImage(string savePath)
    {
        Reset();
        Bitmap bmp = new Bitmap(Bounds.Width, Bounds.Height);
        LockMap = new LockBitmap(bmp);
        LockMap.LockBits();
        if (RandomWalkSegments == 1)
        {
            RandomWalkSingle();
        }
        else
        {
            RandomWalkMulti(RandomWalkSegments);
        }
        LockMap.UnlockBits();
        bmp.Save(savePath);
    }
    public void SetStartPath(int X, int Y)
    {
        StartPath.X = X;
        StartPath.Y = Y;
    }
    private void RandomWalkMulti(int buckets)
    {
        int Buckets = buckets;
        int PathsPerSide = (Buckets + 4) / 4;
        List<Vector2> Positions = new List<Vector2>();
        var w = Bounds.Width;
        var h = Bounds.Height;
        var wInc = w / Math.Max((PathsPerSide - 1),1);
        var hInc = h / Math.Max((PathsPerSide - 1),1);
        //top
        for (int i = 0; i < PathsPerSide; i++)
        {
            var x = Math.Min(Bounds.Left + wInc * i, Bounds.Right - 1);
            Positions.Add(new Vector2(x, Bounds.Top));
        }
        //bottom
        for (int i = 0; i < PathsPerSide; i++)
        {
            var x = Math.Max(Bounds.Right -1 - wInc * i, 0);
            Positions.Add(new Vector2(x, Bounds.Bottom - 1));
        }
        //right and left
        for (int i = 1; i < PathsPerSide - 1; i++)
        {
            var y = Math.Min(Bounds.Top + hInc * i, Bounds.Bottom - 1);
            Positions.Add(new Vector2(Bounds.Left, y));
            Positions.Add(new Vector2(Bounds.Right - 1, y));
        }
        Positions = Positions.OrderBy(x => Math.Atan2(x.X, x.Y)).ToList();
        double cnt = 0;
        List<IEnumerator<bool>> _execs = new List<IEnumerator<bool>>();
        foreach (Vector2 startPath in Positions)
        {
            double pct = cnt / (Positions.Count);
            double pctNext = (cnt + 1) / (Positions.Count);
            var enumer = RandomWalkHueSegment(pct, pctNext, startPath).GetEnumerator();
            _execs.Add(enumer);
            cnt++;
        }
        bool hadChange = true;
        while (hadChange)
        {
            hadChange = false;
            foreach (var e in _execs)
            {
                if (e.MoveNext())
                {
                    hadChange = true;
                }
            }
        }
    }
    private IEnumerable<bool> RandomWalkHueSegment(double hueStart, double hueEnd, Vector2 startPath)
    {
        var colors = new HSLGenerator();
        colors.SetHueLimits(hueStart, hueEnd);
        var colorFileEnum = colors.GetNextFromFile(colorFile).GetEnumerator();
        Vector2 coord = new Vector2(startPath.X, startPath.Y);
        LockMap.SetPixel(coord.X, coord.Y, ColorHelper.HSL2RGB(0, 0, 0));
        while (true)
        {
            if (!colorFileEnum.MoveNext())
            {
                break;
            }
            var rgb = colorFileEnum.Current;
            coord = ChooseNextNeighbor(coord);
            if (coord == null)
            {
                break;
            }
            LockMap.SetPixel(coord.X, coord.Y, rgb);
            yield return true;
        }
    }
    private void RandomWalkSingle()
    {
        Vector2 coord = new Vector2(StartPath.X, StartPath.Y);
        LockMap.SetPixel(coord.X, coord.Y, ColorHelper.HSL2RGB(0, 0, 0));
        int cnt = 1;
        var colors = new HSLGenerator();
        var colorFileEnum = colors.GetNextFromFile(colorFile).GetEnumerator();
        while (true)
        {
            if (!colorFileEnum.MoveNext())
            {
                return;
            }
            var rgb = colorFileEnum.Current;
            var newCoord = ChooseNextNeighbor(coord);
            coord = newCoord;
            if (newCoord == null)
            {
                return;
            }
            LockMap.SetPixel(newCoord.X, newCoord.Y, rgb);
            cnt++;
        }
    }
    private Vector2 ChooseNextNeighbor(Vector2 coord)
    {
        return rwg.ChooseNextNeighbor(coord);
    }
}
```
And here's an example implementation:
```
class Program
{
    static void Main(string[] args)
    {
        {
           // ColorHelper.MakeColorFile();
          //  return;
        }
        string colorFile = "colors.txt";
        var size = new Vector2(1000,1000);
        var ctr = size.Center();
        RandomWalk r = new RandomWalk(size.X,colorFile);
        r.RandomWalkSegments = 8;
        r.SetStartPath(ctr.X, ctr.Y);
        r.CreateImage("test.bmp");
    }
}
```
If RandomWalkSegments = 1, then it basically just starts walking wherever you tell it to, and begins at the first first color in the file. 
It's not the cleanest code I'll admit, but it runs pretty fast!
[![Cropped Output](https://i.stack.imgur.com/rSH7Z.jpg)](https://i.stack.imgur.com/rSH7Z.jpg)
[![3 Paths](https://i.stack.imgur.com/cg2dV.jpg)](https://i.stack.imgur.com/cg2dV.jpg)
[![128 Paths](https://i.stack.imgur.com/phXbQ.jpg)](https://i.stack.imgur.com/phXbQ.jpg)
EDIT:
So I've been learning about OpenGL and Shaders. I generated a 4096x4096 using every color blazing fast on the GPU with 2 simple shader scripts. The output is boring, but figured somebody might find this interesting and come up with some cool ideas:
Vertex Shader
```
attribute vec3 a_position;
varying vec2 vTexCoord;
   void main() {
      vTexCoord = (a_position.xy + 1) / 2;
      gl_Position = vec4(a_position, 1);
  }
```
Frag Shader
```
void main(void){
    int num = int(gl_FragCoord.x*4096.0 + gl_FragCoord.y);
    int h = num % 256;
    int s = (num/256) % 256;
    int l = ((num/256)/256) % 256;
    vec4 hsl = vec4(h/255.0,s/255.0,l/255.0,1.0);
    gl_FragColor = hsl_to_rgb(hsl); // you need to implement a conversion method
}
```
Edit (10/15/16) : Just wanted to show a proof of concept of a genetic algorithm. I am STILL running this code 24 hours later on a 100x100 set of random colors, but so far the output is beautiful! [![enter image description here](https://i.stack.imgur.com/aBwAw.png)](https://i.stack.imgur.com/aBwAw.png)
Edit (10/26/16): Ive been running the genetic algorithm code for 12 days now..and its still optimizing the output. Its basically converged to some local minimum but it apparently is finding more improvement still: [![enter image description here](https://i.stack.imgur.com/WhrZ1.png)](https://i.stack.imgur.com/WhrZ1.png)
Edit: 8/12/17 - I wrote a new random walk algorithm - basically you specify a number of "walkers", but instead of walking randomly - they will randomly choose another walker and either avoid them (choose the next available pixel furthest away) - or walk towards them (choose the next available pixel closest to them). An example grayscale output is here (I will be doing a full 4096x4096 color render after I wire up the coloring!) : [![enter image description here](https://i.stack.imgur.com/gmu5c.jpg)](https://i.stack.imgur.com/gmu5c.jpg)
[Answer]
# Scala
I order all of the colors by walking a 3-dimensional [Hilbert Curve](http://en.wikipedia.org/wiki/Hilbert_curve) via an [L-System](http://en.wikipedia.org/wiki/L-system). I then walk the pixels in the output image along a 2-dimensional Hilbert Curve and lay out all of the colors.
512 x 512 output:
![enter image description here](https://i.stack.imgur.com/Sh0lH.png)
Here's the code. Most of it covers just the logic and math of moving through three dimensions via pitch/roll/yaw. I'm sure there was a better way to do that part, but oh well.
```
import scala.annotation.tailrec
import java.awt.image.BufferedImage
import javax.imageio.ImageIO
import java.io.File
object AllColors {
  
  case class Vector(val x: Int, val y: Int, val z: Int) {
    def applyTransformation(m: Matrix): Vector = {
      Vector(m.r1.x * x + m.r1.y * y + m.r1.z * z, m.r2.x * x + m.r2.y * y + m.r2.z * z, m.r3.x * x + m.r3.y * y + m.r3.z * z)
    }
    def +(v: Vector): Vector = {
      Vector(x + v.x, y + v.y, z + v.z)
    }
    def unary_-(): Vector = Vector(-x, -y, -z)
  }
  
  case class Heading(d: Vector, s: Vector) {
    def roll(positive: Boolean): Heading = {
      val (axis, b) = getAxis(d)
      Heading(d, s.applyTransformation(rotationAbout(axis, !(positive ^ b))))
    }
    
    def yaw(positive: Boolean): Heading = {
      val (axis, b) = getAxis(s)
      Heading(d.applyTransformation(rotationAbout(axis, positive ^ b)), s)
    }
    
    def pitch(positive: Boolean): Heading = {
      if (positive) {
        Heading(s, -d)
      } else {
        Heading(-s, d)
      }
    }
    
    def applyCommand(c: Char): Heading = c match {
      case '+' => yaw(true)
      case '-' => yaw(false)
      case '^' => pitch(true)
      case 'v' => pitch(false)
      case '>' => roll(true)
      case '<' => roll(false)
    }
  }
  
  def getAxis(v: Vector): (Char, Boolean) = v match {
    case Vector(1, 0, 0) => ('x', true)
    case Vector(-1, 0, 0) => ('x', false)
    case Vector(0, 1, 0) => ('y', true)
    case Vector(0, -1, 0) => ('y', false)
    case Vector(0, 0, 1) => ('z', true)
    case Vector(0, 0, -1) => ('z', false)
  }
  
  def rotationAbout(axis: Char, positive: Boolean) = (axis, positive) match {
    case ('x', true) => XP
    case ('x', false) => XN
    case ('y', true) => YP
    case ('y', false) => YN
    case ('z', true) => ZP
    case ('z', false) => ZN
  }
  
  case class Matrix(val r1: Vector, val r2: Vector, val r3: Vector)
  
  val ZP = Matrix(Vector(0,-1,0),Vector(1,0,0),Vector(0,0,1))
  val ZN = Matrix(Vector(0,1,0),Vector(-1,0,0),Vector(0,0,1))
  
  val XP = Matrix(Vector(1,0,0),Vector(0,0,-1),Vector(0,1,0))
  val XN = Matrix(Vector(1,0,0),Vector(0,0,1),Vector(0,-1,0))
  
  val YP = Matrix(Vector(0,0,1),Vector(0,1,0),Vector(-1,0,0))
  val YN = Matrix(Vector(0,0,-1),Vector(0,1,0),Vector(1,0,0))
  
  @tailrec def applyLSystem(current: Stream[Char], rules: Map[Char, List[Char]], iterations: Int): Stream[Char] = {
    if (iterations == 0) {
      current
    } else {
      val nextStep = current flatMap { c => rules.getOrElse(c, List(c)) }
      applyLSystem(nextStep, rules, iterations - 1)
    }
  }
  
  def walk(x: Vector, h: Heading, steps: Stream[Char]): Stream[Vector] = steps match {
    case Stream() => Stream(x)
    case 'f' #:: rest => x #:: walk(x + h.d, h, rest)
    case c #:: rest => walk(x, h.applyCommand(c), rest)
  }
  
  def hilbert3d(n: Int): Stream[Vector] = {
    val rules = Map('x' -> "^>x<f+>>x<<f>>x<<+fvxfxvf+>>x<<f>>x<<+f>x<^".toList)
    val steps = applyLSystem(Stream('x'), rules, n) filterNot (_ == 'x')
    walk(Vector(0, 0, 0), Heading(Vector(1, 0, 0), Vector(0, 1, 0)), steps)
  }
  
  def hilbert2d(n: Int): Stream[Vector] = {
    val rules = Map('a' -> "-bf+afa+fb-".toList, 'b' -> "+af-bfb-fa+".toList)
    val steps = applyLSystem(Stream('a'), rules, n) filterNot (c => c == 'a' || c == 'b')
    walk(Vector(0, 0, 0), Heading(Vector(1, 0, 0), Vector(0, 0, 1)), steps)
  }
  
  def main(args: Array[String]): Unit = {
    val n = 4
    val img = new BufferedImage(1 << (3 * n), 1 << (3 * n), BufferedImage.TYPE_INT_RGB)
    hilbert3d(n * 2).zip(hilbert2d(n * 3)) foreach { case (Vector(r,g,b), Vector(x,y,_)) => img.setRGB(x, y, (r << (24 - 2 * n)) | (g << (16 - 2 * n)) | (b << (8 - 2 * n))) }
    ImageIO.write(img, "png", new File(s"out_$n.png"))
  }
}
```
[Answer]
# HTML5 canvas + JavaScript
I call it randoGraph and you can create as many you want [here](http://www.logikon.net/randograph) 
Some examples: 
![example 1](https://i.stack.imgur.com/TrsEU.png)
![example 2](https://i.stack.imgur.com/oUrJy.png)
![example 3](https://i.stack.imgur.com/smQCF.png)
![example 4](https://i.stack.imgur.com/YGF8F.png)
![example 5](https://i.stack.imgur.com/03MZj.png)
![example 6](https://i.stack.imgur.com/THUzY.png)
![example 7](https://i.stack.imgur.com/WYim8.png)
For example in Firefox you can right click in the canvas (when it finish) and save it as image . Producing 4096x4096 image is a kind of problem due to some browsers memory limit. 
The idea is quite simple but each image is unique. First we create the palette of colors. Then starting by X points we select random colors from the palette and positions for them (each time we select a color we delete it from the palette) and we record where we put it not to put in the same position next pixel.
For every pixel that is tangent to that we create a number (X) of possible colors and then we select the most relevant to that pixel. This goes on until the image is complete. 
The HTML code 
```
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang="el">
<head>
<script type="text/javascript" src="randoGraph.js"></script>
</head>
<body>
    <canvas id="randoGraphCanvas"></canvas> 
</body>
</html>
```
And the JavaScript for randoGraph.js
```
window.onload=function(){
    randoGraphInstance = new randoGraph("randoGraphCanvas",256,128,1,1);
    randoGraphInstance.setRandomness(500, 0.30, 0.11, 0.59);
    randoGraphInstance.setProccesses(10);
    randoGraphInstance.init(); 
}
function randoGraph(canvasId,width,height,delay,startings)
{
    this.pixels = new Array();
    this.colors = new Array(); 
    this.timeouts = new Array(); 
    this.randomFactor = 500;
    this.redFactor = 0.30;
    this.blueFactor = 0.11;
    this.greenFactor  = 0.59;
    this.processes = 1;
    this.canvas = document.getElementById(canvasId); 
    this.pixelsIn = new Array(); 
    this.stopped = false;
    this.canvas.width = width;
    this.canvas.height = height;
    this.context = this.canvas.getContext("2d");
    this.context.clearRect(0,0, width-1 , height-1);
    this.shadesPerColor = Math.pow(width * height, 1/3);
    this.shadesPerColor = Math.round(this.shadesPerColor * 1000) / 1000;
    this.setRandomness = function(randomFactor,redFactor,blueFactor,greenFactor)
    {
        this.randomFactor = randomFactor;
        this.redFactor = redFactor;
        this.blueFactor = blueFactor;
        this.greenFactor = greenFactor;
    }
    this.setProccesses = function(processes)
    {
        this.processes = processes;
    }
    this.init = function()
    {
        if(this.shadesPerColor > 256 || this.shadesPerColor % 1 > 0) 
        { 
            alert("The dimensions of the image requested to generate are invalid. The product of width multiplied by height must be a cube root of a integer number up to 256."); 
        }
        else 
        {
            var steps = 256 / this.shadesPerColor;
            for(red = steps / 2; red <= 255;)
            {
                for(blue = steps / 2; blue <= 255;)
                {
                    for(green = steps / 2; green <= 255;)
                    {   
                        this.colors.push(new Color(Math.round(red),Math.round(blue),Math.round(green)));
                        green = green + steps;
                    }
                    blue = blue + steps; 
                }
                red = red + steps; 
            }   
            for(var i = 0; i < startings; i++)
            {
                var color = this.colors.splice(randInt(0,this.colors.length - 1),1)[0];
                var pixel = new Pixel(randInt(0,width - 1),randInt(0,height - 1),color);
                this.addPixel(pixel);       
            }
            for(var i = 0; i < this.processes; i++)
            {
                this.timeouts.push(null);
                this.proceed(i);
            }
        }
    }
    this.proceed = function(index) 
    { 
        if(this.pixels.length > 0)
        {
            this.proceedPixel(this.pixels.splice(randInt(0,this.pixels.length - 1),1)[0]);
            this.timeouts[index] = setTimeout(function(that){ if(!that.stopped) { that.proceed(); } },this.delay,this);
        }
    }
    this.proceedPixel = function(pixel)
    {
        for(var nx = pixel.getX() - 1; nx < pixel.getX() + 2; nx++)
        {
            for(var ny = pixel.getY() - 1; ny < pixel.getY() + 2; ny++)
            {
                if(! (this.pixelsIn[nx + "x" + ny] == 1 || ny < 0 || nx < 0 || nx > width - 1 || ny > height - 1 || (nx == pixel.getX() && ny == pixel.getY())) )
                {
                    var color = this.selectRelevantColor(pixel.getColor());
                    var newPixel = new Pixel(nx,ny,color);
                    this.addPixel(newPixel);
                }
            }
        }   
    }
    this.selectRelevantColor = function(color)
    {
        var relevancies = new Array(); 
        var relColors = new Array(); 
        for(var i = 0; i < this.randomFactor && i < this.colors.length; i++)
        {
            var index = randInt(0,this.colors.length - 1);
            var c = this.colors[index];
            var relevancy = Math.pow( ((c.getRed()-color.getRed()) * this.redFactor) , 2)
            + Math.pow( ((c.getBlue()-color.getBlue()) * this.blueFactor), 2)
            + Math.pow( ((c.getGreen()-color.getGreen()) * this.greenFactor) , 2);
            relevancies.push(relevancy); 
            relColors[relevancy+"Color"] = index;
        }
        return this.colors.splice(relColors[relevancies.min()+"Color"],1)[0]
    }
    this.addPixel = function(pixel)
    {
        this.pixels.push(pixel);
        this.pixelsIn[pixel.getX() + "x" + pixel.getY() ] = 1;
        var color = pixel.getColor();
        this.context.fillStyle = "rgb("+color.getRed()+","+color.getBlue()+","+color.getGreen()+")";
        this.context.fillRect( pixel.getX(), pixel.getY(), 1, 1);   
    }
    var toHex = function toHex(num) 
    {
        num = Math.round(num);
        var hex = num.toString(16);
        return hex.length == 1 ? "0" + hex : hex;
    }
    this.clear = function()
    {
        this.stopped = true;
    }
}
function Color(red,blue,green)
{   
    this.getRed = function() { return red; } 
    this.getBlue = function() { return blue; } 
    this.getGreen = function() { return green; } 
}
function Pixel(x,y,color)
{   
    this.getX = function() { return x; } 
    this.getY = function() { return y; } 
    this.getColor = function() { return color; } 
}
function randInt(min, max) 
{
    return Math.floor(Math.random() * (max - min + 1)) + min;
}
// @see https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/min
Array.prototype.min = function() 
{
      return Math.min.apply(null, this);
};
// @see http://stackoverflow.com/questions/5223/length-of-javascript-object-ie-associative-array
Object.size = function(obj) 
{
    var size = 0, key;
    for (key in obj) {
        if (obj.hasOwnProperty(key)) size++;
    }
    return size;
};
```
[Answer]
## Python
So here's my solution in python, it takes almost an hour to make one, so there's probably some optimization to be done:
```
import PIL.Image as Image
from random import shuffle
import math
def mulColor(color, factor):
    return (int(color[0]*factor), int(color[1]*factor), int(color[2]*factor))
def makeAllColors(arg):
    colors = []
    for r in range(0, arg):
        for g in range(0, arg):
            for b in range(0, arg):
                colors.append((r, g, b))
    return colors
def distance(color1, color2):
    return math.sqrt(pow(color2[0]-color1[0], 2) + pow(color2[1]-color1[1], 2) + pow(color2[2]-color1[2], 2))
def getClosestColor(to, colors):
    closestColor = colors[0]
    d = distance(to, closestColor)
    for color in colors:
        if distance(to, color) < d:
            closestColor = color
            d = distance(to, closestColor)
    return closestColor
imgsize = (256, 128)
#imgsize = (10, 10)
colors = makeAllColors(32)
shuffle(colors)
factor = 255.0/32.0
img = Image.new("RGB", imgsize, "white")
#start = (imgsize[0]/4, imgsize[1]/4)
start = (imgsize[0]/2, 0)
startColor = colors.pop()
img.putpixel(start, mulColor(startColor, factor))
#color = getClosestColor(startColor, colors)
#img.putpixel((start[0]+1, start[1]), mulColor(color, factor))
edgePixels = [(start, startColor)]
donePositions = [start]
for pixel in edgePixels:
    if len(colors) > 0:
        color = getClosestColor(pixel[1], colors)
    m = [(pixel[0][0]-1, pixel[0][1]), (pixel[0][0]+1, pixel[0][2]), (pixel[0][0], pixel[0][3]-1), (pixel[0][0], pixel[0][4]+1)]
    if len(donePositions) >= imgsize[0]*imgsize[1]:
    #if len(donePositions) >= 100:
        break
    for pos in m:
        if (not pos in donePositions):
            if not (pos[0]<0 or pos[1]<0 or pos[0]>=img.size[0] or pos[1]>=img.size[1]):
                img.putpixel(pos, mulColor(color, factor))
                #print(color)
                donePositions.append(pos)
                edgePixels.append((pos, color))
                colors.remove(color)
                if len(colors) > 0:
                    color = getClosestColor(pixel[1], colors)
    print((len(donePositions) * 1.0) / (imgsize[0]*imgsize[1]))
print len(donePositions)
img.save("colors.png")
```
Here are some example outputs:
![enter image description here](https://i.stack.imgur.com/qdR8N.png) ![enter image description here](https://i.stack.imgur.com/oZfIc.png) ![enter image description here](https://i.stack.imgur.com/7jgYG.png) ![enter image description here](https://i.stack.imgur.com/QEFUr.png) ![enter image description here](https://i.stack.imgur.com/DBZdx.png)
[Answer]
## Mathematica
```
colors = Table[
r = y*256 + x; {BitAnd[r, 2^^111110000000000]/32768., 
BitAnd[r, 2^^1111100000]/1024., BitAnd[r, 2^^11111]/32.}, {y, 0, 
127}, {x, 0, 255}];
SeedRandom[1337];
maxi = 5000000;
Monitor[For[i = 0, i < maxi, i++,
x1 = RandomInteger[{2, 255}];
x2 = RandomInteger[{2, 255}];
y1 = RandomInteger[{2, 127}];
y2 = RandomInteger[{2, 127}];
c1 = colors[[y1, x1]];
c2 = colors[[y2, x2]];
ca1 = (colors[[y1 - 1, x1]] + colors[[y1, x1 - 1]] + 
  colors[[y1 + 1, x1]] + colors[[y1, x1 + 1]])/4.;
ca2 = (colors[[y2 - 1, x2]] + colors[[y2, x2 - 1]] + 
  colors[[y2 + 1, x2]] + colors[[y2, x2 + 1]])/4.;
d1 = Abs[c1[[1]] - ca1[[1]]] + Abs[c1[[2]] - ca1[[2]]] + 
Abs[c1[[3]] - ca1[[3]]];
d1p = Abs[c2[[1]] - ca1[[1]]] + Abs[c2[[2]] - ca1[[2]]] + 
Abs[c2[[3]] - ca1[[3]]];
d2 = Abs[c2[[1]] - ca2[[1]]] + Abs[c2[[2]] - ca2[[2]]] + 
Abs[c2[[3]] - ca2[[3]]];
d2p = Abs[c1[[1]] - ca2[[1]]] + Abs[c1[[2]] - ca2[[2]]] + 
Abs[c1[[3]] - ca2[[3]]];
If[(d1p + d2p < 
  d1 + d2) || (RandomReal[{0, 1}] < 
   Exp[-Log10[i]*(d1p + d2p - (d1 + d2))] && i < 1000000),
temp = colors[[y1, x1]];
colors[[y1, x1]] = colors[[y2, x2]];
colors[[y2, x2]] = temp
]
], ProgressIndicator[i, {1, maxi}]]
Image[colors]
```
Result (2x):
![256x128 2x](https://i.stack.imgur.com/S0tzc.png)
[Original 256x128 image](http://postimg.org/image/7heb6dai5/ "Original 256x128 image")
**Edit:**
by replacing Log10[i] with Log10[i]/5 you get:
![enter image description here](https://i.stack.imgur.com/ZOAh3.png)
The above code is related to simulated annealing. Seen in this way, the second image is created with a higher "temperature" in the first 10^6 steps. The higher "temperature" causes more permutations among the pixels, whereas in the first image the structure of the ordered image is still slightly visible.
[Answer]
## JavaScript
Still a student and my first time posting so my codes probably messy and I'm not 100% sure that my pictures have all the needed colors but I was super happy with my results so I figured I'd post them. 
I know the contest is over but I really loved the results of these and I always loved the look of recursive backtracking generated mazes so I thought it might be cool to see what one would look like if it placed colored pixels. So I start by generating all the colors in an array then I do the recursive backtracking while popping colors off the array.
Here's my JSFiddle <http://jsfiddle.net/Kuligoawesome/3VsCu/>
```
// Global variables
const FPS = 60;// FrameRate
var canvas = null;
var ctx = null;
var bInstantDraw = false;
var MOVES_PER_UPDATE = 50; //How many pixels get placed down
var bDone = false;
var width; //canvas width
var height; //canvas height
var colorSteps = 32;
var imageData;
var grid;
var colors;
var currentPos;
var prevPositions;
// This is called when the page loads
function Init()
{
    canvas = document.getElementById('canvas'); // Get the HTML element with the ID of 'canvas'
    width = canvas.width;
    height = canvas.height;
    ctx = canvas.getContext('2d'); // This is necessary, but I don't know exactly what it does
    imageData = ctx.createImageData(width,height); //Needed to do pixel manipulation
    grid = []; //Grid for the labyrinth algorithm
    colors = []; //Array of all colors
    prevPositions = []; //Array of previous positions, used for the recursive backtracker algorithm
    for(var r = 0; r < colorSteps; r++)
    {
        for(var g = 0; g < colorSteps; g++)
        {
            for(var b = 0; b < colorSteps; b++)
            {
                colors.push(new Color(r * 255 / (colorSteps - 1), g * 255 / (colorSteps - 1), b * 255 / (colorSteps - 1)));
                //Fill the array with all colors
            }
        }
    }
    colors.sort(function(a,b)
    {
        if (a.r < b.r)
            return -1;
        if (a.r > b.r)
            return 1;
        if (a.g < b.g)
            return -1;
        if (a.g > b.g)
            return 1;
        if (a.b < b.b)
            return -1;
        if (a.b > b.b)
            return 1;
        return 0;
    });
    for(var x = 0; x < width; x++)
    {
        grid.push(new Array());
        for(var y = 0; y < height; y++)
        {
            grid[x].push(0); //Set up the grid
            //ChangePixel(imageData, x, y, colors[x + (y * width)]);
        }
    }
    currentPos = new Point(Math.floor(Math.random() * width),Math.floor(Math.random() * height)); 
    grid[currentPos.x][currentPos.y] = 1;
    prevPositions.push(currentPos);
    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
    if(bInstantDraw)
    {
        do
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid);
                if(availableSpaces.length > 0)
                {
                    var test = availableSpaces[Math.floor(Math.random() * availableSpaces.length)];
                    prevPositions.push(currentPos);
                    currentPos = test;
                    grid[currentPos.x][currentPos.y] = 1;
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop());
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop();
                    }
                    else
                    {
                        break;
                    }
                }
            }
        }
        while(prevPositions.length > 0)
        ctx.putImageData(imageData,0,0);
    }
    else
    {
        setInterval(GameLoop, 1000 / FPS);
    }
}
// Main program loop
function GameLoop()
{
    Update();
    Draw();
}
// Game logic goes here
function Update()
{
    if(!bDone)
    {
        var counter = MOVES_PER_UPDATE;
        while(counter > 0) //For speeding up the drawing
        {
            var notMoved = true;
            while(notMoved)
            {
                var availableSpaces = CheckForSpaces(grid); //Find available spaces
                if(availableSpaces.length > 0) //If there are available spaces
                {
                    prevPositions.push(currentPos); //add old position to prevPosition array
                    currentPos = availableSpaces[Math.floor(Math.random() * availableSpaces.length)]; //pick a random available space
                    grid[currentPos.x][currentPos.y] = 1; //set that space to filled
                    ChangePixel(imageData, currentPos.x, currentPos.y, colors.pop()); //pop color of the array and put it in that space
                    notMoved = false;
                }
                else
                {
                    if(prevPositions.length != 0)
                    {
                        currentPos = prevPositions.pop(); //pop to previous position where spaces are available
                    }
                    else
                    {
                        bDone = true;
                        break;
                    }
                }
            }
            counter--;
        }
    }
}
function Draw()
{
    // Clear the screen
    ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    ctx.fillStyle='#000000';
    ctx.fillRect(0, 0, ctx.canvas.width, ctx.canvas.height);
    ctx.putImageData(imageData,0,0);
}
function CheckForSpaces(inGrid) //Checks for available spaces then returns back all available spaces
{
    var availableSpaces = [];
    if(currentPos.x > 0 && inGrid[currentPos.x - 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x - 1, currentPos.y));
    }
    if(currentPos.x < width - 1 && inGrid[currentPos.x + 1][currentPos.y] == 0)
    {
        availableSpaces.push(new Point(currentPos.x + 1, currentPos.y));
    }
    if(currentPos.y > 0 && inGrid[currentPos.x][currentPos.y - 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y - 1));
    }
    if(currentPos.y < height - 1 && inGrid[currentPos.x][currentPos.y + 1] == 0)
    {
        availableSpaces.push(new Point(currentPos.x, currentPos.y + 1));
    }
    return availableSpaces;
}
function ChangePixel(data, x, y, color) //Quick function to simplify changing pixels
{
    data.data[((x + (y * width)) * 4) + 0] = color.r;
    data.data[((x + (y * width)) * 4) + 1] = color.g;
    data.data[((x + (y * width)) * 4) + 2] = color.b;
    data.data[((x + (y * width)) * 4) + 3] = 255;
}
/*Needed Classes*/
function Point(xIn, yIn)
{
    this.x = xIn;
    this.y = yIn;
}
function Color(r, g, b)
{
    this.r = r;
    this.g = g;
    this.b = b;
    this.hue = Math.atan2(Math.sqrt(3) * (this.g - this.b), 2 * this.r - this.g, this.b);
    this.min = Math.min(this.r, this.g);
    this.min = Math.min(this.min, this.b);
    this.min /= 255;
    this.max = Math.max(this.r, this.g);
    this.max = Math.max(this.max, this.b);
    this.max /= 255;
    this.luminance = (this.min + this.max) / 2;
    if(this.min === this.max)
    {
        this.saturation = 0;
    }
    else if(this.luminance < 0.5)
    {
        this.saturation = (this.max - this.min) / (this.max + this.min);
    }
    else if(this.luminance >= 0.5)
    {
        this.saturation = (this.max - this.min) / (2 - this.max - this.min);
    }
}
```
256x128 picture, colors sorted red->green->blue   
![RGB Sorted Colors](https://i.stack.imgur.com/31ccy.png)
256x128 picture, colors sorted blue->green->red   
![BGR Sorted Colors](https://i.stack.imgur.com/z71Wx.png)
256x128 picture, colors sorted hue->luminance->saturation  
![HLS Sorted Colors](https://i.stack.imgur.com/DWNch.png)
And finally a GIF of one being generated   
![Color Labyrinth GIF](https://i.stack.imgur.com/4Ehhy.gif)
[Answer]
# Java
I decided to have a try at this challenge. I was inspired by [this answer](https://codegolf.stackexchange.com/a/19382/30544) to another code golf. My program generates uglier images, but they have all colors.
Also, my first time code golfing. :)
(4k images were too big for my small upload speed, I tried uploading one but after one hour it hasn't uploaded. You can generate your own.)
![](https://puu.sh/aNZMS/9d0cfbf571.png)
Closeup:
![](https://puu.sh/aNZYm/465d3cb352.png)
Generates an image in 70 seconds on my machine, takes about 1.5GB of memory when generating
### Main.java
```
import java.awt.Color;
import java.awt.Graphics2D;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Random;
import javax.imageio.ImageIO;
public class Main {
    static char[][] colors = new char[4096 * 4096][3];
    static short[][] pixels = new short[4096 * 4096][2];
    static short[][] iterMap = new short[4096][4096];  
    public static int mandel(double re0, double im0, int MAX_ITERS) {
        double re = re0;
        double im = im0;
        double _r;
        double _i;
        double re2;
        double im2;
        for (int iters = 0; iters < MAX_ITERS; iters++) {
            re2 = re * re;
            im2 = im * im;
            if (re2 + im2 > 4.0) {
                return iters;
            }
            _r = re;
            _i = im;
            _r = re2 - im2;
            _i = 2 * (re * im);
            _r += re0;
            _i += im0;
            re = _r;
            im = _i;
        }
        return MAX_ITERS;
    }
    static void shuffleArray(Object[] ar) {
        Random rnd = new Random();
        for (int i = ar.length - 1; i > 0; i--) {
          int index = rnd.nextInt(i + 1);
          // Simple swap
          Object a = ar[index];
          ar[index] = ar[i];
          ar[i] = a;
        }
      }
    public static void main(String[] args) {
        long startTime = System.nanoTime();
        System.out.println("Generating colors...");
        for (int i = 0; i < 4096 * 4096; i++) {
            colors[i][0] = (char)((i >> 16) & 0xFF); // Red
            colors[i][1] = (char)((i >> 8) & 0xFF);  // Green
            colors[i][2] = (char)(i & 0xFF);         // Blue
        }
        System.out.println("Sorting colors...");
        //shuffleArray(colors); // Not needed
        Arrays.sort(colors, new Comparator<char[]>() {
            @Override
            public int compare(char[] a, char[] b) {
                return (a[0] + a[1] + a[2]) - (b[0] + b[1] + b[2]);
            }
        });
        System.out.println("Generating fractal...");
        for (int y = -2048; y < 2048; y++) {
            for (int x = -2048; x < 2048; x++) {
                short iters = (short) mandel(x / 1024.0, y / 1024.0, 1024);
                iterMap[x + 2048][y + 2048] = iters;
            }
        }
        System.out.println("Organizing pixels in the image...");
        for (short x = 0; x < 4096; x++) {
            for (short y = 0; y < 4096; y++) {
                pixels[x * 4096 + y][0] = x;
                pixels[x * 4096 + y][1] = y;
            }
        }
        shuffleArray(pixels);
        Arrays.sort(pixels, new Comparator<short[]>() {
            @Override
            public int compare(short[] a, short[] b) {
                return iterMap[b[0]][b[1]] - iterMap[a[0]][a[1]];
            }
        });
        System.out.println("Writing image to BufferedImage...");
        BufferedImage img = new BufferedImage(4096, 4096, BufferedImage.TYPE_INT_RGB);
        Graphics2D g = img.createGraphics();
        for (int i = 0; i < 4096 * 4096; i++) {
            g.setColor(new Color(colors[i][0], colors[i][1], colors[i][2]));
            g.fillRect(pixels[i][0], pixels[i][1], 1, 1);
        }
        g.dispose();
        System.out.println("Writing image to file...");
        File imageFile = new File("image.png");
        try {
            ImageIO.write(img, "png", imageFile);
        } catch (IOException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
        System.out.println("Done!");
        System.out.println("Took " + ((System.nanoTime() - startTime) / 1000000000.) + " seconds.");
        System.out.println();
        System.out.println("The result is saved in " + imageFile.getAbsolutePath());
    }
}
```
[Answer]
# C#
So I started working on this just as a fun exercise and ended up with an output that at least to me looks pretty neat. The key difference in my solution to (at least) most others is that I'm generating exactly the number of colors needed to start with and evenly spacing the generation out from pure white to pure black.
I'm also setting colors working in an inward spiral and choosing the next color based on the average of the color diff between all neighbors that have been set.
Here is a small sample output that I've produced so far, I'm working on a 4k render but I expect it to take upwards of a day to finish.
Here is a sample of the spec output at 256x128:
[![Spec Render](https://i.stack.imgur.com/AJnSA.png)](https://i.stack.imgur.com/AJnSA.png)
Some larger images with still reasonable render times:
[![Render at 360 x 240](https://i.stack.imgur.com/ke9nw.png)](https://i.stack.imgur.com/ke9nw.png)
Second run at 360 x 240 produced a much smoother image
[![Render #2 at 360 x 240](https://i.stack.imgur.com/8ALHF.png)](https://i.stack.imgur.com/8ALHF.png)
After improving performance I was able to run a HD render which took 2 days, I haven't given up on a 4k yet but it could take weeks.
[HD Render](https://github.com/MadillJ/InterstingCodeCollection/blob/master/AllColors/GeneratedImages/1920x1080.png)
```
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Drawing;
using System.Drawing.Imaging;
using System.IO;
using System.Linq;
namespace SandBox
{
    class Program
    {
        private static readonly List<Point> directions = new List<Point>
        {
            new Point(1, 0),
            new Point(0, 1),
            new Point(-1, 0),
            new Point(0, -1)
        };
        static void Main(string[] args)
        {
            if (args.Length != 2)
            {
                HelpFile();
                return;
            }
            try
            {
                var config = new ColorGeneratorConfig
                {
                    XLength = int.Parse(args[0]),
                    YLength = int.Parse(args[1])
                };
                Console.WriteLine("Starting image generation with:");
                Console.WriteLine($"\tDimensions:\t\t{config.XLength} X {config.YLength}");
                Console.WriteLine($"\tSteps Per Channel:\t{config.NumOfSteps}");
                Console.WriteLine($"\tStep Size:\t\t{config.ColorStep}");
                Console.WriteLine($"\tSteps to Skip:\t\t{config.StepsToSkip}\n");
                var runner = new TaskRunner();
                var colors = runner.Run(() => GenerateColorList(config), "color selection");
                var pixels = runner.Run(() => BuildPixelArray(colors, config), "pixel array generation");
                runner.Run(() => OutputBitmap(pixels, config), "bitmap creation");
            }
            catch (Exception ex)
            {
               HelpFile("There was an issue in execution");
            }
            
            Console.ReadLine();
        }
        private static void HelpFile(string errorMessage = "")
        {
            const string Header = "Generates an image with every pixel having a unique color";
            Console.WriteLine(errorMessage == string.Empty ? Header : $"An error has occured: {errorMessage}\n Ensure the Arguments you have provided are valid");
            Console.WriteLine();
            Console.WriteLine($"{AppDomain.CurrentDomain.FriendlyName} X Y");
            Console.WriteLine();
            Console.WriteLine("X\t\tThe Length of the X dimension eg: 256");
            Console.WriteLine("Y\t\tThe Length of the Y dimension eg: 128");
        }
        public static List<Color> GenerateColorList(ColorGeneratorConfig config)
        {
            //Every iteration of our color generation loop will add the iterationfactor to this accumlator which is used to know when to skip
            decimal iterationAccumulator = 0;
            var colors = new List<Color>();
            for (var r = 0; r < config.NumOfSteps; r++)
                for (var g = 0; g < config.NumOfSteps; g++)
                    for (var b = 0; b < config.NumOfSteps; b++)
                    {
                        iterationAccumulator += config.IterationFactor;
                        //If our accumulator has reached 1, then subtract one and skip this iteration
                        if (iterationAccumulator > 1)
                        {
                            iterationAccumulator -= 1;
                            continue;
                        }
                        colors.Add(Color.FromArgb(r*config.ColorStep, g*config.ColorStep,b*config.ColorStep));
                    }
            return colors;
        }
        public static Color?[,] BuildPixelArray(List<Color> colors, ColorGeneratorConfig config)
        {
            //Get a random color to start with.
            var random = new Random(Guid.NewGuid().GetHashCode());
            var nextColor = colors[random.Next(colors.Count)];
            var pixels = new Color?[config.XLength, config.YLength];
            var currPixel = new Point(0, 0);
            var i = 0;
            //Since we've only generated exactly enough colors to fill our image we can remove them from the list as we add them to our image and stop when none are left.
            while (colors.Count > 0)
            {
                i++;
                //Set the current pixel and remove the color from the list.
                pixels[currPixel.X, currPixel.Y] = nextColor;
                colors.RemoveAt(colors.IndexOf(nextColor));
                //Our image generation works in an inward spiral generation GetNext point will retrieve the next pixel given the current top direction.
                var nextPixel = GetNextPoint(currPixel, directions.First());
                //If this next pixel were to be out of bounds (for first circle of spiral) or hit a previously generated pixel (for all other circles)
                //Then we need to cycle the direction and get a new next pixel
                if (nextPixel.X >= config.XLength || nextPixel.Y >= config.YLength || nextPixel.X < 0 || nextPixel.Y < 0 ||
                    pixels[nextPixel.X, nextPixel.Y] != null)
                {
                    var d = directions.First();
                    directions.RemoveAt(0);
                    directions.Add(d);
                    nextPixel = GetNextPoint(currPixel, directions.First());
                }
                //This code sets the pixel to pick a color for and also gets the next color
                //We do this at the end of the loop so that we can also support haveing the first pixel set outside of the loop
                currPixel = nextPixel;
                if (colors.Count == 0) continue;
                var neighbours = GetNeighbours(currPixel, pixels, config);
                nextColor = colors.AsParallel().Aggregate((item1, item2) => GetAvgColorDiff(item1, neighbours) <
                                                                            GetAvgColorDiff(item2, neighbours)
                    ? item1
                    : item2);
            }
            return pixels;
        }
        public static void OutputBitmap(Color?[,] pixels, ColorGeneratorConfig config)
        {
            //Now that we have generated our image in the color array we need to copy it into a bitmap and save it to file.
            var image = new Bitmap(config.XLength, config.YLength);
            for (var x = 0; x < config.XLength; x++)
                for (var y = 0; y < config.YLength; y++)
                    image.SetPixel(x, y, pixels[x, y].Value);
            using (var file = new FileStream($@".\{config.XLength}X{config.YLength}.png", FileMode.Create))
            {
                image.Save(file, ImageFormat.Png);
            }
        }
        static Point GetNextPoint(Point current, Point direction)
        {
            return new Point(current.X + direction.X, current.Y + direction.Y);
        }
        static List<Color> GetNeighbours(Point current, Color?[,] grid, ColorGeneratorConfig config)
        {
            var list = new List<Color>();
            foreach (var direction in directions)
            {
                var xCoord = current.X + direction.X;
                var yCoord = current.Y + direction.Y;
                if (xCoord < 0 || xCoord >= config.XLength|| yCoord < 0 || yCoord >= config.YLength)
                {
                    continue;
                }
                var cell = grid[xCoord, yCoord];
                if (cell.HasValue) list.Add(cell.Value);
            }
            return list;
        }
        static double GetAvgColorDiff(Color source, IList<Color> colors)
        {
            return colors.Average(color => GetColorDiff(source, color));
        }
        static int GetColorDiff(Color color1, Color color2)
        {
            var redDiff = Math.Abs(color1.R - color2.R);
            var greenDiff = Math.Abs(color1.G - color2.G);
            var blueDiff = Math.Abs(color1.B - color2.B);
            return redDiff + greenDiff + blueDiff;
        }
    }
    public class ColorGeneratorConfig
    {
        public int XLength { get; set; }
        public int YLength { get; set; }
        //Get the number of permutations for each color value base on the required number of pixels.
        public int NumOfSteps
            => (int)Math.Ceiling(Math.Pow((ulong)XLength * (ulong)YLength, 1.0 / ColorDimensions));
        //Calculate the increment for each step
        public int ColorStep
            => 255 / (NumOfSteps - 1);
        //Because NumOfSteps will either give the exact number of colors or more (never less) we will sometimes to to skip some
        //this calculation tells how many we need to skip
        public decimal StepsToSkip
            => Convert.ToDecimal(Math.Pow(NumOfSteps, ColorDimensions) - XLength * YLength);
        //This factor will be used to as evenly as possible spread out the colors to be skipped so there are no large gaps in the spectrum
        public decimal IterationFactor => StepsToSkip / Convert.ToDecimal(Math.Pow(NumOfSteps, ColorDimensions));
        private double ColorDimensions => 3.0;
    }
    public class TaskRunner
    {
        private Stopwatch _sw;
        public TaskRunner()
        {
            _sw = new Stopwatch();
        }
        public void Run(Action task, string taskName)
        {
            Console.WriteLine($"Starting {taskName}...");
            _sw.Start();
            task();
            _sw.Stop();
            Console.WriteLine($"Finished {taskName}. Elapsed(ms): {_sw.ElapsedMilliseconds}");
            Console.WriteLine();
            _sw.Reset();
        }
        public T Run<T>(Func<T> task, string taskName)
        {
            Console.WriteLine($"Starting {taskName}...");
            _sw.Start();
            var result = task();
            _sw.Stop();
            Console.WriteLine($"Finished {taskName}. Elapsed(ms): {_sw.ElapsedMilliseconds}");
            Console.WriteLine();
            _sw.Reset();
            return result;
        }
    }
}
```
[Answer]
# Go
Here's another one from me, I think it gives more interesting results:
```
package main
import (
    "image"
    "image/color"
    "image/png"
    "os"
    "math"
    "math/rand"
)
func distance(c1, c2 color.Color) float64 {
    r1, g1, b1, _ := c1.RGBA()
    r2, g2, b2, _ := c2.RGBA()
    rd, gd, bd := int(r1)-int(r2), int(g1)-int(g2), int(b1)-int(b2)
    return math.Sqrt(float64(rd*rd + gd*gd + bd*bd))
}
func main() {
    allcolor := image.NewRGBA(image.Rect(0, 0, 256, 128))
    for y := 0; y < 128; y++ {
        for x := 0; x < 256; x++ {
            allcolor.Set(x, y, color.RGBA{uint8(x%32) * 8, uint8(y%32) * 8, uint8(x/32+(y/32*8)) * 8, 255})
        }
    }
    for y := 0; y < 128; y++ {
        for x := 0; x < 256; x++ {
            rx, ry := rand.Intn(256), rand.Intn(128)
            c1, c2 := allcolor.At(x, y), allcolor.At(rx, ry)
            allcolor.Set(x, y, c2)
            allcolor.Set(rx, ry, c1)
        }
    }
    for i := 0; i < 16384; i++ {
        for y := 0; y < 128; y++ {
            for x := 0; x < 256; x++ {
                xl, xr := (x+255)%256, (x+1)%256
                cl, c, cr := allcolor.At(xl, y), allcolor.At(x, y), allcolor.At(xr, y)
                dl, dr := distance(cl, c), distance(c, cr)
                if dl < dr {
                    allcolor.Set(xl, y, c)
                    allcolor.Set(x, y, cl)
                }
                yu, yd := (y+127)%128, (y+1)%128
                cu, c, cd := allcolor.At(x, yu), allcolor.At(x, y), allcolor.At(x, yd)
                du, dd := distance(cu, c), distance(c, cd)
                if du < dd {
                    allcolor.Set(x, yu, c)
                    allcolor.Set(x, y, cu)
                }
            }
        }
    }
    filep, err := os.Create("EveryColor.png")
    if err != nil {
        panic(err)
    }
    err = png.Encode(filep, allcolor)
    if err != nil {
        panic(err)
    }
    filep.Close()
}
```
It starts with the same pattern as the gif in [my other answer](https://codegolf.stackexchange.com/a/22368/17601). Then, it shuffles it into this:
![just noise](https://i.stack.imgur.com/y5Khh.png)
The more iterations I run the rather uninspired neighbor-comparison algorithm, the more apparent the rainbow pattern becomes.
Here's 16384:
![a very noisy rainbow at 16384 iterations](https://i.stack.imgur.com/bmJ59.png)
And 65536:
![enter image description here](https://i.stack.imgur.com/vrKgn.png)
[Answer]
These images are "Langton's Rainbow". They're drawn rather simply: as Langton's ant moves about, a color is drawn on each pixel the first time that pixel is visitted. The color to draw next is then simply incremented by 1, ensuring that 2^15 colors are used, one for each pixel.
**EDIT:**
I made a version which renders 4096X4096 images, using 2^24 colors. The colors are also 'reflected' so they make nice, smooth gradients. I'll only provide links to them since they're huge (>28 MB)
[Langton's Rainbow large, rule LR](https://dl.dropboxusercontent.com/u/3236504/LangtonsRainbow/LangtonsRainbow_8bpp_Reflect_LR.png)
[Langton's Rainbow large, rule LLRR](https://dl.dropboxusercontent.com/u/3236504/LangtonsRainbow/LangtonsRainbow_8bpp_Reflect_LLRR.png)
*//End of edit.*
This for the classic LR rule set:
[![Langton's Rainbow LR](https://i.stack.imgur.com/eUkV2.png)](https://i.stack.imgur.com/eUkV2.png)
Here is LLRR:
[![Langton's Rainbow LLRR](https://i.stack.imgur.com/MhWMO.png)](https://i.stack.imgur.com/MhWMO.png)
Finally, this one uses the LRRRRRLLR ruleset:
[![Langton's Rainbow LRRRRRLLR](https://i.stack.imgur.com/nLqvd.png)](https://i.stack.imgur.com/nLqvd.png)
Written in C++, using CImg for graphics.
I should also mention how the colors were selected: First, I use an unsigned short to contain the RGB color data. Every time a cell is first visitted, I right shift the bits by some multiple of 5, AND by 31, then multiply by 8. Then the unsigned short color is incremented by 1. This produces values from 0 to 248 at most. However, I've subtract this value *from* 255 in the red and blue components, therefore R and B are in multiples of 8, starting from 255, down to 7:
```
c[0]=255-((color&0x1F)*8);
c[2]=255-(((color>>5)&0x1F)*8);
c[1]=(((color>>10)&0x1F)*8);
```
However, this doesn't apply to the green component, which is in multiples of 8 from 0 to 248. In any case, each pixel should contain a unique color.
Anyways, source code is below:
```
#include "CImg.h"
using namespace cimg_library;
CImgDisplay screen;
CImg<unsigned char> surf;
#define WIDTH 256
#define HEIGHT 128
#define TOTAL WIDTH*HEIGHT
char board[WIDTH][HEIGHT];
class ant
{
  public:
  int x,y;
  char d;
  unsigned short color;
  void init(int X, int Y,char D)
  {
    x=X;y=Y;d=D;
    color=0;
  }
  void turn()
  {
    ///Have to hard code for the rule set here.
    ///Make sure to set RULECOUNT to the number of rules!
    #define RULECOUNT 9
    //LRRRRRLLR
    char get=board[x][y];
    if(get==0||get==6||get==7){d+=1;}
    else{d-=1;}
    if(d<0){d=3;}
    else if(d>3){d=0;}
  }
  void forward()
  {
    if(d==0){x++;}
    else if(d==1){y--;}
    else if(d==2){x--;}
    else {y++;}
    if(x<0){x=WIDTH-1;}
    else if(x>=WIDTH){x=0;}
    if(y<0){y=HEIGHT-1;}
    else if(y>=HEIGHT){y=0;}
  }
  void draw()
  {
    if(board[x][y]==-1)
    {
      board[x][y]=0;
      unsigned char c[3];
      c[0]=255-((color&0x1F)*8);
      c[2]=255-(((color>>5)&0x1F)*8);
      c[1]=(((color>>10)&0x1F)*8);
      surf.draw_point(x,y,c);
      color++;
    }
    board[x][y]++;
    if(board[x][y]==RULECOUNT){board[x][y]=0;}
  }
  void step()
  {
    draw();
    turn();
    forward();
  }
};
void renderboard()
{
  unsigned char white[]={200,190,180};
  surf.draw_rectangle(0,0,WIDTH,HEIGHT,white);
  for(int x=0;x<WIDTH;x++)
  for(int y=0;y<HEIGHT;y++)
  {
    char get=board[x][y];
    if(get==1){get=1;unsigned char c[]={255*get,255*get,255*get};
    surf.draw_point(x,y,c);}
    else if(get==0){get=0;unsigned char c[]={255*get,255*get,255*get};
    surf.draw_point(x,y,c);}
  }
}
int main(int argc, char** argv)
{
  screen.assign(WIDTH*3,HEIGHT*3);
  surf.assign(WIDTH,HEIGHT,1,3);
  ant a;
  a.init(WIDTH/2,HEIGHT/2,2);
  surf.fill(0);
  for(int x=0;x<WIDTH;x++)
  for(int y=0;y<HEIGHT;y++)
  {
    board[x][y]=-1;
  }
  while(a.color<TOTAL)
  {
    a.step();
  }
  screen=surf;
  while(screen.is_closed()==false)
  {
    screen.wait();
  }
  surf.save_bmp("LangtonsRainbow.bmp");
  return 0;
}
```
[Answer]
# Ruby
I decided I would go ahead and make the PNG from scratch, because I thought that would be interesting. This code is literally outputting the **raw** binary data into a file.
I did the 512x512 version. (The algorithm is rather uninteresting, though.) It finishes in about 3 seconds on my machine.
```
require 'zlib'
class RBPNG
  def initialize
    # PNG header
    @data = [137, 80, 78, 71, 13, 10, 26, 10].pack 'C*'
  end
  def chunk name, data = ''
    @data += [data.length].pack 'N'
    @data += name
    @data += data
    @data += [Zlib::crc32(name + data)].pack 'N'
  end
  def IHDR opts = {}
    opts = {bit_depth: 8, color_type: 6, compression: 0, filter: 0, interlace: 0}.merge opts
    raise 'IHDR - Missing width param' if !opts[:width]
    raise 'IHDR - Missing height param' if !opts[:height]
    self.chunk 'IHDR', %w[width height].map {|x| [opts[x.to_sym]].pack 'N'}.join +
                       %w[bit_depth color_type compression filter interlace].map {|x| [opts[x.to_sym]].pack 'C'}.join
  end
  def IDAT data; self.chunk 'IDAT', Zlib.deflate(data); end
  def IEND; self.chunk 'IEND'; end
  def write filename; IO.binwrite filename, @data; end
end
class Color
  attr_accessor :r, :g, :b, :a
  def initialize r = 0, g = 0, b = 0, a = 255
    if r.is_a? Array
      @r, @g, @b, @a = @r
      @a = 255 if !@a
    else
      @r = r
      @g = g
      @b = b
      @a = a
    end
  end
  def hex; '%02X' * 4 % [@r, @g, @b, @a]; end
  def rgbhex; '%02X' * 3 % [@r, @g, @b]; end
end
img = RBPNG.new
img.IHDR({width: 512, height: 512, color_type: 2})
#img.IDAT ['00000000FFFFFF00FFFFFF000000'].pack 'H*'
r = g = b = 0
data = Array.new(512){ Array.new(512){
  c = Color.new r, g, b
  r += 4
  if r == 256
    r = 0
    g += 4
    if g == 256
      g = 0
      b += 4
    end
  end
  c
} }
img.IDAT [data.map {|x| '00' + x.map(&:rgbhex).join }.join].pack 'H*'
img.IEND
img.write 'all_colors.png'
```
Output (in `all_colors.png`) (click any of these images to enlarge them):
[![Output](https://i.stack.imgur.com/HempOm.png)](https://i.stack.imgur.com/HempO.png)
Somewhat more interesting gradient-ish output (by changing the 4th to last line to `}.shuffle }`):
[![Output 2](https://i.stack.imgur.com/RWBtbm.png)](https://i.stack.imgur.com/RWBtb.png)
And by changing it to `}.shuffle }.shuffle`, you get crazy color lines:
[![Output 3](https://i.stack.imgur.com/KR6GKm.png)](https://i.stack.imgur.com/KR6GK.png)
[Answer]
# Python
![plasma](https://i.stack.imgur.com/cWDJ0.png)
Using python to sort the colors by luminance, generating a luminance pattern and picking the most appropriate color. The pixels are iterated in random order so that the less favorable luminance matches that naturally happen when the list of available colors gets smaller are evenly spread throughout the picture.
```
#!/usr/bin/env python
from PIL import Image
from math import pi, sin, cos
import random
WIDTH = 256
HEIGHT = 128
img = Image.new("RGB", (WIDTH, HEIGHT))
colors = [(x >> 10, (x >> 5) & 31, x & 31) for x in range(32768)]
colors = [(x[0] << 3, x[1] << 3, x[2] << 3) for x in colors]
colors.sort(key=lambda x: x[0] * 0.2126 + x[1] * 0.7152 + x[2] * 0.0722)
def get_pixel(lum):
    for i in range(len(colors)):
        c = colors[i]
        if c[0] * 0.2126 + c[1] * 0.7152 + c[2] * 0.0722 > lum:
            break
    return colors.pop(i)
def plasma(x, y):
    x -= WIDTH / 2
    p = sin(pi * x / (32 + 10 * sin(y * pi / 32)))
    p *= cos(pi * y / 64)
    return 128 + 127 * p
xy = []
for x in range(WIDTH):
    for y in range(HEIGHT):
        xy.append((x, y))
random.shuffle(xy)
count = 0
for x, y in xy:
    l = int(plasma(x, y))
    img.putpixel((x, y), get_pixel(plasma(x, y)))
    count += 1
    if not count & 255:
        print "%d pixels rendered" % count
img.save("test.png")
```
[Answer]
# Java
```
import java.awt.Point;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.ArrayList;
import java.util.logging.Level;
import java.util.logging.Logger;
import javax.imageio.ImageIO;
/**
 *
 * @author Quincunx
 */
public class AllColorImage {
    public static void main(String[] args) {
        BufferedImage img = new BufferedImage(4096, 4096, BufferedImage.TYPE_INT_RGB);
        int num = 0;
        ArrayList<Point> points = new ArrayList<>();
        for (int y = 0; y < 4096; y++) {
            for (int x = 0; x < 4096 ; x++) {
                points.add(new Point(x, y));
            }
        }
        for (Point p : points) {
            int x = p.x;
            int y = p.y;
            img.setRGB(x, y, num);
            num++;
        }
        try {
            ImageIO.write(img, "png", new File("Filepath"));
        } catch (IOException ex) {
            Logger.getLogger(AllColorImage.class.getName()).log(Level.SEVERE, null, ex);
        }
    }
}
```
I went for 4096 by 4096 because I couldn't figure out how to get all the colors without doing so.
Output:
Too big to fit here. This is a screenshot:
![enter image description here](https://i.stack.imgur.com/UkkHN.png)
With a little change, we can get a more beautiful picture:
Add `Collections.shuffle(points, new Random(0));` between generating the points and doing the colors:
```
import java.awt.Point;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Random;
import java.util.logging.Level;
import java.util.logging.Logger;
import javax.imageio.ImageIO;
/**
 *
 * @author Quincunx
 */
public class AllColorImage {
    public static void main(String[] args) {
        BufferedImage img = new BufferedImage(4096, 4096, BufferedImage.TYPE_INT_RGB);
        int num = 0;
        ArrayList<Point> points = new ArrayList<>();
        for (int y = 0; y < 4096; y++) {
            for (int x = 0; x < 4096 ; x++) {
                points.add(new Point(x, y));
            }
        }
        Collections.shuffle(points, new Random(0));
        for (Point p : points) {
            int x = p.x;
            int y = p.y;
            img.setRGB(x, y, num);
            num++;
        }
        try {
            ImageIO.write(img, "png", new File("Filepath"));
        } catch (IOException ex) {
            Logger.getLogger(AllColorImage.class.getName()).log(Level.SEVERE, null, ex);
        }
    }
}
```
![enter image description here](https://i.stack.imgur.com/62Flm.jpg)
Closeup:
![enter image description here](https://i.stack.imgur.com/kc1J8.png)
[Answer]
# C++11
(*Update:* only afterwards did I notice that [a similar approach](https://codegolf.stackexchange.com/a/22636/17698) has already been tried --- with more patience with regards to the number of iterations.)
For each pixel, I define a set of neighbor pixels. I define the discrepancy between two pixels to be the sum of squares of their R/G/B differences. The penalty of a given pixel is then the sum of the discrepancies between the pixel and its neighbors.
Now, I first generate a random permutation, then start picking random pairs of pixels. If swapping the two pixels reduces the sum of the total penalties of all pixels, the swap goes through. I repeat this for a million times.
The output is in the PPM format, which I have converted into PNG using standard utilities.
Source:
```
#include <iostream>
#include <fstream>
#include <cstdlib>
#include <random>
static std::mt19937 rng;
class Pixel
{
public:
    int r, g, b;
    Pixel() : r(0), g(0), b(0) {}
    Pixel(int r, int g, int b) : r(r), g(g), b(b) {}
    void swap(Pixel& p)
    {
        int r = this->r,  g = this->g,    b = this->b;
        this->r = p.r;    this->g = p.g;  this->b = p.b;
        p.r = r;          p.g = g;        p.b = b;
    }
};
class Image
{
public:
    static const int width = 256;
    static const int height = 128;
    static const int step = 32;
    Pixel pixel[width*height];
    int penalty[width*height];
    std::vector<int>** neighbors;
    Image()
    {
        if (step*step*step != width*height)
        {
            std::cerr << "parameter mismatch" << std::endl;
            exit(EXIT_FAILURE);
        }
        neighbors = new std::vector<int>*[width*height];
        for (int i = 0; i < width*height; i++)
        {
            penalty[i] = -1;
            neighbors[i] = pixelNeighbors(i);
        }
        int i = 0;
        for (int r = 0; r < step; r++)
        for (int g = 0; g < step; g++)
        for (int b = 0; b < step; b++)
        {
            pixel[i].r = r * 255 / (step-1);
            pixel[i].g = g * 255 / (step-1);
            pixel[i].b = b * 255 / (step-1);
            i++;
        }
    }
    ~Image()
    {
        for (int i = 0; i < width*height; i++)
        {
            delete neighbors[i];
        }
        delete [] neighbors;
    }
    std::vector<int>* pixelNeighbors(const int pi)
    {
        // 01: X-shaped structure
        //const int iRad = 7, jRad = 7;
        //auto condition = [](int i, int j) { return abs(i) == abs(j); };
        //
        // 02: boring blobs
        //const int iRad = 7, jRad = 7;
        //auto condition = [](int i, int j) { return true; };
        //
        // 03: cross-shaped
        //const int iRad = 7, jRad = 7;
        //auto condition = [](int i, int j) { return i==0 || j == 0; };
        //
        // 04: stripes
        const int iRad = 1, jRad = 5;
        auto condition = [](int i, int j) { return i==0 || j == 0; };
        std::vector<int>* v = new std::vector<int>;
        int x = pi % width;
        int y = pi / width;
        for (int i = -iRad; i <= iRad; i++)
        for (int j = -jRad; j <= jRad; j++)
        {
            if (!condition(i,j))
                continue;
            int xx = x + i;
            int yy = y + j;
            if (xx < 0 || xx >= width || yy < 0 || yy >= height)
                continue;
            v->push_back(xx + yy*width);
        }
        return v;
    }
    void shuffle()
    {
        for (int i = 0; i < width*height; i++)
        {
            std::uniform_int_distribution<int> dist(i, width*height - 1);
            int j = dist(rng);
            pixel[i].swap(pixel[j]);
        }
    }
    void writePPM(const char* filename)
    {
        std::ofstream fd;
        fd.open(filename);
        if (!fd.is_open())
        {
            std::cerr << "failed to open file " << filename
                      << "for writing" << std::endl;
            exit(EXIT_FAILURE);
        }
        fd << "P3\n" << width << " " << height << "\n255\n";
        for (int i = 0; i < width*height; i++)
        {
            fd << pixel[i].r << " " << pixel[i].g << " " << pixel[i].b << "\n";
        }
        fd.close();
    }
    void updatePixelNeighborhoodPenalty(const int pi)
    {
        for (auto j : *neighbors[pi])
            updatePixelPenalty(j);
    }
    void updatePixelPenalty(const int pi)
    {
        auto pow2 = [](int x) { return x*x; };
        int pen = 0;
        Pixel* p1 = &pixel[pi];
        for (auto j : *neighbors[pi])
        {
            Pixel* p2 = &pixel[j];
            pen += pow2(p1->r - p2->r) + pow2(p1->g - p2->g) + pow2(p1->b - p2->b);
        }
        penalty[pi] = pen / neighbors[pi]->size();
    }
    int getPixelPenalty(const int pi)
    {
        if (penalty[pi] == (-1))
        {
            updatePixelPenalty(pi);
        }
        return penalty[pi];
    }
    int getPixelNeighborhoodPenalty(const int pi)
    {
        int sum = 0;
        for (auto j : *neighbors[pi])
        {
            sum += getPixelPenalty(j);
        }
        return sum;
    }
    void iterate()
    {
        std::uniform_int_distribution<int> dist(0, width*height - 1);       
        int i = dist(rng);
        int j = dist(rng);
        int sumBefore = getPixelNeighborhoodPenalty(i)
                        + getPixelNeighborhoodPenalty(j);
        int oldPenalty[width*height];
        std::copy(std::begin(penalty), std::end(penalty), std::begin(oldPenalty));
        pixel[i].swap(pixel[j]);
        updatePixelNeighborhoodPenalty(i);
        updatePixelNeighborhoodPenalty(j);
        int sumAfter = getPixelNeighborhoodPenalty(i)
                       + getPixelNeighborhoodPenalty(j);
        if (sumAfter > sumBefore)
        {
            // undo the change
            pixel[i].swap(pixel[j]);
            std::copy(std::begin(oldPenalty), std::end(oldPenalty), std::begin(penalty));
        }
    }
};
int main(int argc, char* argv[])
{
    int seed;
    if (argc >= 2)
    {
        seed = atoi(argv[1]);
    }
    else
    {
        std::random_device rd;
        seed = rd();
    }
    std::cout << "seed = " << seed << std::endl;
    rng.seed(seed);
    const int numIters = 1000000;
    const int progressUpdIvl = numIters / 100;
    Image img;
    img.shuffle();
    for (int i = 0; i < numIters; i++)
    {
        img.iterate();
        if (i % progressUpdIvl == 0)
        {
            std::cout << "\r" << 100 * i / numIters << "%";
            std::flush(std::cout);
        }
    }
    std::cout << "\rfinished!" << std::endl;
    img.writePPM("AllColors2.ppm");
    return EXIT_SUCCESS;
}
```
Varying the step of neighbors gives different results. This can be tweaked in the function Image::pixelNeighbors(). The code includes examples for four options: (see source)
![example 01](https://i.stack.imgur.com/w6V7b.png)
![example 02](https://i.stack.imgur.com/E7GWQ.png)
![example 03](https://i.stack.imgur.com/7vl41.png)
![example 04](https://i.stack.imgur.com/79jXO.png)
*Edit:* another example similar to the fourth one above but with a bigger kernel and more iterations:
![example 05](https://i.stack.imgur.com/PSKyx.png)
*One more:* using
```
const int iRad = 7, jRad = 7;
auto condition = [](int i, int j) { return (i % 2==0 && j % 2==0); };
```
and ten million iterations, I got this:
![example 06](https://i.stack.imgur.com/1iTja.png)
[Answer]
# AWK and friends.
## Look mom! I've shaken the colors away!
The 'x' file:
```
BEGIN {
    N=5
    C=2^N
    print "P3\n"2^(3*N-int(3*N/2))" "2^int(3*N/2)"\n"C-1
    for(x=0;x<C;x++)
        for(y=0;y<C;y++)
            for(z=0;z<C;z++)
                print x^4+y^4+z^4"\t"x" "y" "z | "sort -n | cut -f2-" 
}
```
Run:
```
awk -f x > x.ppm
```
Output:
N=5:
![N=5.png](https://i.stack.imgur.com/GLRYW.png)
N=6:
![N=6.png](https://i.stack.imgur.com/GOAeR.png)
[Answer]
Not the most elegant code, but interesting on two counts: Computing the number of colors from the dimensions (as long as the product of dimensions is a power of two), and doing trippy color space stuff:
```
void Main()
{
    var width = 256;
    var height = 128;
    var colorCount = Math.Log(width*height,2);
    var bitsPerChannel = colorCount / 3;
    var channelValues = Math.Pow(2,bitsPerChannel);
    var channelStep = (int)(256/channelValues);
    var colors = new List<Color>();
    var m1 = new double[,] {{0.6068909,0.1735011,0.2003480},{0.2989164,0.5865990,0.1144845},{0.00,0.0660957,1.1162243}};
    for(var r=0;r<255;r+=channelStep)
    for(var g=0;g<255;g+=channelStep)
    for(var b=0;b<255;b+=channelStep)   
    {
        colors.Add(Color.FromArgb(0,r,g,b));
    }
    var sortedColors = colors.Select((c,i)=>
                            ToLookupTuple(MatrixProduct(m1,new[]{c.R/255d,c.G/255d,c.B/255d}),i))
                            .Select(t=>new
                                            {
                                                x = (t.Item1==0 && t.Item2==0 && t.Item3==0) ? 0 : t.Item1/(t.Item1+t.Item2+t.Item3),
                                                y = (t.Item1==0 && t.Item2==0 && t.Item3==0) ? 0 :t.Item2/(t.Item1+t.Item2+t.Item3),
                                                z = (t.Item1==0 && t.Item2==0 && t.Item3==0) ? 0 :t.Item3/(t.Item1+t.Item2+t.Item3),
                                                Y = t.Item2,
                                                i = t.Item4
                                            })
                            .OrderBy(t=>t.x).Select(t=>t.i).ToList();
    if(sortedColors.Count != (width*height))
    {
        throw new Exception(string.Format("Some colors fell on the floor: {0}/{1}",sortedColors.Count,(width*height)));
    }
    using(var bmp = new Bitmap(width,height,PixelFormat.Format24bppRgb))
    {
        for(var i=0;i<colors.Count;i++)
        {
            var y = i % height;
            var x = i / height;
            bmp.SetPixel(x,y,colors[sortedColors[i]]);
        }
        //bmp.Dump(); //For LINQPad use
        bmp.Save("output.png");
    }
}
static Tuple<double,double,double,int>ToLookupTuple(double[] t, int index)
{
    return new Tuple<double,double,double,int>(t[0],t[1],t[2],index);
}
public static double[] MatrixProduct(double[,] matrixA,
    double[] vectorB)
{
    double[] result=new double[3];
    for (int i=0; i<3; ++i) // each row of A
        for (int k=0; k<3; ++k)
            result[i]+=matrixA[i,k]*vectorB[k];
    return result;
}
```
Some interesting variations can be had just by changing the OrderBy clause:
x:
> 
> ![enter image description here](https://i.stack.imgur.com/spFVA.png)
> 
> 
> 
y:
> 
> ![enter image description here](https://i.stack.imgur.com/oQwri.png)
> 
> 
> 
z:
> 
> ![enter image description here](https://i.stack.imgur.com/mWLbo.png)
> 
> 
> 
Y:
> 
> ![enter image description here](https://i.stack.imgur.com/B2aLs.png)
> 
> 
> 
I wish I could figure out what was causing the odd lines in the first three
]