# Images with all colors

Similar to the images on 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)
• 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();
}
}
}


## 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

• When you say "Dithering is allowed", what do you mean? Is this an exception to the rule "each pixel is a unique color"? If not, what are you allowing which was otherwise forbidden? – Peter Taylor Feb 25 '14 at 22:02
• It means you can place colors in a pattern, so when viewed with the eye, they blend into a different color. For example, see the image "clearly all RGB" on the allRGB page, and many others there. – Mark Jeronimus Feb 26 '14 at 6:42
• I actually find your trivial permutation example to be quite pleasing to the eye. – Jason C Feb 27 '14 at 0:48
• @Zom-B Man, I freakin' love this post. Thanks! – Jason C Feb 27 '14 at 17:26
• Beautiful results/answers! – EthanB Feb 28 '14 at 3:37

# 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.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)
}

// 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)

// 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:

256x128 pixels, starting in the top left corner, minimum selection:

256x128 pixels, starting in the middle, average selection:

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):

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:

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):

Another combination, where the coral form is kept until the end: hue ordered with average selection, with a 30-frame animgif:

# 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, 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 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:

The 2048's which appear in my video:

The first 4096 renders (TODO: they are being uploaded, and my website cannot handle the big traffic, so they are temporarily relocated):

• Now this is cool! – Jaa-c Feb 27 '14 at 15:41
• Very nice :-D Now make some bigger ones! – squeamish ossifrage Feb 27 '14 at 16:03
• You're a true artist! :) – A.L Feb 27 '14 at 17:55
• How much for a print? – primo Feb 28 '14 at 6:31
• I'm working on huge renders and an 1080p video. Gonna take hours or days. I hope someone will be able to create a print from a big render. Or even a t-shirt: code on one side, image on the other. Can anyone arrange that? – fejesjoco Feb 28 '14 at 8:41

# 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. (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 (tileable)! Here it is scaled down (and many more below), original 2048x1024:

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

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))

// 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) {
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:
break;
case DIAG_CW:
break;
case ALL_CW:
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):

Others (left two ordered, right two random, top two path length limited, bottom two unlimitted):

This one can be tiled:

Mode 2:

These ones can be tiled:

512x512 selections:

Tileable diamonds, my favorite from mode 2; you can see in this one how the paths walk around existing objects:

Larger path step and max path length, tileable:

Random mode 1, tileable:

More selections:

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 (same one I linked to at start of this post)

2048x1024 diamonds (I love this one!), scaled down:

4096x4096 big tileable diamonds (Finally! Click 'download' in Dropbox link; it's too large for their previewer), scaled way down:

4096x4096 another cool one

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!

• It reminds me of close-up views of some minerals. – Morwenn Feb 27 '14 at 9:22
• Not part of the contest, but I thought this was kinda cool; I applied a big gaussian blur and auto contrast enhance to one of the random mode 1 pics in photoshop and it made kind of a nice desktop background-y sort of thing. – Jason C Feb 28 '14 at 4:40
• whoa, these are cool pictures! – sevenseacat Feb 28 '14 at 6:51
• Reminds me of Gustav Klimt textures. – Kim Feb 28 '14 at 15:29
• Did you know you can hotlink images in Dropbox? Just copy the download URL, remove the dl=1 and the token_hash=<something> part and make a link to your image like this: [![Alt text of my small preview image](https://i.stack.imgur.com/smallpreview.png)](https://dl.dropbox.com/linktoyourfullsiz‌​eimage.png). Another tip: you can compress your images (I get good results with TruePNG (Download)). I was able to save 28.1% of the file size on this image. – user2428118 Mar 3 '14 at 14:40

## Python w/ PIL

This is based on a Newtonian 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.

Original (33.7 MB)

A close-up of the very center (actual size):

A different vantage point using these values:

xstart = 0
ystart = 0

xd = 1 / dim[0]
yd = 1 / dim[1]


Original (32.2 MB)

And another using these:

xstart = 0.5
ystart = 0.5

xd = 0.001 / dim[0]
yd = 0.001 / dim[1]


Original (27.2 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:

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

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-12

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
l = 1
while abs(l-z) > tol and abs(z) > tol:
l = z
z -= (z**5-1)/(5*z**4)
c += 1
if z == 0: c = maxint
p = int(phase(z))

a[p] += (c,abs(d-z), 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,d,x,y in a[p]:
draw.point((x,y), t[p][r[p]])
r[p] += 1

img.save("out.png")

• Finally a fractal :) Love those. Also, that green at 144 degrees is my favorite color (as opposed to pure green at 120 degrees which is just boring). – Mark Jeronimus Mar 1 '14 at 11:15
• I dunno, I actually kind of like the AllRGB versions better; the need to use the full luminance space nicely emphasizes the gradients. – Ilmari Karonen Mar 1 '14 at 20:38
• +1 Finally some good fractals! The last one is my personal favorite. You should make a video zooming in! (@Quincunx: Saw yours too; it had my vote from day 1!) – Jason C Mar 3 '14 at 0:12
• @JasonC I've added an animation ;) – primo Mar 3 '14 at 8:43
• @primo I know I'm late, but I just wanted to say these images are spectacular. – Ashwin Gupta Jan 20 '16 at 15:21

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.
6. 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

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;

}

@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
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

• 2048×1024
• slightly tiled to 1920×1080 desktop
• 30 seconds
• negative in photoshop

• 2048×1024
• 8 seeds
• 27 seconds

• 512×512
• 40 random seeds
• 6 seconds

• 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]

** 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]

• Increased the initial search cube to 5x5x5

• Even bigger, 9x9x9

• Accident 1. Disabled the permutation so the search space is always linear.

• Accident 2. Tried a new search technique using a fifo queue. Still have to analyze this but I thought it was worth sharing.

• 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...

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];

}

@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 {
// }
// 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
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)

• Angular(64)

• CRT

• Dither

• Flower(5, X), where X ranges from 0.5 to 20 in steps of X=X×1.2

• Mod

• Pythagoras

• Random

• Scanline

• 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)

• Split

• SquareSpiral

• XOR

## New eye-food

• Effect of color selection by max(r, g, b)

• 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)

• Effect of color selection by max(r, min(g, b))

• Effect of color selection by gray value 299*r + 436*g + 114*b

• Effect of color selection by 1*r + 10*g + 100*b

• Effect of color selection by 100*r + 10*g + 1*b

• Happy accidents when 299*r + 436*g + 114*b overflowed in a 32-bit integer

• Variant 3, with gray value and Radial scheduler

• I forgot how I created this

• 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:

• InverseSpiralScheduler(64) (new)

• Another XOR

• First successful 4096 render after the bugfix. I think this was version 3 on SpiralScheduler(1) or something

(50MB!!)

• Version 1 4096, but I accidentally left the color criteria on max()

(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

(50MB!!)

• Cool. Your final image is similar to a second idea I've been tossing around, although I have a feeling mine won't look as good as that. BTW, there is a similar cool one at allrgb.com/diffusive. – Jason C Mar 1 '14 at 3:00
• It was meant as just a teaser, but I edited it in fear of being flagged, which apparently happened :) – Mark Jeronimus Mar 1 '14 at 11:02
• Even the accidents look nice :). The color cube seems like a very good idea, and your render speeds are amazing, compared to mine. Some designs on allrgb do have a good description, for example allrgb.com/dla. I wish I had more time to do more experiments, there are so many possibilities... – fejesjoco Mar 2 '14 at 18:56
• I almost forgot, I just uploaded some of my big renders. I think one of them, the rainbow smoke/spilled ink thingy, is better than anything on allrgb :). I agree, the others are not so stunning, that's why I made a video to make something more out of them :). – fejesjoco Mar 2 '14 at 19:09
• Added source code and the link to the Digisoft library, so you can actually compile my code – Mark Jeronimus Mar 2 '14 at 21:06

## C++ w/ Qt

I see you version:

using normal distribution for the colors:

or first sorted by red / hue (with a smaller deviation):

or some other distributions:

Cauchy distribution (hsl / red):

sorted cols by lightness (hsl):

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;
}

• Nicely done. However, mightn't image.pixel(x, y) == 0 fail and overwrite the first placed pixel? – Mark Jeronimus Feb 26 '14 at 6:36
• @Zom-B: it can, but then the last one will be black, so it's within the rules.. – Jaa-c Feb 26 '14 at 11:04
• No rule problem though. I just thought you might have missed it. Might as well count from 1 then. I love your other ones! – Mark Jeronimus Feb 26 '14 at 21:48
• @Zom-B: thanks, I might add a few more, I kinda like it :P – Jaa-c Feb 26 '14 at 22:09
• The one with two circles and the one below it together kinda look like a monkey face. – Jason C Feb 28 '14 at 4:45

# In Java:

import java.awt.Color;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.Collections;

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) {
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() {
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)) {
chosen = c;
} else {
}
}
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:

I generate something like this:

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.

• ouch; 32 days didnt sounded funny..... the average algorithm in fejesjocos answer on 4k before optimize would have taken probably multiple months – masterX244 Mar 8 '14 at 21:59
• I love his punk eyebrows! – Level River St Mar 9 '14 at 12:56

# 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++)
{
}
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;
}
}


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++)
{
}
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;
}
}


• There is already a QuickSort version on the allRGB page. – Mark Jeronimus Feb 28 '14 at 23:11
• @Zom-B Quicksort is a different algorithm than Bubblesort – masterX244 Feb 28 '14 at 23:43

# 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:

Sample image converted from PPM to demo complete color coverage:

Later on, when it's all blended into grey, you can still see it spinning: longer sequence.

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;
}

• You know it's C when thing happen for "reasons I don't understand". – Nit Feb 26 '14 at 20:22
• Yeah, usually I know what to expect, but here I was just playing around to see what patterns I could get, and this non-terminating order-within-chaos sequence came up. – Yimin Rong Feb 26 '14 at 21:02
• It vortexes because your comparison function doesn't follow the triangle inequality. For example, r>b, b>g, g>r. I can't even port it to Java because it's mergesort relies on this very property, so I get the exception "Comparison method violates its general contract!" – Mark Jeronimus Feb 26 '14 at 22:32
• I'll try p->b * 6 - q->g; but if it wrecks the vortex, won't fix it! – Yimin Rong Feb 26 '14 at 23:52
• +1 for reasons I don't understand. – Jason C Feb 27 '14 at 4:49

## 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

try {
ImageIO.write(img, "png", new File(getFileName()));
} catch(IOException e){
System.out.println("suck it");
}
}

public static void shuffle(BufferedImage img, int radius){
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){
} else {
fileName += "no_shuffle";
}
return fileName + ".png";
}
}


As written, it outputs:

If you run it with shuffle_block = true, it shuffles the colors in each 64x64 block:

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:

• ooh these pictures are the prettiest – sevenseacat Feb 27 '14 at 8:57
• These are really great 😍 – Matthew Jul 2 '17 at 21:14

# 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.

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.)

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);
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");


}

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);
}


• Because its not full cyan at all. It's (0,217,217). All 32 combinations are present though, just not stretched [0,255]. Edit: You're using steps of 7 but I can't find this in the code. Must be a Processing thing. – Mark Jeronimus Feb 27 '14 at 6:20
• @steveverrill In Processing, you can do save("filename.png") to save the current frame buffer to an image. Other image formats are also supported. It'll save you the trouble of taking screenshots. The image is saved to the sketch's folder. – Jason C Feb 27 '14 at 7:56
• @Jasonc thanks for the tip, I was sure there must be a way, but I don't think I'll edit these. I left the frame around the images partially to separate them (2 files for such small images was overkill.) I want to do some images in 512x512 (and there's one in particular I have an idea for) so I will upload those in the way you suggest. – Level River St Feb 27 '14 at 11:10
• @steveverrill Haha, the Warhols are a nice touch. – Jason C Feb 27 '14 at 22:52
• @Zom-B Processing seems to do many things that (annoyingly) aren't mentioned in its documentation: not using the full 256 logical colour channel values in its physical output, blending colours when you don't want, using a full core of my CPU even after it's finished drawing. Still it's simple to get into and you can work around these issues once you know they are there (except the first one, I haven't solved that yet...) – Level River St Mar 2 '14 at 14:27

I just arranged all 16-bit colors (5r,6g,5b) on a Hilbert curve in JavaScript.

Previous, (not Hilbert curve) image:

JSfiddle: 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:

http://jsfiddle.net/jej2d/5/

• Nice! Welcome to PPCG. – Jonathan Van Matre Mar 3 '14 at 23:13
• What does it look like when the walk through the color cube also a 3D Hilbert curve? Edit nm. someone did just that. – Mark Jeronimus Mar 4 '14 at 8:19

## 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:

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...

But the longer it runs (25000), ...

...the more certain patterns start to emerge (100000).

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. 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:

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:

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:

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:

### 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.

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:

# 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.

Click for HD image #2

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;
}

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));
pack();

}

public static void main(String[] args){
new ColorSpan().setVisible(true);
}
}

• That second one really deserves to have a 4096 x 4096 24bit version... – trichoplax Apr 15 '14 at 20:32
• Imgur has been processing the image for about a half an hour. I guess it's probably trying to compress it. Anyway, I added a link: SSend.it/hj4ovh – John P May 3 '14 at 16:51
• There's a problem with the download. – SuperJedi224 Aug 2 '15 at 20:56

# 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++) {
}
}
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):

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:

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;
}


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;
}


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;
}


It looks so fractal-ly. XOR is so beautiful, especially closeup:

Another closeup:

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;
}


# Scala

I order all of the colors by walking a 3-dimensional Hilbert Curve via an 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:

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)
}

def yaw(positive: Boolean): Heading = {
val (axis, b) = getAxis(s)
}

def pitch(positive: Boolean): Heading = {
if (positive) {
} else {
}
}

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")) } }  # 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 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! 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! 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: 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!) : • A little belated, but welcome to PPCG! This is an excellent first post. – quartata Dec 22 '15 at 20:47 • Thank you! I look forward to completing more challenges! I've been doing more image coding stuff lately, it's my new hobby – applejacks01 Jan 25 '16 at 3:36 • Wow these are awesome; I'm glad I came back to this post today and checked out all the later stuff. – Jason C Oct 13 '16 at 19:46 • Thank you! I'm actually doing some genetic algorithm coding now to produce interesting gradients. Basically, take 10000 colors, forming 100x100 grid. For each pixel, get the neighbor pixels. For each, get the CIEDE2000 distance. Sum that up. Sum that up for all 10000 pixels. Genetic algorithm attempts to reduce that total sum. Its slow, but for a 20x20 image its output is really interesting – applejacks01 Oct 14 '16 at 1:39 # HTML5 canvas + JavaScript I call it randoGraph and you can create as many you want here Some examples: 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; };  • That's nice but it looks like the C# answer from fejesjoco. Is it only by chance? – A.L Mar 9 '14 at 21:48 • The algorithms are here and anyone can read and understand that are real different. This answer published after C# answer from fejesjoco declared as winner motivated of how nice its result is. Then I thought a whole different approach of processing and selecting neighbour colours, and this is it. Of course both answers have same basis, like evenly distribution of the colors used along the visible spectrum, the concept of relevant colours, and starting points, maybe fowling those basis someone could think that the images produced have a resemblance in some cases. – konstantinosX Mar 11 '14 at 3:29 • Okay, I'm sorry if you thought I was criticizing your answer. I just wondered if you were inspired by fejesjoco's answer since the resulting output looks similar. – A.L Mar 13 '14 at 17:34 • “Defining methods of a class inside the constructor instead of using the prototype chain is really inefficient, especially if said class is used several times.” is very interesting comment Patrick Roberts. Do you have any reference with example that validates that ? , I sincerely would like to know if this claim has any base ( in order to stop using that ) , and what is it. – konstantinosX Aug 8 '16 at 19:59 • Regarding the use of prototype: it works in much the same way that a static method would. When you have the function defined in the object literal, every new object you create must create a new copy of the function as well, and store them with that object instance (so 16 million color objects means 16 million copies of that exact same function in memory). By comparison, using prototype will only create it once, to be associated with the "class" rather than the object. This has obvious memory benefits as well as potential speed benefits. – Mwr247 Oct 18 '16 at 17:20 ## 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: • Looks like some crazy sound waveforms – Mark Jeronimus Mar 15 '14 at 12:51 # Java I decided to have a try at this challenge. I was inspired by this answer 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.) Closeup: 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()); } }  ## 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): Original 256x128 image Edit: by replacing Log10[i] with Log10[i]/5 you get: 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. ## 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 256x128 picture, colors sorted blue->green->red 256x128 picture, colors sorted hue->luminance->saturation And finally a GIF of one being generated • Your colors are clipped in the brightest regions, causing duplicates. Change r * Math.ceil(255 / (colorSteps - 1) to r * Math.floor(255 / (colorSteps - 1), or even better: r * 255 / (colorSteps - 1) (untested, since you didn't supply a jsfiddle) – Mark Jeronimus Mar 9 '14 at 12:08 • Whoops, yeah I had a feeling that was going to cause problems, hopefully its fixed now, and sorry about the lack of jsfiddle (I didn't know it existed!) Thanks! – Kuligoawesome Mar 9 '14 at 16:26 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 Langton's Rainbow large, rule LLRR //End of edit. This for the classic LR rule set: Here is LLRR: Finally, this one uses the LRRRRRLLR ruleset: 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; }  # 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: Some larger images with still reasonable render times: Second run at 360 x 240 produced a much smoother image 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 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];
}
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;
}

{
private Stopwatch _sw;
{
_sw = new Stopwatch();
}

{
Console.WriteLine($"Starting {taskName}..."); _sw.Start(); task(); _sw.Stop(); Console.WriteLine($"Finished {taskName}. Elapsed(ms): {_sw.ElapsedMilliseconds}");
Console.WriteLine();
_sw.Reset();
}

{
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;
}
}
}

• If anyone has any thoughts on how to improve the performance of the color selection algorithm please let me know, as it stands the 360*240 renders take about 15 minutes. I don't believe it can be parrallelized but I do wonder if there would be a faster way to get the lowest color diff. – Phaeze Aug 3 '16 at 23:24
• How does an image of 360*240 constitute 'all colors'? How are you producing cbrt(360*240)=44.208377983684639269357874002958 colors per component? – Mark Jeronimus Aug 5 '16 at 11:05
• What language is this? Randomizing a list sort and Random is a bad idea regardless, because depending on the algorithm and implementation it may cause a biased result or an exception stating that "Comparison method violates its general contract!": because the contract states that (x.compareTo(y)>0 && y.compareTo(z)>0) implies x.compareTo(z)>0. To randomize a list, use some provided Shuffle method. (colors.Shuffle() ?) – Mark Jeronimus Aug 5 '16 at 13:10
• @MarkJeronimus I admit I missed the spec about the 256x128 image, I will re do the simple renders using those sizes, I was focusing on the every pixel is a unique color aspect of the challenge and larger renders as other submissions have done. – Phaeze Aug 5 '16 at 15:44
• @MarkJeronimus I realize the random sort is bad, in fact there is a comment saying as much. This was just a remnant of another approach I started taking and I was prioritizing getting the large renders done as they take a very long time. – Phaeze Aug 5 '16 at 15:46

# 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
@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):

Somewhat more interesting gradient-ish output (by changing the 4th to last line to }.shuffle }):

And by changing it to }.shuffle }.shuffle, you get crazy color lines:

• Thats really cool. Is there a way that you could make it more pretty though? Maybe randomize the pixels? Scoring is by vote. Vote for the most beautiful images made by the most elegant code. – user12183 Feb 25 '14 at 23:47
• @LowerClassOverflowian Ok, edited – Doorknob Feb 26 '14 at 0:20
• Much Better!!!!!!! – user12183 Feb 26 '14 at 1:10
• What will happen if you changed the 4th to last line to }.shuffle }.shuffle }.shuffle? – John Odom Feb 26 '14 at 14:30
• @John Erm, syntax error, probably? – Doorknob Feb 26 '14 at 17:58

# 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. Then, it shuffles it into this:

The more iterations I run the rather uninspired neighbor-comparison algorithm, the more apparent the rainbow pattern becomes.

Here's 16384:

And 65536:

• +1 I like that a pattern emerges from that; you should make an animation of it! – Jason C Feb 28 '14 at 3:47

# Python

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")


# 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++) {
}
}
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:

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++) {
}
}
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);
}
}
}


Closeup:

• You call a big grey blob "beautiful"? – Doorknob Feb 26 '14 at 2:39
• @Doorknob Yes. I call it very beautiful. I find it amazing that all the colors can be arranged into a big grey blob. I do find the blob more interesting when I zoom in. With a little bit more detail, you can see how un-random Java's rng is. When we zoom in even more, like the second screen-shot, it becomes clear how many colors are in that thing. When I zoom even further, it looks like a Piet program. – Justin Feb 26 '14 at 3:05
• I got the colors in smaller versions by dropping the lower bits. – Mark Jeronimus Feb 26 '14 at 6:29
• Yes, the lower bits for r, g and b separately, but I was dealing with them as one number. – Justin Feb 26 '14 at 6:35
• I see you have figured out teh b1t magicz in your next answer. On topic, it might be interesting experimenting with your own Random subclass that produces even less ideal random numbers. – Mark Jeronimus Feb 26 '14 at 6:38

# C++11

(Update: only afterwards did I notice that a similar approach 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)

Edit: another example similar to the fourth one above but with a bigger kernel and more iterations:

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:

# Java

This was a much better idea. This is some very short Java code; the main method is only 13 lines long:

import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
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);

for (int r = 0; r < 256; r++) {
for (int g = 0; g < 256; g++) {
for (int b = 0; b < 256; b++) {
img.setRGB(((r & 15) << 8) | g, ((r >>> 4) << 8 ) | b, (((r << 8) | g) << 8) | b);
}
}
}
try {
ImageIO.write(img, "png", new File("Filepath"));
} catch (IOException ex) {
Logger.getLogger(AllColorImage.class.getName()).log(Level.SEVERE, null, ex);
}
}
}


Generates blocks of "color pickers". Basically, in the first block, r=0, in the second, r=1, etc. In each block, g increments with respect to x, and b with respect to y.

I really like bitwise operators. Let me break down the setRGB statement:

img.setRGB(((r & 15) << 8) | g, ((r >>> 4) << 8 ) | b, (((r << 8) | g) << 8) | b);

((r & 15) << 8) | g         is the x-coordinate to be set.
r & 15                      is the same thing as r % 16, because 16 * 256 = 4096
<< 8                        multiplies by 256; this is the distance between each block.
| g                         add the value of g to this.

((r >>> 4) << 8 ) | b       is the y-coordinate to be set.
r >>> 4                     is the same thing as r / 16.
<< 8 ) | b                  multiply by 256 and add b.

(((r << 8) | g) << 8) | b   is the value of the color to be set.
r << 8                      r is 8 bits, so shift it 8 bits to the left so that
| g                         we can add g to it.
<< 8                        shift those left 8 bits again, so that we can
| b                         add b


As a result of the bitwise operators, this takes only 7 seconds to complete. If the r & 15 is replaced with r % 16, it takes 9 seconds.

I chose the 4096 x 4096

Output (screenshot, too big otherwise):

Output with evil grin drawn on it by freehand-red-circles:

• Link to the original so I can verify the validness (count colors) – Mark Jeronimus Feb 26 '14 at 6:31
• Lol! I forgot I can run Java code. The first image passes, and I can't reproduce the second image (lol)☺ – Mark Jeronimus Feb 26 '14 at 6:40
• The freehand circles all have the same color, disqualified. :P – Nick T Feb 27 '14 at 0:16
• @Quincunx +1 if you can draw a scary face and still keep the color requirements! – Jason C Feb 27 '14 at 10:29
• @JasonC See my answer. Credit goes to Quincunx for the inspiration. – Level River St Feb 27 '14 at 21:18

# Java

unintentionally inspired by the color chooser solution but in 4096x4096; got some other ideas in pipeline already

import java.awt.image.BufferedImage;
import java.io.BufferedOutputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.OutputStream;
import java.util.Arrays;
import javax.imageio.ImageIO;

/*
* To change this template, choose Tools | Templates
* and open the template in the editor.
*/

/**
*
* @author LH
*/
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);
for (int j = 0; j < 256; j++)//red //255=interesting quirk
{
for (int k = 0; k < 16; k++)//blue_MSBs
{
for (int l = 0; l < 256; l++)//green 255=interesting quirk
{
for (int m = 0; m < 16; m++)//blue_lsbs
{

int val = (j<<16)+(k<<12)+(l)+(m<<8);
//System.out.println("(idx|j|k|l|m|val)=("+idx+"|"+j+"|"+k+"|"+l+"|"+m+"|"+val+"|)");
x[idx]=val;
idx++;
}
}
}
}
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.png"));
ImageIO.write(i, "png", out);
}
}