A rainbow rendering of the mandelbrot set. This created by sorting every colour by Hue, then randomly shuffling each set of pixels that share the same iteration in the fractal via histogram generation. Posted on http://allrgb.com/rainbow-fractal.

allrgb.cpp

// AllRGB.cpp
// Calculates an image containing every RGB color 
// once and once only in a vague mandelbrot kind of shape.
// To use:
// gcc allrgb.cpp
// ./a.out > allrgb.ppm

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <cstdlib>

const int iters = 256;

int mandelbrot(float x0, float y0)
{
    x0 = (x0 * 2.0f) - 1.5f;
    y0 = (y0 * 2.0f) - 1.0f;
    float x = 0.0f, y = 0.0f;
    int i = 0;
    float pow16 = pow(2.0f, 16.0f);
    while (x*x + y*y < pow16 && i<iters)
    {
        float xtemp = x*x - y*y + x0;
        y = 2*x*y + y0;
        x = xtemp;
        i++;
    }

    return i;
}

const int histCount = iters;
int histogram[histCount+1];
int histogramInd[histCount+1];
const int size = 4096;
int image[size*size];

struct color
{
    union
    {
        int col;
        struct
        {
            char r;
            char g;
            char b;
        } c;
    } colors;
    float hue;
};
color colormap[size*size];

int compareColor(const void* a, const void* b)
{
    int ahue = ((color*)a)->hue;
    int bhue = ((color*)b)->hue;

    if (ahue < bhue) 
        return -1;
    else if (ahue == bhue) 
        return 0;
    else 
        return 1;
}

float rgb2hue(const color& in)
{
    double      min, max, delta;
    float r = in.colors.c.r * 100.0f, g = in.colors.c.g * 100.0f, b = in.colors.c.b * 100.0f;

    min = r < g ? r : g;
    min = min < b ? min : b;

    max = r > g ? r : g;
    max = max  > b ? max  : b;

    delta = max - min;
    if( max <= 0.0 )
        return 0.0f;

    float outh;

    if( r >= max )
        outh = ( g - b ) / delta;        // between yellow & magenta
    else if( g >= max )
        outh = 2.0 + ( b - r ) / delta;  // between cyan & yellow
    else
        outh = 4.0 + ( r - g ) / delta;  // between magenta & cyan

    outh *= 60.0;                              // degrees

    if( outh < 0.0 )
        outh += 360.0;

    return outh;
}


void makecolormap()
{
    float sqrt3 = sqrt(3.0f);

    //Generate uniform colormap
    for (int i = 0; i<size*size; i++)
    {
        colormap[i].colors.col = i;
        colormap[i].hue = -rgb2hue(colormap[i]);
    }

    //Sort by hue
    qsort(colormap, size*size, sizeof(color), compareColor);
}

int main()
{
    fprintf(stderr, "Make colormap\n");
    makecolormap();

    for (int i = 0; i<=histCount; i++)
    {
        histogram[i] = 0;
        histogramInd[i] = 0;
    }

    fprintf(stderr, "Calculate mandelbrot\n");
    printf("P6 %d %d 255 ", size, size);
    int i = 0;
    int highestC = 0;
    for(int y=size;y--;)
        for(int x=size;x--;)
        {
            int c = mandelbrot(x/(float)size, y/(float)size);
            image[i++] = c;

            if (c > highestC)
                highestC = c;

            histogram[c]++;
        }

    //Cumulative sum each histogram bucket
    int sum = 0;
    for (int i = 0; i<=histCount; i++)
    {
        int hVal = histogram[i];
        histogram[i] = sum;
        sum += hVal;
    }
    fprintf(stderr, "Total Colours: %d, Highest C: %d\n", sum, highestC);

    fprintf(stderr, "Randomising buckets\n");
    for (int i = 0; i<=histCount; i++)
    {
        int offset = histogram[i];
        int nextOffset = (i==histCount) ? sum : histogram[i+1];
        int delta = nextOffset - offset;
        for (int j = offset; j<nextOffset; j++)
        {
            color tmp = colormap[j];
            int other = offset + (rand() % delta);
            colormap[j] = colormap[other];
            colormap[other] = tmp;
        }
    }

    fprintf(stderr, "Output image\n");
    i = 0;
    int highestCol = 0;
    for(int y=size;y--;)
        for (int x=size;x--;)
        {
            int mandelInd = image[i++];
            int col = histogram[mandelInd] + histogramInd[mandelInd]++;
            if (col > highestCol)
                highestCol = col;
            printf("%c%c%c", colormap[col].colors.c.r, colormap[col].colors.c.g, colormap[col].colors.c.b);
        }

    fprintf(stderr, "Highest Color Index: %d\n", highestCol);
}