C Mandelbrot Set Coloring

Question

I am working on the following code in C. So far it has all been working and it is zoomed to the correct level, etc, however I am struggling with getting the colors to work as I want. Ideally I would like to end up with something like this regardless of color:

Mandelbrot Set w/ correct colors

however my program as it is below currently produces something like this:

Current Mandelbrot Set

Therefore, I would appreciate any help I could get with making the colors turn out as I want them to.

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

#define ITERMAX 100.0
#define DIVERGING 1.1
#define XMAX 500
#define YMAX 500
#define COLORINTENSITY 255

/* allow up to ITERMAX feedbacks searching for convergence
for the feedback
  z0 = 0 + 0i
  znew = z^2 + c
If we have not diverged to distance DIVERGING before ITERMAX feedbacks
we will assume the feedback is convergent at this value of c.
We will report divergence if |z|^2 > DIVERGING
*/

/* We will print color values for each pixel from (0, 0) to (XMAX, YMAX)
The color of pixel (cx, cy) will be set by convergent()
                                    or by divergent()
depending on the convergence or divergence of the feedback
when c = cx + icy
*/

/* The max value of the red, green, or blue component of a color */

void convergent();   /* one color for convergence */
void divergent();    /* a different color for divergence */

void feedback(double *x, double *y, double cx, double cy);
void pixel(char red, char green, char blue);
FILE *fp;


int main()
{
  fp = fopen("mandelbrot.ppm", "wb");
  double x, y, cx, cy;
  int iteration,squarex, squarey, pixelx, pixely;
  double grow=1.0;

/* header for PPM output */
fprintf(fp, "P6\n# CREATOR: EK, BB, RPJ via the mandel program\n");
fprintf(fp, "%d %d\n%d\n",XMAX, YMAX, COLORINTENSITY);

for (pixely = 0; pixely < YMAX; pixely++)  {
    for (pixelx = 0; pixelx < XMAX; pixelx++)  {
        cx = (((float)pixelx)/((float)XMAX)-0.5)/grow*3.0-0.7;
        cy = (((float)pixely)/((float)YMAX)-0.5)/grow*3.0;
        x = 0.0; y = 0.0;
        for (iteration=1;iteration<ITERMAX;iteration++)  {
                     feedback(&x, &y, cx, cy);
                     if (x*x + y*y > 100.0) iteration = 1000;
        }
        if (iteration==ITERMAX) {
          iteration = x*x + y*y;
          pixel((char) 0, (char) 0, (char) 0);
        }
        else {
          iteration = sqrt(x*x + y*y);
          pixel((char) iteration, (char) 0, (char) iteration);
               }
           }
    }
}

void feedback(double *x, double *y, double cx, double cy) {
/* Update x and y according to the feedback equation
 xnew = x^2 - y^2 + cx
 ynew = 2xy + cy
 (these are the real and imaginary parts of the complex equation:
  znew = z^2 + c)
*/
 double xnew = (*x) * (*x) - (*y) * (*y) + cx;
 double ynew  = 2 * *x * *y + cy;
 *x = xnew;
 *y = ynew;
}

void pixel(char red, char green, char blue)  {
/* put a r-g-b triple to the standard out */
 fputc(red, fp);
 fputc(green, fp);
 fputc(blue, fp);
}

Your color is always the same because you are always setting the R and B values to the iteration number, and G to zero. Rethink that... — Eugene Sh., May 02 '16 at 21:27
Preset a colour array of `ITERMAX` elements, to fade from `R=0, G=0, B=255` to `R=255, G=255, B=255` over the iteration range. It could be an array of `struct`, or one array for each colour. But if you want *every* map to go from blue to white, regardless of zoom, you'll have to find the smallest number of iterations in each map, and range the colours from there. — Weather Vane, May 02 '16 at 21:40
Just an aside about coding style: you should pick one indent amount per block level and stick with it. 4 per block level is pretty common. — lurker, May 03 '16 at 00:15

score 3 · Answer 1 · answered May 03 '16 at 02:33

To fix the banding, you need to iterate over your tables to find your maximum value for the iteration count, then scale your other values to be relative to this max (ie. normalize the values). You may also wish to logarithmically rescale the values to adjust the slope of the color-change.

And you probably don't want to work directly in RGB space. If you define your colors in HSB space, you can set a constant hue and saturation, and vary the brightness proportionally to the normalized iteration counts.

C Mandelbrot Set Coloring

1 Answers1