Rendering the Mandelbrot set using OpenCL

This weekend I decided to play around with OpenCL, something I had never used before. As first project I built a Mandelbrot set renderer. This seemed fitting, since in high school I wrote an extremely slow version in TI Basic on a TI84 graphic calculator. Rendering a single image took about 45 minutes.

The math behind the Mandelbrot set is relatively simple. A point \(c\) on the complex plane is included in the set if the sequence \(z_{n+1} = z_n^2 + c\) with \(z_0 = 0\) is bounded. For simplicity we interpret “bounded” as \(\vert z\vert < 4\) after 256 iterations. To add some nice coloring to the points outside of the set, we can count how many iterations it takes for the sequence to go “unbounded”.

I translated the pseudo code from Wikipedia into the following OpenCL kernel:

__kernel void mandelbrot(__write_only image2d_t out) {
  int2 pos = (int2)(get_global_id(0), get_global_id(1));
  int2 size = get_image_dim(out);

  // Scale x to -2.5 to 1
  float x0 = (float)pos.x / size.x;
  x0 = x0*3.25 - 2;

  // Scale y to -1 to 1
  float y0 = (float)pos.y / size.y;
  y0 = y0*2.0 - 1.0;


  float x = 0.0;
  float y = 0.0;

  uint max_its = 256;
  uint i = 0;
  float d = 0.0;

  while (i < max_its && d < 4.0){
    float xtemp = x*x - y*y + x0;
    y = 2*x*y + y0;
    x = xtemp;

    d = x*x + y*y;
    i++;
  }

  uint4 color = (255, 255, 255, 255);

  if (d < 4.0){
    color.xyz = (uint3)(0, 0, 0);
  } else {
    color.xyz = get_color(i);

  }

  write_imageui(out, pos, color);
}

The complete code can be found on my GitHub repo.