Mandelbrot set

Another cool routine built off of some relatively simple mathematics is the mandelbrot set. Wikipedia has a really good write up if you’re a little rusty on the ins and outs of a mandelbrot set.

This tutorial assumes that you’ve already got a video display ready with a pointer to your buffer. We’ll just focus on the function that makes the doughnuts. Here’s the code, explanation to follow. This code has been lifted out of a file that I had in an old dos program. It was written using turbo C, but will port over to anything pretty easily.

Anyway, on to the code!

void mandelbrot_frame(double zoom, int max_iter, int xofs, int yofs) {
	double zx = 0, zy = 0, cx = 0, cy = 0;

    /* enumerate all of the rows */
	for (int y = 0; y < 200; y ++) {

        /* enumerate all of the columns */
		for (int x = 0; x < 320; x ++) {

            /* initialize step variables */
			zx = zy = 0;
			cx = (x - xofs) / zoom;
			cy = (y - yofs) / zoom;

			int iter = max_iter;

            /* calculate the iterations at this particular point */
			while (zx * zx + zy * zy < 4 && iter > 0) {
				double tmp = zx * zx - zy * zy + cx;
				zy = 2.0 * zx * zy + cy;
				zx = tmp;

				iter --;
			}

            /* plot the applicable pixel */
			video[x + (y * 320)] = (unsigned char) iter & 0xff;
		}
	}
}

So, you can see this code is very simple - to the point. We need to investigate all of the pixels (in this case 320x200 - or 64,000) and we calculate the iteration intersection at each point. The variables passed into the function allows the caller to animate the mandelbrot. zoom will take you further into the pattern, xofs and yofs will translate your position by this (x,y) pair. max_iter just determines how many cycles the caller wants to spend working out the iteration count. A higher number means that the plot comes out more detailed, but it slower to generate.