Blender Cycles OSL: Mandelbrot Fractal

Hi. Today I'm going to show you an OSL code to get a Mandelbrot Fractal, like this:

This fractal uses the following complex numbers formula:

Z(n+1) = Z(n) ^ 2  + C

I have parameterized the exponent of the formula and the bailout value, that is, the value to stop the iterations. So the code is this:

shader mandelbrot_fractal_zn_zoom(
    float Scale = 1.0,
    float Zoom = 3.5,
    vector Vector = (vector)P,    
    float CenterX = 0.0,
    float CenterY = 0.0,
    int MaxIterations = 64,
    int Exponent = 2,
    float Bailout = 2.0,
    output float Fac = 0.0)
{
    point p = (point)Vector*Scale/(2*Zoom);
    int i = 0;
    int j = 0;
    int prevIteration = MaxIterations;
    float factor = 0.0;
    float foo = 0.0;
  
    // Starting point
    p[0] += CenterX;
    p[1] += CenterY;
 
    // Initialize 
    point pa = point(0.0);
    point pb = point(0.0);
    point pc = point(0.0);
    
    // Mandelbrot algorithm
    do
    {
        // z^j
        for(j = 1; j < Exponent; j++) {
            pc[0] = pa[0] * pb[0] - pa[1] * pb[1];
            pc[1] = pa[0] * pb[1] + pa[1] * pb[0];

            // for next product
            pb[0] = pc[0];
            pb[1] = pc[1];
        }

        // z^exponent + c
        pa = pc + p;
        pb[0] = pa[0];
        pb[1] = pa[1];
       
        i++;

        if ((prevIteration == MaxIterations) && (sqrt((pa[0]*pa[0]) + (pa[1]*pa[1])) > Bailout)) {
            prevIteration = i + 1;
        }        
    } while (i < prevIteration);
 
    // Factor to colorize
    factor = float(i);
    foo = sqrt((pa[0]*pa[0]) + (pa[1]*pa[1]));
    factor = factor - (log(log(foo))/log(Bailout));
    factor = factor / float(MaxIterations); 
  
    Fac = factor;
}

And this is the node setup to get the image before:

As it is using a exponential formula, if you change the exponent you can get another fractals (the power node and the color ramp could be slightly different):

• Exponent 3

• Exponent 4

• Exponent 6

• Exponent 7

• Exponent 8

• Exponent 9

• Exponent 11

You can see other fractal renders using this code here.


Bye