Monday, August 25, 2008

Using povray to select interesting portions of Mandelbrot fractal space

I was looking for interesting regions of the Mandelbrot fractal set. I developed an algorithm in povray to visit random points, and then determine if they were interesting or not. Basically, I was looking for a color difference in the highest magnification-- such that the difference of the lengths of the color vector were at least a certain distance. In the code below, I had previously defined a pigment "thefracpig".

#declare ready=0;

#declare lokey= <-0.540,-0.5435,0> +.25*<0.5-rand(ppp),0.5-rand(ppp),0>;

#declare pigoo=eval_pigment(thefracpig,lokey);

#declare pigoo2=eval_pigment(thefracpig,lokey+1e-11*<1,1,0>);

#declare yow=vlength(

#declare yow2=vlength(

#if (abs(yow-yow2)>0.3)

#declare ready=ready+10000;


#declare ready=ready+1;


What was interesting here is that I learned, if my limited sampling has any value, something about the geography of the Mandelbrot fractal space. I was hoping I'd find all kinds of little Mandelbrot nurseries-- the kinds of places where the characteristic "overlapping spheres" were being birthed. This is the kinds of places that in my experience makes the kind of art that folks like to see posters made out of. Instead I found lots of places where the set is changing extremely rapidly. In these places of rapid change, it may be impossible to apply a color pattern to it that will have any aesthetic value. The first image below is an example of what I'm talking about.

Now, on to develop an algorithm where I can find "Mandelbrot nurseries"!

No comments: