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Author Topic: Fractals using periodic boundaries  (Read 4386 times)
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msltoe
Iterator
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Posts: 187


« on: December 21, 2010, 02:43:47 AM »

I've been looking at simple 3-d kaleidoscopic-like fractals. What about using periodic lattices
such as the cubic lattice?

The main issue is what is a good escape condition?

Here's a simple one that looks like a pollen particle:

 r1=2; norm = 0;
 while ((norm<50)&&(iter<imax)) {

   x = x - (int)(x);
   y = y - (int)(y);
   z = z - (int)(z);
  
   r = 1/(x*x+y*y+z*z); // Sphere inversion
  
   x=r1*x*r+a;y=r1*y*r+b;z=r1*z*r+c;
   norm = x*x+y*y+z*z;
   iter++;  
 }

Another version, sierpinski-like, r1=1.5, norm<40

« Last Edit: December 21, 2010, 02:58:56 AM by msltoe » Logged
msltoe
Iterator
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Posts: 187


« Reply #1 on: December 21, 2010, 04:46:08 AM »

Fractal tennis ball with cutaway:
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fractower
Iterator
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Posts: 173


« Reply #2 on: December 21, 2010, 07:09:19 AM »

The last on looks like a Menger sponge that has been left in the sink too long.
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