Fractals using periodic boundaries

[msltoe]

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

[msltoe]

Fractal tennis ball with cutaway:

[fractower]

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