Okay it turns out my above function is hopelessly inefficient (it's a miracle I coaxed a giant iteration 7 image out of it). The worst case time complexity is around O( n(9^n) ). Compare that to the one I created below which is O(n). Yep, just a tiny bit faster (!).
The great thing is now, any amount of iterations (even thousands) are trivial to do, and very fast, and eat up next to no memory. I'm in the middle of some giant 3D brot images, but I can't resist a couple more menger sponge renders:
bool MengerSponge(double x, double y, double z) {
int iterations=7;
if(x<0.0 || x>1 || y<0 || y>1 || z<0 || z>1 ) { return 0; } // Not part of menger sponge
double p=3.0;
for(int m=1; m<iterations; m++) {
double xa = floatmod(x*p, 3);
double ya = floatmod(y*p, 3);
double za = floatmod(z*p, 3);
if(
(xa > 1.0 && xa < 2.0 && ya > 1.0 && ya < 2.0) ||
(ya > 1.0 && ya < 2.0 && za > 1.0 && za < 2.0) ||
(xa > 1.0 && xa < 2.0 && za > 1.0 && za < 2.0)
) {return 0;} // Not part of menger sponge
p*=3;
}
return 1; // Is part of menger sponge
}
Full sizes are available
here and
here (8000x5000 pixels!). The first one is 9 iterations. No more are needed because the resolution would need to be even larger to contain the tiny holes.
April 02, 2007, 03:16:32 AM
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