Title: Fractals using periodic boundaries Post by: msltoe 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++; } (http://nocache-nocookies.digitalgott.com/gallery/4/803_21_12_10_2_36_45.jpeg) Another version, sierpinski-like, r1=1.5, norm<40 (http://nocache-nocookies.digitalgott.com/gallery/4/803_21_12_10_2_56_33.jpeg) Title: Re: Fractals using periodic boundaries Post by: msltoe on December 21, 2010, 04:46:08 AM Fractal tennis ball with cutaway:
(http://nocache-nocookies.digitalgott.com/gallery/4/803_21_12_10_4_43_06.jpeg) Title: Re: Fractals using periodic boundaries Post by: fractower 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. |