Few days ago I found on Internet some pictures of Sierpinski Triangle and Sierpinski Temple (David Makin's pictures). It is very beautiful mathematical form. Unfortunately I didn't find any detailed algorithm. I decided to found proper algorithm by myself. I made lots of trials and before I understood how this kind of iterative algorithms works I get some interesting pictures. One of these is below.
http://www.fractalforums.com/gallery/?sa=view;id=1088Finally I found proper algorithm and rendered this "Sierpinski's Planet"
http://www.fractalforums.com/gallery/1/640_22_11_09_9_01_17.jpgBellow is my iteration algorithm in C
double k=2.0;
double a_off = 0;
double b_off = 0;
for (L = 0; L < N; L++)
{
xx = fmod(a * k+a_off, 2.0);
yy = fmod(b * k+b_off, 2.0);
zz = fmod(c * k, 2.0);
if ((zz>1.0)&&(xx<0.5 || xx>1.5 || yy<0.5 || yy>1.5))
{
result = 0;
break;
}
k *= 2.0;
result = 1;
if(zz>1.0)
{
a_off = 1.0;
b_off = 1.0;
}
else
{
a_off = 0;
b_off = 0;
}
}
February 02, 2010, 12:02:18 AM
very simple sierpinski triangle in conways game of life
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