[duncan_bayne]

Reminds me of Sierpinski triangles:

http://en.wikipedia.org/wiki/Sierpinski_triangle

I'm sure someone with a greater intuition for mathematics than I have will be able to explain why.

[daxelrod]

My first thought is that it has something to do with the fact that you get a Sierpenski Triangle from a Pascal's triangle when you assign one color to even numbers and another to odd: http://en.wikipedia.org/wiki/Pascal%27s_triangle#Overall_pat...