C(n,k) mod p = 0 → void · mod p ≠ 0 → filled · fractal dimension = log(3)/log(2) ≈ 1.585
Mode: Pascal mod 2
Rows: 0
Filled: 0%
dim = 1.585
Coloring Pascal's triangle entries by C(n,k) mod p reveals exact self-similar fractals. For p=2: the Sierpiński gasket (Kummer 1852: C(n,k) is odd iff k has no carrying in binary addition with n−k).
The IFS attractor uses three affine maps each scaling by 1/2. The chaos game converges to the same fractal.