Self-similar fractal — chaos game, subdivision, and Pascal's triangle mod 2
6
1.5
200
1000
Chaos game: randomly pick a vertex, move halfway there — after warm-up, only Sierpinski points are visited. Subdivision: remove center triangle at each step (IFS with 3 contractions by 1/2). Pascal mod 2: colour Pascal's triangle entries by parity — row n shows binary carry pattern. Hausdorff dimension = log(3)/log(2) ≈ 1.585 — between a line and a plane.