Sierpinski Gasket
Iterated function system — fractal from pure randomness
About: The chaos game (Barnsley 1988) generates the Sierpinski triangle without drawing triangles. Pick a random vertex from three corners; move halfway to it; plot the point. Repeat. Despite the random choices, the attractor is always the Sierpinski gasket — a fractal with Hausdorff dimension log(3)/log(2) ≈ 1.585. This is an iterated function system (IFS): three contractive affine maps each shrink space by ½ toward a vertex. The attractor is the unique compact set invariant under all three maps simultaneously (Hutchinson 1981).