IFS attractor via the chaos game — Sierpiński and beyond
0.5
1000
The chaos game: start at any point, repeatedly jump r of the way toward a randomly chosen vertex. Despite the randomness, the orbit converges to the IFS fractal attractor with Hausdorff dimension d_H = log(N)/log(1/r). Barnsley's fern uses an affine IFS with 4 transformations — probability-weighted, not vertex-based.