Two methods to create the Sierpinski triangle: the Chaos Game (randomly jumping half-way to a chosen vertex) and recursive subdivision (removing the central triangle at each level). Hausdorff dimension ≈ 1.585.
The Chaos Game plots thousands of random points. Each point jumps halfway to a randomly chosen vertex. Miraculously, this random process produces a perfect fractal — order from randomness.
Switch between Chaos Game and recursive modes. Adjust iteration count and colour scheme. Pan and zoom to explore self-similarity.
Wacław Sierpiński described this triangle in 1915. Its Hausdorff dimension of log(3)/log(2) ≈ 1.585 means it's "more than a line but less than a plane" — a fraction of a dimension.