Play a game of pure randomness — and watch fractal order appear out of chance. Pick a random vertex of a triangle, move halfway toward it, repeat. After enough steps, the Sierpiński triangle magically emerges.
Despite each step being random, the attractor of the iterated function system is always the same fractal — the Sierpiński triangle. The forbidden gap regions are never reached regardless of starting position.
Press play and watch dots accumulate. Adjust speed to see thousands of dots per second. Change to 4, 5, or 6 vertices with different fraction rules to discover unexpected fractal structures.
The Sierpiński triangle has a Hausdorff fractal dimension of log(3)/log(2) ≈ 1.585 — more than a 1D line but less than a 2D plane. It contains infinitely many points yet has zero area.