Diffusion-Limited Aggregation
Random walks that get stuck — and grow corals
Plant a single seed pixel. Release particles one at a time, each performing a random walk; the moment a wandering particle touches the cluster, it freezes there. Repeat ten thousand times and a branching, dendritic structure grows out from the seed — the same fractal shape that copper takes when electroplated, that lichen takes on a wall, that lightning leaves on bare skin. Witten and Sander showed in 1981 that the result has fractal dimension ≈ 1.71 in two dimensions, no matter what you seed it with.
