particles 0 radius 0 fractal dim. — ready
Diffusion limited aggregation (Witten & Sander, 1981) grows a cluster one particle at a time. A particle is released far from the seed and wanders in a random walk until it bumps into the cluster, where it sticks. The tips of the branches catch most of the wanderers and shield the fjords between them, so the cluster grows into branching fractals like frost, mineral dendrites and electroplated copper. In two dimensions the fractal dimension comes out near 1.71. Watch the estimate above settle as a point-seeded cluster grows.
Try lowering stickiness: wanderers then slip deeper into the cluster before they stick, so the branches get thicker. Switching to 8 neighbours gives spikier growth along the diagonals. Colours show when each particle arrived, from red at the seed outward. Tick show walkers to watch hundreds of particles diffuse at once. More reading: Wikipedia.