PercolationFill each square of a grid at random with probability p. Below a sharp threshold — p_c ≈ 0.5927 for this lattice — the filled squares form only small isolated islands; a hair above it, one giant cluster suddenly spans the whole grid and liquid could seep straight through. This abrupt change is a genuine phase transition, and right at p_c the clusters are fractal on every scale. It is the simplest model of coffee brewing, forest fires, porous rock and epidemic spread. The journey: every filled cell starts with its own ID, then repeatedly copies the smallest ID among its filled neighbours; cells sharing an ID are one cluster, and each gets its own colour.