Sandpile

Self-organized criticality. The sandpile model (Bak, Tang, Wiesenfeld, 1987) demonstrates how simple local rules produce complex global behavior. Each cell holds grains of sand. When a cell accumulates four or more grains, it topples: it loses four grains and each orthogonal neighbor gains one. Grains that fall off the edge are lost.

A single grain can trigger nothing — or a cascade spanning the entire grid. The system drives itself to a critical state where avalanche sizes follow a power law: small avalanches are common, large ones rare, but no characteristic scale separates them. No tuning is required. The criticality is self-organized.