The sandpile model and self-organized criticality — power laws from simple rules
Bak, Tang & Wiesenfeld (1987) discovered that a simple sandpile model self-organizes to a critical state without tuning parameters. Each cell has a height. When it exceeds threshold z_c, it topples, redistributing sand to neighbors — potentially triggering a chain reaction. Avalanche sizes follow a power law: P(s) ~ s-τ with τ ≈ 1.2 in 2D. The histogram below shows this distribution building up.