BTW Sandpile — Avalanche Size Distribution

Self-organized criticality: P(s) ~ s^{−τ}, τ ≈ 1.2
The Bak-Tang-Wiesenfeld sandpile is the paradigm of self-organized criticality (SOC). Grains are added randomly; when a site has ≥4 grains it topples, distributing to neighbors. No parameter tuning is needed — the system self-organizes to a critical state where avalanche sizes follow P(s) ~ s^{-τ} with τ ≈ 1.2 (2D).