BTW model: avalanche statistics follow a power law P(s) ~ s^(−τ), τ ≈ 1.22
The Bak–Tang–Wiesenfeld (BTW) sandpile self-organizes to a critical state: grains pile up until a local threshold (height ≥ 4) causes toppling, which can cascade into avalanches of all scales. No parameter tuning needed — the system drives itself to criticality. Avalanche sizes follow a power law P(s) ~ s^(−1.22) with no characteristic scale.