Bak–Tang–Wiesenfeld Sandpile

Self-organized criticality: grains added randomly, avalanches follow a power law P(s) ∝ s⁻¹·⁵.

40
5
Grains added: 0 | Avalanches: 0 | Max avalanche: 0

The BTW sandpile model: each cell has height h. When h≥4, it topples: loses 4 grains, each neighbor gains 1. Grains at boundaries are lost. The system self-organizes to criticality without tuning — avalanche sizes follow P(s)∝s⁻τ with τ≈1.5 in 2D.