🏔️ Sand Pile Criticality
Drop grains of sand one by one onto a pile. Most land quietly — but occasionally a catastrophic avalanche cascades across the entire grid. The system organises itself to a critical state where avalanche sizes follow a power law: there is no typical size, only scale-free disorder at the edge of chaos.
🌊 Self-Organised Criticality (SOC)
Bak, Tang and Wiesenfeld (1987) showed that many driven dissipative systems naturally evolve toward a critical state — without any fine-tuning of parameters. The sand pile is the archetype: add grains slowly, and the pile steepens until the average slope sits just at the stability threshold.
Toppling rule (BTW model):
Avalanche sizes n follow P(n) ∝ n−τ with τ ≈ 1 (log-log plot is a straight line). This power law means huge events are rare but inevitable — just like earthquakes and stock crashes.