Self-Organized Criticality — Rice Pile

The Oslo rice pile model (Christensen et al 1996) is a canonical model of self-organized criticality. Grains are added at the left; a site topples when its slope exceeds a random threshold (1 or 2), passing grains to the right. Grains leaving the right edge are "lost." The system self-organizes to a critical state — avalanche sizes follow a power law P(s) ∝ s⁻ᵞ with γ ≈ 1.55, generating 1/f noise. No fine-tuning of parameters is needed — criticality is an attractor.