Self-Organized Criticality — Rice Pile (Oslo Model)

Power-law avalanches emerge without tuning — the system drives itself to criticality

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Statistics

Total grains dropped0
Total avalanches0
Last avalanche size0
Max avalanche0
Mean avalanche0
Power-law exponent τ—

The Oslo Model & Self-Organized Criticality

Bak, Tang & Wiesenfeld (1987) proposed that many complex systems spontaneously organize to a critical state — without any tuning of parameters. The Oslo rice pile model (Frette et al. 1996) is a canonical example: grains added to the top create slopes; when the local slope z exceeds a random threshold z_c (which is reset after toppling), an avalanche propagates. Grains fall off the right edge.

At the critical state, avalanche sizes follow a power law: P(s) ~ s-τ with τ ≈ 1.55 in 1D. The histogram (log-log scale) accumulates the size distribution. Unlike equilibrium critical points requiring parameter fine-tuning, the pile drives itself to criticality via the slow driving + fast relaxation separation of timescales.