Self-Organized Criticality

A sandpile model demonstrating spontaneous tuning toward the critical state

Lattice State
Power Law Distribution
τ = — (power law slope)
subcritical critical supercritical
0
Total Grains
0
Avalanches
0
Largest Event
Avalanche
Topple at 4 grains
Max event 10k
Self-tuning active

In 1987, Bak, Tang, and Wiesenfeld demonstrated that certain dynamical systems naturally evolve toward a critical state without external tuning. Grains of sand are dropped one at a time; when a cell accumulates four grains, it topples, distributing grains to neighbors. The system self-organizes to produce avalanches following a power law—the signature of criticality.