Bak–Tang–Wiesenfeld (1987) · Self-organized criticality · Click to add grains
Grains: 0 | Avalanches: 0 | Last size: 0
The abelian sandpile: each site topples when it reaches 4 grains, distributing one grain to each neighbor. Toppling is abelian — order doesn't matter, only the set of topplings. The system self-organizes to criticality: avalanche sizes follow a power law P(s) ~ s^(−5/4). The fractal boundary (visible in color) has Hausdorff dimension ~2.