Abelian Sandpile
Self-organized criticality and fractal avalanche patterns
0 grains
1 grain
2 grains
3 grains
toppling
Grains: 0 | Avalanche size: 0 | Total topplings: 0
The Abelian sandpile model (Bak, Tang, Wiesenfeld 1987) is the canonical example of
self-organized criticality. Sand grains are added one at a time; cells with ≥4 grains
topple, distributing grains to 4 neighbors. The steady-state boundary forms a remarkable
fractal pattern with intricate self-similar structure. Avalanche sizes follow a
power law: P(s) ~ s−τ.