Abelian Sandpile Model

Self-organized criticality — click to add grains, watch fractal avalanches

0 grains
1 grain
2 grains
3 grains
toppling!
Grid: 64×64
Total grains: 0
Topple events: 0
Avalanche size: 0
Max height: 0

Self-organized criticality:
avalanche sizes follow
power-law distribution
P(s) ~ s, τ ≈ 1.2

Click anywhere on the grid to add grains. When a cell reaches height ≥ 4, it topples — sending one grain to each of its 4 neighbors. Grains falling off the boundary are lost. The resulting patterns are self-similar fractals.