Self-organized criticality — avalanche dynamics on a grid
0 grains
1 grain
2 grains
3 grains
4+ (toppling)
Avalanche size: 0
Total grains: 0
About: The Abelian Sandpile Model (Bak, Tang, Wiesenfeld 1987) is the canonical example of self-organized criticality. Each cell holds 0–3 grains; when a cell reaches 4 it "topples," distributing one grain to each neighbor. The system naturally evolves to a critical state where avalanches follow a power-law size distribution — no tuning required. The model is abelian: the final state is independent of the order topplings occur. Click anywhere on the grid to add grains; watch fractal avalanche patterns emerge.