Abelian Sandpile

Self-organized criticality, toppling waves & the abelian group

Controls

Grains added: 0
Topplings: 0
Active cells: 0
Avalanche size: 0
z(x,y) ≥ 4 → topple
Δz = -4 + Σneighbors
Each cell topples when it has ≥4 grains, distributing one grain to each neighbor. The group of legal configurations forms an abelian group — adding configurations commutes!

Power law avalanche sizes show SOC: the system self-organizes to the critical point.