Each site holds a grain count. If height ≥ 4, it topples: loses 4 grains, each neighbor gains 1. Grains at the boundary are lost (open boundary = sink).
The model is abelian: the final stable configuration is independent of toppling order. This makes the set of stable configurations a group under the addition operation.
The identity element of this group is a fractal-like pattern computable by: start with 3 everywhere, add the max-stable config (2 everywhere) twice, then stabilize. The result is remarkably symmetric.
Avalanche sizes obey a power law P(s) ~ s^(−τ) with τ ≈ 1.29 — self-organized criticality (SOC). The system self-tunes to the critical state without parameter tuning.
Click the canvas to add grains at that position.