Sandpile Group Identity Element

The abelian sandpile model: grains topple when a cell reaches threshold 4. The identity element of the sandpile group forms a stunning self-similar fractal.

Sandpile Controls

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Rule: If grid[i][j] ≥ 4, topple:
grid[i][j] -= 4
neighbors += 1 each

Identity: The unique stable config e such that for all stable s:
s ⊕ e = s

Computed as: identity = max_stable − (max_stable ⊕ max_stable)

The fractal structure emerges from self-organized criticality — power law avalanche sizes!