Abelian Sandpile Model

The Abelian sandpile model exhibits self-organized criticality: sand grains are added to a grid, and when a cell accumulates 4 or more grains it topples, distributing one grain to each neighbor. The resulting patterns — fractal, recursive, and symmetric — are called the sandpile identity element. Click to add sand.

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Each topple distributes 1 grain to 4 neighbors. Boundary cells lose grains (sink). The order of toppling never matters — that's the "abelian" property.