Abelian Sandpile
Drop grains of sand on a grid cell; whenever a cell holds four grains it topples, giving one to each neighbour, possibly triggering avalanches. Feeding grains endlessly into the centre grows an intricate four-fold fractal pattern — the abelian sandpile — whose final state famously does not depend on the order in which unstable cells topple. It is the textbook example of self-organised criticality: avalanches of every size emerge with no tuning at all.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- A cell with 4 or more grains topples, sending one grain to each of its four neighbours.
- "Abelian": the final configuration is independent of the topple order — only the grain count matters.
- Avalanche sizes follow a power law, the signature of self-organised criticality.
- Runs 100% in your browser — simulations are computed locally on your device.
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