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For Students · Abelian Sandpile

Abelian Sandpile for a fish school

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a fish school live below — adjust the inputs and watch it respond, right in your browser.

Abelian SandpileLive

self-organized criticality

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Grains drop on the center cell. When a cell reaches 4 grains it topples, sending one to each neighbor — which can trigger chain-reaction avalanches. The pile self-organizes into an intricate fractal at the critical slope.

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Data Inspector

Grains added0

Last avalanche0

Topple at4 grains

Governing equation

z_{ij} \geq 4 : z_{ij} \to z_{ij} - 4, z_{nbr} \to z_{nbr} + 1; grains = 0

Reading this result: The pile is still filling toward its critical slope; once cells reach 4 grains, chain-reaction topples begin.

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Frequently asked questions

Is this good for students?: Yes — this version of "Abelian Sandpile for a fish school" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.