Toppling rules form a group — fractal identity element
Abelian Sandpile Model: Each cell fires (topples) when height ≥ 4, sending 1 grain to each neighbor. Boundary sinks excess.
The set of stable recurrent configurations forms a finite abelian group under "addition + relaxation."
The identity element has a remarkable self-similar fractal structure — it looks the same regardless of how you compute it.
Adding any recurrent config to the identity returns that config. Click "Compute Identity" to build it iteratively.