Abelian Sandpile — Identity Element

The abelian sandpile group on a finite grid has a remarkable identity configuration with fractal self-similar structure. Adding sand and toppling (fire when ≥ 4 grains) forms a commutative group — the identity element is the unique stable configuration satisfying e + e = e (up to stabilization).

Grid size
101×101
Total topplings
0
Max grains
0
Sandpile group: (Δ, +̃) where a +̃ b = stabilize(a + b); identity e satisfies e +̃ e = e