Abelian Sandpile — Identity Element & Toppling Avalanches
Self-organized criticality, abelian group structure, and the fractal identity configuration
Controls
Grid size L:
40
Drop rate:
continuous
Compute Identity
Reset to maximal
Drop grain
Pause
Sandpile rule:
If h(i,j) ≥ 4: topple
h(i,j) -= 4, neighbors += 1
Identity element:
e⊕e = e (under ⊕ = stabilize(a+b))
Computed: 6·max - stabilize(6·max)
Exhibits fractal self-similarity!