Anisotropic Sandpile & Ricepile

SOC Universality Classes — Avalanche Statistics

Isotropic (Bak-Tang-Wiesenfeld):
topple if z(i,j) ≥ z_c
→ τ_s ≈ 1.22 (2D)

Anisotropic (Manna / ricepile):
stochastic redistribution
→ τ_s ≈ 1.55 (2D)

Threshold z_c 4

Anisotropy p (0=BTW, 1=Manna) 0.0

Drop rate 5/frame

BTW sandpile (isotropic): deterministic toppling rules give exponent τ≈1.22. Manna/ricepile (anisotropic): stochastic redistribution gives a different universality class τ≈1.55. Both are self-organized critical but belong to different universality classes — proving SOC is not a single phenomenon.