Controls
State
Total chips: —
Topplings: —
Max height: —
Stable: —
Theory
Abelian Sandpile:
Toppling rule: if h(v)≥4, fire vertex v:
Identity element: unique e s.t. e⊕s = s for all stable s. Computed as:
Toppling rule: if h(v)≥4, fire vertex v:
h(v) → h(v)−4
h(u) → h(u)+1 for u~v
Sandpile group: stable configs under ⊕ form a finite abelian group.Identity element: unique e s.t. e⊕s = s for all stable s. Computed as:
e = stab(6·max − max − max)
Shows fractal/harmonic structure — self-similar, 4-fold symmetric.