Abelian Sandpile Model
Recurrent States, Burning Numbers & Self-Organized Criticality
Controls
Grid size:
60
Add grains at click
+100 center
+1000 center
Actions
Topple All
Identity
Reset
Statistics
Total grains
0
Topplings
0
Avalanche size
0
Lost (boundary)
0
Mode
normal
Theory
Toppling rule: if z(v) ≥ 4,
z(v) → z(v) − 4
z(neighbor) → z(neighbor) + 1
Abelian property: order of topplings doesn't matter — same stable state.
Identity element e: e ⊕ e = e
(unique recurrent state s.t. adding e gives same stable config)
Color Legend
■
0 grains (black)
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1 grain (dark green)
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2 grains (amber)
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3 grains (orange-red)
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≥4 unstable (magenta)