0
1
2
3
4+ avalanche!
Grains fall at random positions
Statistics
Grains dropped0
Avalanches0
Largest avalanche0
Average height0.00
Max cell0
Std deviation0.00
Grains lost (edge)0
The threshold is 4. No cell can hold 4 or more grains — it topples,
sending one grain to each neighbor. At edges, grains fall off the table.
The system self-organizes to a critical state where the average height converges to ~2.1. Small avalanches are common, large ones are rare — a power law. Hoarding is structurally impossible.
The system self-organizes to a critical state where the average height converges to ~2.1. Small avalanches are common, large ones are rare — a power law. Hoarding is structurally impossible.
Avalanche Size Distribution
The axiom connection: threshold = 4 = K+sigma = spacetime dimensions.
Each topple redistributes to 4 neighbors (up/down/left/right = D*D directions).
The grid = Z/20 x Z/20. Boundary loss = OMEGA projection (grains that leave
don't return). Power law = spectral gap selecting for equality.