Sandpile Grid

0 grains
1 grain
2 grains
3 grains
Toppling!

Avalanche Size Distribution

Log-log scale: Power law appears as straight line

50
Total Grains
0
Total Avalanches
0
Current Avalanche
0
Largest Avalanche
0

🏔️ The Sandpile Paradox

Drop grains of sand one at a time. Eventually the pile reaches a critical state where adding ONE grain can trigger avalanches of ANY size—from 1 toppling to millions! The system tunes itself to criticality without external adjustment.

⚡ The Rules

Each cell holds 0-3 grains. When a cell reaches 4 grains, it "topples"—sending 1 grain to each of its 4 neighbors. This can trigger cascading avalanches. Grains at the edge fall off.

zi ≥ 4 → zi -= 4, neighbors += 1

📊 Power Law Distribution

Avalanche sizes follow a power law: small avalanches are common, large ones rare, but POSSIBLE. This is the signature of criticality—no characteristic scale!

P(s) ∼ s-τ, τ ≈ 1.2

🌍 Ubiquitous in Nature

Earthquakes, forest fires, extinctions, stock crashes, neural avalanches, and even wars show this pattern! Bak, Tang & Wiesenfeld (1987) proposed SOC explains 1/f noise everywhere in nature.