Self-Organized Criticality

Bak, Tang & Wiesenfeld (1987) -- Beinhocker Ch 8, p.178

Imagine slowly piling sand on a table. At first, nothing much happens. But as the pile grows steeper, a single grain can trigger avalanches of all sizes -- from tiny slips to catastrophic collapses that reshape the entire pile.


This is self-organized criticality: the system drives itself to a critical state where events of all magnitudes occur, following a power law. No tuning required -- criticality emerges spontaneously.

Beinhocker's Insight

The same mathematics governs earthquakes, stock market crashes, forest fires, and species extinctions. These systems sit at the "edge of chaos" -- poised between order and disorder. Small causes can have enormous effects, and the distribution of event sizes follows a power law, not a bell curve. This is why "normal" risk models systematically underestimate the probability of extreme events.

Parameters

10/tick

Live Statistics

0
Grains Dropped
0
On Grid
0
Lost (edges)
0.00
Mean Height
0
Avalanches
0
Max Avalanche
--
Power-Law Exp
0
Max Height

Experiments

Avalanche Size Distribution (Log-Log)

Avalanche Time Series

Cumulative Grains on Grid

Height Distribution

What You're Seeing

The grid shows sand grain heights as a heatmap. Light cells are nearly empty; warm-toned cells are near the critical threshold.

Watch for cascading avalanches -- a single grain can trigger a chain reaction across the entire grid.

Drop grains to begin building toward criticality...

The Power Law

If the system is truly at criticality, the avalanche size distribution on the log-log plot should form a straight line. This means there is no "typical" avalanche size -- events of all scales occur.

The slope of this line is the power-law exponent. For the 2D BTW model, theory predicts values around 1.0-1.2.

Earthquakes & Markets

Beinhocker (p.178): "The same statistical signature -- power-law distributions -- appears in earthquake magnitudes, stock market returns, city sizes, and species extinctions."

The sandpile is the simplest model that produces this behavior. It demonstrates that extreme events are not outliers -- they are an inherent property of the system's dynamics.

Recent Avalanches

Waiting for avalanches...
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