Self-Organised Criticality — Forest Fire Model

Growth

Growth rate3.0%

Chance an empty cell grows a tree each step.

Ignition

Lightning rate0.05%

Chance a standing tree ignites on its own each step. Kept far below the growth rate, this is what lets the forest rebuild between fires rather than never establishing at all.

Speed 10

Forest Grid

Step 0

Empty

Tree

Burning

Forest Cover

Cells Alight

Last Fire Size

Biggest Fire So Far

Forest Cover Over Time

Watch for the sawtooth: cover climbs steadily as trees grow, then drops sharply when a fire runs through. That shape, not a smooth average, is the signature of the system finding its own critical point.

Fire Sizes (each event)

Most fires stay tiny. Occasionally one clears a large fraction of the grid. Nothing about how that fire started marks it out in advance, it is the state of the forest at that moment, not the size of the spark, that decides.

How to read this model

Each cell is empty, holding a tree, or on fire. Two rules run every step, an empty cell may grow a tree, and a tree may ignite, either because a neighbouring cell is burning or, far more rarely, on its own. Run it and watch the forest cover chart rather than the grid; the pattern is in the rhythm, not any single frame.

This is the Drossel-Schwabl forest-fire model, a standard illustration of self-organised criticality: a system that, left to run under simple local rules with no external tuning, drives itself toward the edge of its own stability. Below that edge, fires stay small and the forest looks safe. At the edge, fire size stops being predictable from the rules and starts depending on the accumulated structure of the forest itself.

Why it matters beyond trees: nothing in this model decides in advance how big the next fire will be. The forest becomes more or less fire-prone purely as a function of its own growth, with no policy change, no bad actor, and no external shock required. A system can drift toward a large failure entirely through the normal operation of the rule that also makes it flourish.

This is a simplified, generic illustration of the mechanism, not a model of any specific forest, organisation, or event. Its purpose is to show how local growth and local risk, run long enough with no outside intervention, can produce large-scale instability that was never separately decided by anyone.

Model: Drossel, B. & Schwabl, F. (1992), "Self-organized critical forest-fire model", Physical Review Letters, 69(11), 1629–1632. Implementation and design original to this page.