Forest Fire
Each cell is empty, a tree, or burning. Empty cells grow trees with probability p; trees ignite from burning neighbours, or spontaneously by lightning with probability f. The Drossel–Schwabl model self-organizes to a critical state where fire sizes follow a power law.
How it works
Press Start to run the model. Teal cells are trees, black cells are actively burning, and light cells are empty ground. Each timestep every burning cell turns to ash, every tree next to a fire catches, empty ground regrows a tree with probability p, and any tree may be struck by lightning with probability f.
When lightning strikes, the connected cluster of trees around it is exactly what the fire will consume, so that cluster's size is recorded as one outbreak. The graph plots the log-binned frequency N(s) of outbreaks of size s on log-log axes. As the forest self-organizes it approaches a critical state and the distribution straightens into a power law — small fires are common, system-spanning ones are rare but never absent. The separation of timescales matters: the smaller f/p is, the cleaner the scaling.