Forest fire

A simple model for forest fires as an example of a system displaying self-organized criticality. The longer a forest is allowed to grow uninterrupted, the larger the fire can grow.

Lattice side(48–320)

Growth rate p2.0e-3

Lightning rate f1.0e-5

Sweeps per second30

Tree cover 0% · 0 fires recorded · largest 0 trees.

The separation of timescales is f/p = 5.0e-3. Click the lattice to start a fire yourself.

Click anywhere on the forest to strike lightning yourself!

The setup

Each site is empty, a tree, or burning, and every sweep applies four rules at once:

a burning site becomes empty;
a tree with a burning neighbour catches fire;
any other tree is struck by lightning with probability $f$ ;
an empty site grows a tree with probability $p$ .

Criticality is not tuned, but it does need a separation of timescales: $f \ll p \ll 1$ , so that a fire finishes long before the forest regrows, and the forest regrows long before the next strike. Push $f/p$ up with the controls and the scaling washes out — fires start before the forest has recovered, and the large ones never form.

The distribution of burned cluster sizes then follows

P(s) \sim s^{-\tau}

with $\tau$ near 1.15 for this two-dimensional version, though a finite lattice run for a finite time gives a slope that wanders around it. The value under the lattice is a least-squares fit through the fire sizes recorded so far, so it settles as they accumulate.