The Drossel-Schwabl forest-fire model

2D `Forest-fire' model: Each site on the 2D square grid is either vacant, or occupied by a `tree'. Each time step, a tree is added at a site that is chosen at random with equal probabilities. Also, each step, an `ignition' occurs with probability f, where f is a small number. When an ignition occurs, a randomly chosen site catches fire, and the entire cluster of trees connected to the ignited site burns down, and becomes vacant.

A picture of the forest-fire model with f = 0.001 on a 500 x 500 grid.