This probabilistic cellular automata follows rules motivated by forest fire and growth. The rules are as follows, at each step:

1. A burning tree (white cell) becomes an empty site (brown cell).
2. A tree (green cell) becomes a burning tree (white cell) if at least one of its nearest neighbors is burning.
3. At an empty site (brown cell), a tree grows with probability p.
4. A tree without a burning nearest neighbor becomes a burning tree with probability f (e.g. lightening strike).

At the start of this model, you will see trees growing uncontrollably. After a while, lightening strikes will start fires. The fires will spread, destroying trees in big swaths. Behind the fires, new trees will grow up again. If you have pGrowth and pBurn set at the right levels, you should see clusters of trees develop and burn. Otherwise, you just get random distributions of empty, tree and burning cells. The default values give clustering behavior.

You can adjust the probabilities of growth and spontaneous combustion in the pGrowth and pBurn fields. Both probabilities should be given as values between 0 and 1 inclusively. For example, to have a model where there is a 50% probability of a tree growing at any given time step, enter 0.5 for pGrowth. Typically the probability of a lightening strike is very low, here the default is 0.00006 (0.006%). While the probability of growth is larger, here the default is 0.05 (5%). The current values are displayed.

The Start and Stop buttons will start and stop the iterations. The box in the upper left corner shows the number of iterations. It typically takes 50+ iterations to get the stable clustering behavior.

It should be noted that the rules here are inspired by forest fire dynamics, but clearly aren't a realistic representation of how real forests behave. Real fire facts can be found here and here.

* taken from Cellular Automata Modeling of Physical Systems, Chopard B. and Droz M., Cambridge University Press, 1998.