The Forest Fire Model

Fire! is a customization of the CA Framework that models the optimal number of trees in a forest to maximize the biomass while minimizing the spread of forest fires. Here's a screen shot:

Imagine each patch is a patch of ground in a forest. The state of a patch has three possible values: "has-tree" (pcolor = green), "burned" (pcolor = black), and "empty" (pcolor = brown). A patch also has a fertility attribute, which is a number between 0 and 1. Initially the state of a patch is empty and its fertility is set to a constant, init-fertility, which the user can adjust with a slider.

Every spring (cycles = an even number), each patch grows a tree with probability = fertility. Each summer (cycles = an odd number) lightening strikes a patch with probability = burn-probability, which the user can control with a slider.

If a patch has a tree and is struck by lightening, then its state changes to "burned". The fire spreads: all neighboring patches with trees burn. Their treed neighbors burn, and so on until the fire reaches a fire break of some sort.

A plotter plots the percentage of the patches that are in the have-tree state.

A histogram shows the frequency of fires according to their sizes: at least 50 trees burned, at least 100, at least 150, etc. This histogram should follow a power law.

Will fire breaks naturally grow? Will the percentage of patches in the have-tree state stabalize under certain settings for fertility? Will the forest naturally find the optimal tree covering?

We can add adaptation to our patches as follows: when a patch is updated it first counts the number of burned neighbors. If this number is above some critical number, for example, if more than four neighbors are in the burned state, then the patch decreases its fertility by some adjustable fertility-adaptation-factor. Otherwise the patch resets its fertility to the initial value. Be careful. The fertility of a patch should always be a number between 0 and 1. After updating its fertility, the patch either grows a tree, burns, or does nothing as before.

What setting for the fertility-adaptation-factor produces the largest number of trees?