Forest Fire Model

A forest-fire model is any of a number of dynamical systems displaying self-organized criticality. The model of Drossel and Schwabl (1992) is defined by four rules which are executed simultaneously:

1. A burning cell turns into an empty cell
2. A tree will burn if at least one neighbor is burning
3. A tree ignites with probability f even if no neighbor is burning
4. An empty space fills with a tree with probability p

The controlling parameter of the model is p/f which gives the average number of trees planted between two lightning strikes (see Schenk et al. (1996) and Grassberger (1993)). In order to exhibit a fractal frequency-size distribution of clusters a double separation of time scales is necessary

$f\ll p\ll T_{\mathrm {smax} }\,$

where T_smax is the burn time of the largest cluster. The scaling behavior is not simple, however ( Grassberger 1993,2002 and Pruessner et al. 2002,2004).