Difference between revisions of "Forest Fire Model"
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# An empty space fills with a tree with probability ''p'' | # 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 | + | The controlling parameter of the model is ''p''/''f'' which gives the average number of trees planted between two lightning strikes . In order to exhibit a fractal frequency-size distribution of clusters a double separation of time scales is necessary |
:<math>f \ll p \ll T_\mathrm{smax}\,</math> | :<math>f \ll p \ll T_\mathrm{smax}\,</math> | ||
| − | where ''T''<sub>smax</sub> is the burn time of the largest cluster | + | where ''T''<sub>smax</sub> is the burn time of the largest cluster. |
Latest revision as of 22:13, 5 November 2012
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:
- A burning cell turns into an empty cell
- A tree will burn if at least one neighbor is burning
- A tree ignites with probability f even if no neighbor is burning
- 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 . In order to exhibit a fractal frequency-size distribution of clusters a double separation of time scales is necessary
where Tsmax is the burn time of the largest cluster.
