Forest Fire Model

DEFINITION

burning → empty
tree → burning if any neighbour burns, else burning with probability f
empty → tree with probability p

NOTES

Three states on a lattice and two probabilities, and the result is a fire whose sizes follow a power law nobody tuned it to produce. Bak, Chen and Tang wrote the model in 1990 while arguing that turbulence might be self-organised criticality; their version had no lightning, and it burns out. Drossel and Schwabl added the spark two years later — an occupied cell ignites spontaneously with probability f — and that one term is what makes the system drive itself back to the critical point forever after. The control is the ratio p/f, the number of trees grown per lightning strike: raise it and fires grow rarer and larger, and the distribution of their sizes stretches into a straight line on a log-log plot. Nothing here is tuned to criticality. The lattice finds it on its own, which is the entire claim of the paper.

PROVENANCE

Origin

P. Bak, K. Chen & C. Tang, “A forest-fire model and some thoughts on turbulence”, Physics Letters A 147(5–6), 1990, 297–300

The lightning

B. Drossel & F. Schwabl, “Self-organized critical forest-fire model”, Physical Review Letters 69, 1992, 1629–1632. The 1990 model has no spontaneous ignition and does not reach a critical state; the f term is theirs, and so is the self-organised criticality the model is now named for. Credited here in the order the work happened, the same way gibbs and levyc are

Standing

Public domain — three transition rules

Constants

The published control is the ratio p/f — trees grown per lightning strike. Large ratios give rare, lattice-spanning fires

Source

doi:10.1016/0375-9601(90)90451-S