by Dirk Brockmann

This explorable illustrates, as a representative of a broad range of dynamic phenomena, a simple model for the spatial spread of forest fires and the dynamic patterns they generate. In the model two antagonistic processes interplay, the reproductive growth of vegetation that continously covers the landscape with trees susceptible to fires and spontaneously seeded (lightning strikes) forest fires that spread across areas of dense vegetation.

For a broad range of parameters the model generates a dynamic equilibrium in which the size of single fires has no characteristic scale. One observes frequent, small fires as well as rare, large ones.

This model can also be used to describe the spread of epidemics and similar phenomena. The explorables Critical HexSIRSize and Barista's Secret are related to this one.

Press play and keep on reading.

This is how it works

The model is very simple. The foundation of the model is a two-dimensional lattice. Each lattice site can be in one of three states. 1. empty (black): no vegetation exists and a fire cannot invade the site 2. tree (green, obviously): the site is susceptible to a fire and 3. fire (red-ish): the site is burning and can ignite a neighboring tree site.


First, trees can reproduce. A tree site can turn a neighboring empty site into tree site. The rate at which this happens can be controlled with the vegetation growth rate slider. Without fires, the entire landscape would eventually turn green. But this doesn't happen because...

... with a small rate lightning strikes randomly and ignites a local fire if it hits a tree. The rate at which lightning strikes can be adjusted with the corresponding slider.

A burning site can ignite neighboring tree sites. The likelihood of this is controlled with the ignition probability slider.

Long distance dispersal

In addition to the three parameters discussed above, the model has an additional feature: Long distance dispersal. With long distance dispersal trees can generate offspring at sites far away from their location. The effect generates more dilute areas of vegetation through which a fire cannot spread as easily. By default long distance dispersal is turned off.

Fractal Structures

Although this will require a bit of patience, you can observe the most interesting patterns when the vegetation growth rate, the lightning rate, and long-distance dispersal are low. The patterns of vegetation patches should become fractal-like and scale-free.


  • P. Bak, K. Chen, and C. Tang, Phys. Lett. A 147, 297 (1990).
  • B. Drossel and F. Schwabl, Phys. Rev. Lett. 69, 1629 (1992).

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