&Cartridge; physics 14, p93

When the density of trees changes in a forest that can catch fire, self-organizing properties are observed for decades.

Michael Hersen / Danita Delimont / stock.adobe.com

Forest Fire Models (FFMs) are used to study dynamic relationships between the density of a forest, its rate of growth, and the spread of forest fires. In the 30 years since the first FFM was proposed, researchers have also used the models to study more generally how complex systems create “self-organized criticality” – a property of systems, including neural networks and solar flares. Diego Rybski from the Potsdam Institute for Climate Impact Research in Germany and colleagues have now discovered that an FFM from the 1990s shows self-organizing behavior that has been overlooked for decades [1] . The prediction suggests that new behaviors might be found in other well-studied models of complex systems.

An FFM is a cellular automaton-based model in which a forest is approximated by a 2D array of cells, with filled cells indicating areas that contain trees and empty cells indicating areas that are not forested. At every tick of the model’s clock, every empty cell can be forested with a probability P., and every wooded cell has a likelihood of being struck by lightning Q (Q is much smaller than P.). A lightning strike starts a fire that instantly spreads from the struck cell to any connected wooded cell.

Previous analyzes of FFMs looked for self-organized criticality in the relationship between P., Q, and the size of the resulting fire. Instead, Rybski and his colleagues examined how these variables affect the density of forested cells over time. They discovered that great values ​​of P. Forests emerge whose density fluctuates between two different values. For small values ​​of P., these different densities disappear, but quasi-periodic oscillations remain with a frequency roughly proportional to P.. The researchers say that such vibrations could occur in real ecosystems that are adapted to periodic burning.

–Marric Stephens

Marric Stephens is the corresponding editor for physics based in Bristol, UK.


  1. D. Rybski et al., “Self-organized multistability in the forest fire model”, Phys. Rev. E104, L012201 (2021).

areas of expertise

Related articles

Discrete or Continuum?  It's important for cells
A macroscopic study of quantum states
Black Hole Law Tested

Black Hole Law Tested

By comparing the size of black holes before and after a merger, researchers tested Hawking’s theorem about the areas of black holes. Continue reading “

More articles


Please enter your comment!
Please enter your name here