SELF ORGANIZATION IN A FOREST-FIRE MODEL

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 1022-1029 ◽  
Author(s):  
B. DROSSEL ◽  
F. SCHWABL
Keyword(s):  
Forest Fire ◽  
Critical Line ◽  
Continuous Phase ◽  
Excitable Media ◽  
Fire Model ◽  
Fire Propagation ◽  
Self Organized ◽  
Forest Fire Model ◽  
New Type ◽  
Fire Spreading

We generalize the forest-fire model of P. Bak et al., which contains a tree nearest growth probability p and fire spreading to the neighbors, by including a lightning probability f and an immunity g which is the probability that a tree catches no fire although one of its neighbors is burning. The model becomes self-organized critical in the limit f/p→0, provided the time scales of tree growth and burning down of forest clusters are separated. The size distribution of forest clusters obeys a power law. We calculate the critical exponents in one dimension. A continuous phase transition is observed in the general forest-fire model when g reaches its critical value. We determine the critical line gC(p) and show that the critical fire propagation represents a new type of percolation. Finally, we point out similarities between the forest-fire model and excitable media, which comprise such different systems as chemical reactions, spreading of diseases and populations, and propagation of electrical activity in neurons.

Forest Fires

2017 ◽  
Author(s):  
Paul Charbonneau
Keyword(s):  
Forest Fire ◽  
Forest Fires ◽  
Model Simulation ◽  
Percolation Cluster ◽  
Natural Process ◽  
Wildfire Management ◽  
Fire Model ◽  
Self Organized ◽  
Forest Fire Model ◽  
Self Organized Criticality

This chapter explores how a “natural” process generates dynamically something that is conceptually similar to a percolation cluster by using the case of forest fires. It first provides an overview of the forest-fire model, which is essentially a probabilistic cellular automata, before discussing its numerical implementation using the Python code. It then describes a representative simulation showing the triggering, growth, and decay of a large fire in a representative forest-fire model simulation on a small 100 x 100 lattice. It also considers the behavior of the forest-fire model as well as its self-organized criticality and concludes with an analysis of the advantages and limitations of wildfire management. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.

scholarly journals Universality in the One-Dimensional Self-Organized Critical Forest-Fire Model

1994 ◽  
Vol 49 (9) ◽  
pp. 856-860
Author(s):  
Barbara Drossel ◽  
Siegfried Clar ◽  
Franz Schwabl
Keyword(s):  
Size Distribution ◽  
Forest Fire ◽  
Nearest Neighbor ◽  
The Self ◽  
One Dimension ◽  
Fire Model ◽  
One Dimensional ◽  
Self Organized ◽  
Forest Fire Model ◽  
The One

Abstract We modify the rules of the self-organized critical forest-fire model in one dimension by allowing the fire to jum p over holes of ≤ k sites. An analytic calculation shows that not only the size distribution of forest clusters but also the size distribution of fires is characterized by the same critical exponent as in the nearest-neighbor model, i.e. the critical behavior of the model is universal. Computer simulations confirm the analytic results.

scholarly journals Exact results for the one-dimensional self-organized critical forest-fire model

1993 ◽  
Vol 71 (23) ◽  
pp. 3739-3742 ◽  
Author(s):  
Barbara Drossel ◽  
Siegfried Clar ◽  
Franz Schwabl
Keyword(s):  
Forest Fire ◽  
Exact Results ◽  
Fire Model ◽  
One Dimensional ◽  
Self Organized ◽  
Forest Fire Model ◽  
The One

Fractality and Self-Organized Criticality of Wars

Fractals ◽  
1998 ◽  
Vol 06 (04) ◽  
pp. 351-357 ◽  
Author(s):  
D. C. Roberts ◽  
D. L. Turcotte
Keyword(s):  
Forest Fire ◽  
Power Law ◽  
Forest Fires ◽  
Size Dependence ◽  
Fire Model ◽  
Self Organized ◽  
Battle Deaths ◽  
Forest Fire Model ◽  
Alternative Measures ◽  
Self Organized Criticality

This paper considers the frequency-size statistics of wars. Using several alternative measures of the intensity of a war in terms of battle deaths, we find a fractal (power-law) dependence of number on intensity. We show that the frequency-size dependence of forest fires is essentially identical to that of wars. The forest-fire model provides a basis for understanding the distribution of forest firest in terms of self-organized criticality. We extend the analogy to wars in terms of the initial ignition (outbreak of war) and its spread to a group of metastable countries.

The Self-Organized Critical Forest-Fire Model with Trees and Bushes

1995 ◽  
Vol 5 (9) ◽  
pp. 1233-1238 ◽  
Author(s):  
B. Strocka ◽  
J. A.M.S. Duarte ◽  
M. Schreckenberg
Keyword(s):  
Forest Fire ◽  
The Self ◽  
Fire Model ◽  
Self Organized ◽  
Forest Fire Model

scholarly journals A simple model for the earthquake cycle combining self-organized complexity with critical point behavior

2002 ◽  
Vol 9 (5/6) ◽  
pp. 453-461 ◽  
Author(s):  
W. I. Newman ◽  
D. L. Turcotte
Keyword(s):  
Forest Fire ◽  
Power Law ◽  
Substantial Improvement ◽  
Earthquake Cycle ◽  
Power Law Distribution ◽  
Time Step ◽  
Fire Model ◽  
Inverse Cascade ◽  
Self Organized ◽  
Forest Fire Model

Abstract. We have studied a hybrid model combining the forest-fire model with the site-percolation model in order to better understand the earthquake cycle. We consider a square array of sites. At each time step, a "tree" is dropped on a randomly chosen site and is planted if the site is unoccupied. When a cluster of "trees" spans the site (a percolating cluster), all the trees in the cluster are removed ("burned") in a "fire." The removal of the cluster is analogous to a characteristic earthquake and planting "trees" is analogous to increasing the regional stress. The clusters are analogous to the metastable regions of a fault over which an earthquake rupture can propagate once triggered. We find that the frequency-area statistics of the metastable regions are power-law with a negative exponent of two (as in the forest-fire model). This is analogous to the Gutenberg-Richter distribution of seismicity. This "self-organized critical behavior" can be explained in terms of an inverse cascade of clusters. Small clusters of "trees" coalesce to form larger clusters. Individual trees move from small to larger clusters until they are destroyed. This inverse cascade of clusters is self-similar and the power-law distribution of cluster sizes has been shown to have an exponent of two. We have quantified the forecasting of the spanning fires using error diagrams. The assumption that "fires" (earthquakes) are quasi-periodic has moderate predictability. The density of trees gives an improved degree of predictability, while the size of the largest cluster of trees provides a substantial improvement in forecasting a "fire."

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