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Scale-dependent dimension in the forest fire model

Chen1, Bak

  • 1Department of Computational Science, National University of Singapore, Singapore 117543, Singapore and Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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A forest fire model reveals fractal dimensions in fire distribution, varying with scale. This model offers insights into turbulence and the spatial distribution of cosmic matter.

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Astrophysics

Background:

  • Forest fires exhibit complex spatial patterns.
  • Reaction-diffusion models are used to simulate localized dissipation and uniform energy injection.

Purpose of the Study:

  • To analyze the spatial distribution of fires using a reaction-diffusion model.
  • To investigate the fractal dimension and scaling properties of fire patterns.

Main Methods:

  • Developed a three-dimensional and two-dimensional forest fire reaction-diffusion model.
  • Examined how fractal dimension changes with length scale and growth rate.

Main Results:

  • In 3D, fractal dimension increases logarithmically from 0 to 3 with length scale, reaching homogeneity beyond a correlation length.

Related Experiment Videos

  • Correlation length diverges with growth rate (p) as xi ~ p(-2/3).
  • In 2D, dimension increases to 1, then jumps to 2 at a crossover length scale (l ~ 1/p).

    • Conclusions:

    • The model explains intermediate-range turbulence scaling and offers a new perspective on spatial patterns.
    • The findings suggest potential applicability to the distribution of luminous matter in the universe.