Forest fires and the structure of the universe

The forest fire model (Phys. Lett. A 147 (1990) 297) was proposed as a toy model of turbulent systems, where energy (in the form of trees) is injected uniformly and globally, but is dissipated (burns) locally. We found a novel scaling form for the spatial distribution of dissipation (fires) in the forest fire model. The fractal dimension describing the fire distribution gradually increases from zero to three as the length scale increases from the smallest scale to a correlation length. We suggest that this picture might applies to “intermediate dissipative range” of turbulence. A study of galaxy catalogues indicates that the distribution of luminous matter in the universe follows a similar pattern. At small distances, the universe is zero-dimensional and point-like; at distances of the order of 1 Mpc the dimension is unity, indicating perhaps a filamentary, string-like structure. When viewed at larger scales it gradually becomes two dimensional; finally, at the correlation length, 300 Mpc, it becomes uniform.