An inverse cascade model for self-organized complexity and natural hazards

Abstract

The concept of self-organized complexity evolved from the scaling behaviour of several cellular automata models, examples include the sandpile, slider-block and forest-fire models. Each of these systems has a large number of degrees of freedom and shows a power-law frequency-area distribution of avalanches with N∝A−α and α ≈ 1. Actual landslides, earthquakes and forest fires exhibit a similar behaviour. This behaviour can be attributed to an inverse cascade of metastable regions. The metastable regions grow by coalescence which is self-similar and gives power-law scaling. Avalanches sample the distribution of smaller clusters and, at the same time, remove the largest clusters. In this paper we build on earlier work (Gabrielov et al.) and show that the coalescence of clusters in the inverse cascade is identical to the formation of fractal drainage networks. This is shown analytically and demonstrated using simulations of the forest-fire model.