FRACTAL CLUSTERS AND SELF-ORGANIZED CRITICALITY

Abstract

Self-organized criticality (SOC) and fractals have been shown to be related in various ways. On the one hand, the original idea of SOC suggests that the common explanation of the origin of fractal shapes in nature may be based on self-organized processes. Thus different models exhibiting SOC result in relaxation clusters or avalanches whose geometrical characteristics could be described by fractals. On the other hand, there exist several models for fractal growth phenomena, such as viscous fingering, invasion percolation, dielectric breakdown, etc., and it is possible that the concept of SOC may help in finding the common feature of these models. In this paper we review the recent results on self-organized critical behaviour in various fractal growth models. Next we discuss the relation of fractals and self-organized criticality by concentrating on the geometrical properties of SOC clusters in 2–4 dimensions. A short analysis of the cluster growth processes is given as well.