SELF-ORGANIZED CRITICALITY AND FRACTAL GROWTH

Growth processes are argued to develop self-organized critical states. This new characterization of growth phenomena yields insight into the origin of fractal pattern formation, and the associated exponents give information on scaling properties beyond that provided by the usual multifractal description. As a major example, the dielectric-breakdown model is considered. The fractal dimension is estimated to be D=ln3/ln2 1.585 for =1. This value is compared with results obtained for different geometries and with values found when lattice effects are present. Also, the limiting cases 0 and are discussed. © 1990 The American Physical Society.