Random successive growth model for pattern formation

Abstract

In order to explain patterns formed during crystallization of metal-semiconductor films and during bacterial colony growth, a random successive growth model where no long-range diffusion is necessary has been proposed. In this model the growth is controlled by two local conditions: growth probability of the neighboring sites around the cluster and occupation ratio of the sites of the cluster inside a small circle with the potential growth site as its center. Varying these conditions, fractal, dense-branching, and compact growth patterns have been obtained.