Morphology of a Class of Kinetic Growth Models

Abstract

We study a class of local probabilistic growth processes that includes the kinetic-growth algorithm for generating percolation clusters. The shapes of the growing clusters are controlled by $p$, the probability of growth. For $p>\mathrm{}{p}_c$, the shapes are scale invariant with time and show interesting morphological features including both smoothly curved sections and straight facets. The facets are shown to be related to the problem of directed percolation and disappear below the directed-percolation threshold. A simple random-walk model for computing the shapes of our clusters is described.