Branch distribution in diffusion-limited aggregation: a maximum entropy approach

Abstract

A new approach to the branching structure of diffusion-limited aggregation (DLA) clusters is proposed, in which the stress is laid not on the (traditionally used) order of the branches, but on their mass. The branch distribution n(s, M) (to be defined) of DLA is computed and its properties are compared with those found in self-similar deterministic fractal sets. A power-law behaviour is found in both cases. DLA also shows a striking corssover, which is independent of the cluster size. The Maximum Entropy formalism, a well-known method in statistical physics, is applied in order to derive the functional form of n(s, M). The fit is achieved by means of a constraint concerning the information in the ensemble of all DLA clusters. We believe this constraint is a preliminar hint towards a new conceptual framework for the study of fractal growth phenomena.