Self-similarity of the branching structure in very large DLA clusters and other branching fractals

Abstract

We study the branching structure of very large DLA clusters, of up to 100 million particles. The Horton-Strahler ordering of the branches in these clusters shows a relaxation towards a state with the stream numbers forming a geometric series. This behaviour is compared with those of several self-similar trees. It indicates that DLA clusters converge to topologically self-similar objects.