The branching structure of diffusion-limited aggregates
Exxon Research and Engineering - Route 22 East, Annandale,
NJ 08801, USA
Accepted: 30 May 1997
I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two dimensions is , in good agreement with the numerically obtained result of . In high dimensions, ; the bifurcation ratio is thus a decreasing function of dimensionality. This analysis also determines the scaling properties of the ramification matrix, which describes the hierarchy of branches.
PACS: 61.43.Hv – Fractals; macroscopic aggregates (including diffusion-limited aggregates) / 47.53.+n – Fractals / 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion
© EDP Sciences, 1997