The branching structure of diffusion-limited aggregates

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 B approximate to 4.9, in good agreement with the numerically obtained result of B approximate to 5.2. In high dimensions, B --> 3.12; 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.