Number of branches in diffusion-limited aggregates: The skeleton.

We develop the skeleton algorithm to define the number of main branches Nb of diffusion-limited aggregation (DLA) clusters. The skeleton algorithm provides a systematic way to remove dangling side branches of the DLA cluster and has successfully been applied to study the ramification properties of percolation. We study the skeleton of comparatively large (≈ 10 sites) off-lattice DLA clusters in two, three and four spatial dimensions. We find that initially with increasing distance from the cluster seed the number of branches increases in all dimensions. In two dimensions, the increase in the number of branches levels off at larger distances, indicating a fixed number of Nb = 7.5 ± 1.5 main branches of DLA. In contrast, in three and four dimensions, the skeleton continues to ramify strongly as one proceeds from the cluster center outward, and we find no indication of a constant number of