Branch-height distribution in diffusion-limited deposition

We analyze diffusion-limited aggregation (DLA) [T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47, 1400 (1981); Phys. Rev. B 23, 5686 (1983)] with a branchless needle model. We modify the growth rules of our needles by assigning them a fractal dimension of ${\mathit{D}}_{\mathit{b}}$≊1.7, the fractal dimension of DLA. We then construct a mean-field theory of the evolution of the number of needles having particular heights. Our model accounts for the correlations within a needle. We argue that DLA is an isotropic fractal with a scaling density profile and that the fractal dimension of the individual branches should be the same as the dynamical dimension of the aggregate.