Diffusion-limited aggregation as branched growth

Abstract

I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys. Rev. A 46, 7793 (1992)]. This leads to a result for the cluster dimensionality, D≊1.66, which is close to numerically obtained values. In addition, the multifractal exponent τ(3)=D in this theory, in agreement with a proposed ‘‘electrostatic’’ scaling law.