Asymptotic shape of diffusion-limited aggregates with anisotropy

Abstract

On the basis of a renormalization group in the space of shapes, conformal mapping techniques, and numerical simulations, it is argued that noise-reduced and regular diffusion-limited aggregates on a lattice are in the same universality class. These models lead to the same asymptotic shape of fractal aggregates. This shape is a fixed point of a functional equation, realized by a conformal transformation.