Anisotropy and Fluctuation in Diffusion Limited Aggregation

Abstract

Diffusion limited aggregation (DLA) models many different physical phenomena from dielectric breakdown to viscous finger instabilities. The resulting patterns can be analysed in terms of fractal geometries. They depend in a very sensitive way on the anisotropy and the noise of the growth rules. Here, several different variants of DLA are reviewed. In particular, simulations with enhanced growth in the direction of the axes of the underlying lattice are analysed to show that even a slight anisotropy distroys the spherical, self-similar structure in favor of a self-affine structure whose scaling properties depend on the symmetry of the lattice. Growth on a square lattice suggests that there is a crossover from off-lattice DLA with a fractal dimension of D=1.71 to a cross-like self-affine pattern with D_∥=1.5 along the axes and D_⊥=2.0 along the diagonals. Qualitative arguments are advanced to explain these results in terms of classical aggregation, i.e. neglecting fluctuations.