Diffusion limited aggregation and its response to anisotropy

The stability of diffusion limited growths with n equivalent major fingers is investigated in two dimensions using a conformal mapping. The results imply that square lattice but not hexagonal lattice bias are relevant in simple Diffusion Limited Aggregation (DLA). In general it is found that the maximum number of fingers stable with respect to finger loss by competition is given by nmax = 2 + 2(D − 1), where D is the apparent fractal dimension of the fingers, at least when n is even.