Topological and geometrical properties of DLA clusters

Abstract

Three new exponents are calculated for diffusion limited aggregates in two dimensions via computer simulation. The 1/N=0 limit gives zeta =1.52, nu =0.91 and dw=2.56. These results confirm Martin's conjecture D= zeta / nu , and are consistent with previous work indicating that topological rather than geometrical properties of random fractals are responsible for variations in fractal dimension. Diffusion on DLA clusters is anomalous with an exponent that is consistent with the Alexander-Orbach conjecture and satisfies the Einstein relation.