Fractal dimensions of zero-noise diffusion-limited aggregation

Abstract

We investigate the scaling of cluster size with mass for zero-noise needle-star DLA clusters on the square (d = 2) and cubic (d = 3) lattices. We find that the clusters are essentially planar (D = 2). However, estimates of the isotropic self-similar fractal dimension via the radius of gyration yield D = 1.5 for d = 2 and D {reversed tilde equals} 1.7 for d = 3. The same scaling exponents are derived from an algebraic model. We show that the planar result D = 2 is consistent with self-affine fractal geometry. Show more