Monte Carlo Simulations of the Generalized Diffusion Limited Aggregation

Abstract

Two-dimensional Monte Carlo simulations are performed for the generalized diffusion-limited aggregation (DLA) model which is equivalent to the dielectric breakdown model proposed by Niemeyer et al. It is found that the simulated patterns are self-similar, and the fractal dimensions of these patterns agree well with the theoretical formula, d_f={d_s²+η(d_w−1)}⁄{d_s+η(d₂−1)}, derived by Matsushita et al., where d_s is the spatial dimension, d_w the fractal dimension of the random-walker trajectory, and η an exponent contained in the local growth probability at the perimeter site. Further, our simulation results suggest that effect of lattice anisotropy becomes prominent when increasing the exponent η.