Monte Carlo Simulations of the Generalized Diffusion Limited Aggregation

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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 s 2 +η( d s -1)}/{ d s +η( d 2 -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.