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, [formula omitted], derived by Matsushita et al., where ds is the spatial dimension, dw 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.
ASJC Scopus subject areas
- Physics and Astronomy(all)