1986 年 55 巻 8 号 p. 2479-2482
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, df={ds2+η(dw−1)}⁄{ds+η(d2−1)}, 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.
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