Abstract
Improved algorithms have been developed for both off-lattice and hypercubic lattice diffusion-limited aggregation (DLA) in dimensionalities (
d
) 3-8 and for two-dimensional off-lattice DLA. In two-dimensional off-lattice DLA a fractal dimensionality (
D
) of about 1.71 was obtained for clusters containing up to 10
6
particles. This is significantly larger than the value of (
d
2
+ 1)/(
d
+ 1) (5/3 for
d
= 2) predicted by mean field theories. For
d
> 2 the off-lattice simulations give results that are consistent with the mean field theories. For
d
= 3 and
d
= 4 the effects of lattice anisotropy can easily be seen for clusters containing 3 x 10
6
and 10
6
sites respectively and the effective fractal dimensionalities are slightly smaller for the lattice model clusters than for the off-lattice clusters. Results are also presented for two-, three- and four- dimensional lattice model clusters with noise reduction.
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