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Improved algorithms have been developed to simulate both off-lattice and hypercubic-lattice diffusion-limited aggregation (DLA) in dimensionalities d in the range 28. For the two-dimensional cases using off-lattice clusters containing up to 10^6 particles, we find that the effective fractal dimensionality is essentially independent of cluster size s for clusters containing more than a few thousand particles and has a value of 1. 7150. 004 (significantly higher than the mean-field value of (5/3). For d=3, 4, and 5, it appears to be possible to approach quite close to the asymptotic (s) regime and the effective fractal dimensionality for off-lattice clusters is equal to the mean-field value given by D= (d^2+1) / (d+1) (within a few tenths of 1%). For d5 we were not able to approach near enough to the asymptotic limit to make an accurate estimate of the limiting fractal dimensionality. However, the simulation results are consistent with the mean-field theory predictions. For d4 the effects of lattice anisotropy can be seen in the overall shapes of the clusters and the dependence of the cluster radius of gyration on s. For d5 clusters containing 10^5 sites are still in the fluctuation-dominated regime and the dependence of R₆ on s is essentially the same for both off-lattice and hypercubic-lattice models. For d=2 the effective value of, which describes how the width of the active zone grows, increases with increasing cluster size and approaches a value of 1/1. 715.
Tolman et al. (Sat,) studied this question.