Abstract
We study the multifractal properties of the set of growth probabilities {${\mathit{p}}_{\mathit{i}}$} for three-dimensional (3D) off-lattice diffusion-limited aggregation (DLA) in two distinct ways: (i) from the histogram of the ${\mathit{p}}_{\mathit{i}}$ and (ii) by Legendre transform of the moments of the distribution of ${\mathit{p}}_{\mathit{i}}$. We calculate the {${\mathit{p}}_{\mathit{i}}$} for 50 off-lattice clusters with cluster masses up to 15 000. We discover that for 3D DLA, in contrast to 2D DLA, there appears to be no phase transition in the multifractal spectrum. We interpret this difference in terms of the topological differences between two and three dimensions.
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