How anisotropy beats fractality in two-dimensional on-lattice DLA growth

Abstract

We study the fractal structure of Diffusion-Limited Aggregation (DLA) clusters on the square lattice by extensive numerical simulations (with clusters having up to $10^8$ particles). We observe that DLA clusters undergo strongly anisotropic growth, with the maximal growth rate along the axes. The naive scaling limit of a DLA cluster by its diameter is thus deterministic and one-dimensional. At the same time, on all scales from the particle size to the size of the entire cluster it has non-trivial box-counting fractal dimension which corresponds to the overall growth rate which, in turn, is smaller than the growth rate along the axes. This suggests that the fractal nature of the lattice DLA should be understood in terms of fluctuations around one-dimensional backbone of the cluster.

References in corpus (5)

• Exact Multifractal Exponents for Two-Dimensional Percolation
• Radial DLA: two fractal dimensions and deviations from self-similarity
• Diffusion-limited aggregation as branched growth
• The Harmonic Measure of Diffusion-Limited Aggregates including Rare Events
• Bias-free simulation of diffusion-limited aggregation on a square lattice

Cited by in corpus (5)

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• Analysing the anisotropy in morphological evolution and readjustment effects in cluster-cluster aggregation of AuNPs using Shannon entropy
• SLE scaling limits for a Laplacian random growth model