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Multifractal analysis of the branch structure of diffusion-limited aggregates

W. G. Hanan and D. M. Heffernan

Department of Mathematical Physics, National University of Ireland Maynooth, County Kildare, Ireland

Phys. Rev. E 85, 021407 – Published 27 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.021407

Abstract

We examine the branch structure of radial diffusion-limited aggregation (DLA) clusters for evidence of multifractality. The lacunarity of DLA clusters is measured and the generalized dimensions $D (q)$ of their mass distribution is estimated using the sandbox method. We find that the global $n$ -fold symmetry of the aggregates can induce anomalous scaling behavior into these measurements. However, negating the effects of this symmetry, standard scaling is recovered.

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