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Radial DLA: two fractal dimensions and deviations from self-similarity

Benoit B. Mandelbrot·Boaz Kol·Amnon Aharony
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Abstract

When suitably rescaled, the distribution of the angular gaps between branches of off-lattice radial DLA is shown to approach a size-independent limit. The power-law expected from an asymptotic fractal dimension D=1.71 arises only for very small angular gaps, which occur only for clusters significantly larger than one million particles. Intermediate size gaps exhibit an effective dimension around 1.66, even for cluster sizes going to infinity. They dominate the distribution for clusters with less than a million particles. The largest gap approaches a finite limit extremely slowly, with a correction of order M^{-0.17}, where M is the cluster mass.

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Benoit B. Mandelbrot, Boaz Kol, Amnon Aharony. 2001-12-03. Radial DLA: two fractal dimensions and deviations from self-similarity. https://doi.org/10.1103/physrevlett.88.055501

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