Multifractal scaling of 3D diffusion-limited aggregation

Stefan Schwarzer, Shlomo Havlin and H.Eugene Stanley

Physica A: Statistical Mechanics and its Applications, 1992, vol. 191, issue 1, 117-122

Abstract: We study the multifractal (MF) properties of the set of growth probabilities {pi} for 3D off-lattice diffusion-limited aggregation (DLA). We find that: (i) the {pi} display MF scaling for all moments-in contrast to 2D DLA, where one observes a “phase transition” in the MF spectrum for negative moments; (ii) multifractality is also displayed by the pi located in a shell of reduced radius x ≡ rRg, where Rg is the radius of gyration of the cluster and r the radius of the shell; (iii) the average value αav of α ≡ -In p/InM in a shell of reduced radius x in a cluster of mass M is a function that does not depend on the cluster mass but only on x.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:191:y:1992:i:1:p:117-122

DOI: 10.1016/0378-4371(92)90514-Q

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