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Multifractal scaling of 3D diffusion-limited aggregation

Author

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  • Schwarzer, Stefan
  • Havlin, Shlomo
  • Stanley, H.Eugene

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.

Suggested Citation

  • Schwarzer, Stefan & Havlin, Shlomo & Stanley, H.Eugene, 1992. "Multifractal scaling of 3D diffusion-limited aggregation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 117-122.
    • Handle: RePEc:eee:phsmap:v:191:y:1992:i:1:p:117-122
    DOI: 10.1016/0378-4371(92)90514-Q
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