Multifractal scaling of 3D diffusion-limited aggregation

Stefan Schwarzer, Shlomo Havlin, H. Eugene Stanley

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 ≡ r Rg, 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.

Original languageEnglish
Pages (from-to)117-122
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-4
StatePublished - 15 Dec 1992

Bibliographical note

Funding Information:
We would like to thank P. Meakin for useful discussionsa nd for supplying cluster coordinates. We further thank M. Gyure, G. Huber, H. Larralde, S. Sastry, T. Udale, T. Vicsek and M. Wolf for comments and discussions. Financial support from NSF is gratefully acknowledged.


Dive into the research topics of 'Multifractal scaling of 3D diffusion-limited aggregation'. Together they form a unique fingerprint.

Cite this