## Abstract

We study the multifractal (MF) properties of the set of growth probabilities {p_{i}} for 3D off-lattice diffusion-limited aggregation (DLA). We find that: (i) the {p_{i}} 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 p_{i} located in a shell of reduced radius x ≡ r R_{g}, where R_{g} is the radius of gyration of the cluster and r the radius of the shell; (iii) the average value α_{av} 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 language | English |
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Pages (from-to) | 117-122 |

Number of pages | 6 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 191 |

Issue number | 1-4 |

DOIs | |

State | Published - 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.