How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth

Denis S. Grebenkov, Dmitry Beliaev

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    We study the fractal structure of diffusion-limited aggregation (DLA) clusters on a square lattice by extensive numerical simulations (with clusters having up to 108 particles). We observe that DLA clusters undergo strongly anisotropic growth, with the maximal growth rate along the axes. The naive scaling limit of a DLA cluster by its diameter is thus deterministic and one-dimensional. At the same time, on all scales from the particle size to the size of the entire cluster it has a nontrivial box-counting fractal dimension which corresponds to the overall growth rate, which, in turn, is smaller than the growth rate along the axes. This suggests that the fractal nature of the lattice DLA should be understood in terms of fluctuations around the one-dimensional backbone of the cluster.

    Original languageEnglish
    Article number042159
    JournalPhysical Review E
    Volume96
    Issue number4
    DOIs
    Publication statusPublished - 30 Oct 2017

    Fingerprint

    Dive into the research topics of 'How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth'. Together they form a unique fingerprint.

    Cite this