Generalization and the Fractal Dimensionality of Diffusion-Limited Aggregation

Mitsugu Matsushita, Katsuya Honda, Hiroyasu Toyoki, Yoshinori Hayakawa, Hiroshi Kondo

    Research output: Contribution to journalArticlepeer-review

    79 Citations (Scopus)


    Diffusion-limited aggregation (DLA) model is generalized to incorporate the dielectric breakdown model proposed by Niemeyer et al., and the new simulation method is proposed. While a growing cluster is still in the diffusion (Laplace) field, the local growth probability at a perimeter site Pps of the cluster is now given by pg(Pps) ∼|∇φ(Pps)|η, where Φ(P) is the probability of finding at a point P a random walker launched far away from the cluster. Ordinary DLA corresponds to η=1. Based on the theory of DLA proposed by Honda et al., the fractal dimension df for this generalized DLA is derived as [formula omitted], where ds is the dimension of space in which aggregation processes take place and dw is the fractal dimension of random walker trajectory. Both ds and dw are allowed to take any number larger than or equal to one. This formula is also applicable to Eden model (η=0) correctly, which means that the generalized DLA model naturally bridges a gap between ordinary DLA and Eden models.

    Original languageEnglish
    Pages (from-to)2618-2626
    Number of pages9
    Journaljournal of the physical society of japan
    Issue number8
    Publication statusPublished - 1986 Aug

    ASJC Scopus subject areas

    • Physics and Astronomy(all)


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