Hierarchical model for the multifractality of diffusion-limited aggregation

We propose a deterministic model of diffusion-limited aggregation (DLA), based on the concept of an infinite hierarchy of voids connected by narrow channels. This hierarchical model reproduces many features of DLA: (1) The growth-site probability distribution shows multifractal behavior, (2) the minimum growth probability decreases with size L as ln${\mathit{p}}_{\min }$(L)∼-(lnL${)}^2$, and (3) the maximum growth probability scales as ${\mathit{p}}_{\max }$(L)∼${\mathit{L}}_{\min }^{\mathrm{-}\mathrm{\alpha }}$.