Mass Multifractality in Cluster Growth Models

Abstract

It is demonstrated that clusters constructed by asymmetric recursion rules can be described in terms of mass multifractality. The set of generalized dimensions D q associated with the geometry of such objects is determined numerically for the growing asymmetric Cantor set using the box counting and the sand box methods. These approaches are not found equally efficient in evaluating the D q values. The direct determination of the f(α) spectrum corresponding to the singular distribution of mass in very large off-lattice diffusion-limited aggregates indicates the mass multifractality of these clusters as well.KeywordsSingular DistributionOccupied Lattice SiteMultifractal DistributionExact Recursion RelationCell Renormalization GroupThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.