Mass Multifractality in Cluster Growth Models
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 Distribution Occupied Lattice Site Multifractal Distribution Exact Recursion Relation Cell Renormalization Group
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