Statistics and Geometry for the Collection of Fractal Fragments

概要

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We propose a multifractal formalism to analyze a self-similar fractal pattern con-sisting of fractal fragments whicla may have distributed dimensions. To characterxzestatistical and geometrical structure of tlae entire pattern, the function f (7)) is ixa-troduced, w'hicla pla'ys a similar role to the singularity spectrum of multifractal pat-ferns. As the first application, we analyze a collection of contour lines generated bycutting a self-affine Brow'nian surface at an average level. Woe clarify w'ith an aid ofmodel consideration that tlae fractal dimextsion of ex'ery single line should be uniqueand f (D) consists of only' two points corresponding to each coxatour auad the entirepattern, respectively. On the other hand, the continauous f (D) is clearly found foreach cluster in a kind of cluster-cluster aggregation model applied as another exam-pie. The maximum of f (D) is associated w'ith the size distribution of the clusters.
社団法人日本物理学会の論文
1992-12-15