Size distribution and the Hausdorff-Besicovitch dimension of two-scale Cantor dusts

Avner Peleg, Baruch Meerson

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Simple fractal sets (for example, Cantor dust) can be characterized by a distribution function of sizes of the set’s “building blocks.” This characterization can be useful in problems of fractal growth and coarsening. We test it on a simple example of a two-scale deterministic Cantor dust. In the limit of [Formula Presented] (where m is the number of iterations in the fractal generating algorithm), the discrete binomial distribution of sizes of this set can be approximated by a continuous distribution. This continuous distribution gives an accurate estimate for the Hausdorff-Besicovitch dimension. An algorithm is suggested for generating a random two-scale Cantor dust with a tunable fractal dimension.

Original languageAmerican English
Pages (from-to)1238-1241
Number of pages4
JournalPhysical Review E
Volume59
Issue number1
DOIs
StatePublished - 1999

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