Fractal analysis of tree figures

Author

Fujimori, S.

Author_Institution

Dept. of Electr. Eng., Tokai Univ., Hiratsuka, Japan

fYear

1991

fDate

8-12 Jul 1991

Firstpage

131

Abstract

Two methods for calculating fractal dimensions, the cover method and the method of gyration radius, are discussed. The cover method is applicable to both tree-type tree patterns and aegagropila-type tree patterns. The method of gyration radius is also applicable to aegagropila-type patterns but those fractal dimensions take slightly different values depending on how the center of the gyration radius is put in the pattern. This method was not very applicable to the three-type tree patterns. The multifractal dimension of tree-type tree patterns is also discussed. The dimensions are calculated by the cover method. The multifractal dimension of the tree-type tree patterns gradually increases from 0.6 to 1.84, in the average, when the moment order increases from -4 to 8, though the dimension generally decreases depending on the moment order

Keywords

electric breakdown of solids; fractals; aegagropila-type tree patterns; cover method; electric trees; fractal dimensions calculation; method of gyration radius; multifractal dimension; tree figure fractal analysis; tree-type tree patterns; Chaos; Diffusion processes; Electric breakdown; Energy measurement; Entropy; Fractals; Geometry; Laplace equations; Pattern analysis; Solids;

fLanguage

English

Publisher

ieee

Conference_Titel

Properties and Applications of Dielectric Materials, 1991., Proceedings of the 3rd International Conference on

Conference_Location

Tokyo

Print_ISBN

0-87942-568-7

Type

conf

DOI

10.1109/ICPADM.1991.172031

Filename

172031