Multifractal dimensions of tree patterns

Abstract

In electrical discharge o r electrical breakdown s t u d i e s , e s p e c i a l l y in t h e s t u d i e s o f s o l i d dielectrics, one of serious problems is tree initiations and its developments. Physical o r chemical properties have been studied, but its morphological and global examinations just have started based on the concept "fractal" proposed by Mandelbrot for discussing a self-similar patterns or complex patternslll. Computer simulated tree patterns o r the patterns inputted into computer from tree photographs are now analyzed numerically by using the fractal theory, and related studies have been gradually developed C21. T h e examinations have gradually progressed. Now, this fractal concept is extended into multifractal conceptE31, which offers more detailed and more precise informations of patterns. In this paper we will discuss the relations between tree patterns, tree-type and aegaglopira-type tree patterns and their multifractal dimensions.