Self-Similar Planar Fractals Based on Branching Trees and Bushes

概要

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Branching trees and bushes are obtained from a segment by an infinite sequence of two elementary transformations - rotation for a positive angle 〓 < π and stretching with a factor r < 1. Trees and bushes themselves are not self-similar, but the resulting limiting sets of points are. Typical questions about tree fractals are: at what relation between r and 〓 the branches of the tree will meet (overlap), and what will be the limiting surrounding curve, when there is no overlapping. By summation of complex geometric progressions, we find an explicit connection between r and 〓 for this boundary case. We obtain polynomial equations and solve them exactly, when this is possible, but in most cases numerically. The results are of interest for different natural sciences and medicine.
一般社団法人日本物理学会の論文
2003-09-30