Author:
Zhang Baoxing,Zheng Hongchan,Chen Yingwei
Abstract
Self-similar fractals can be generated using subdivision and the subdivision curves/surfaces are actually attractors. Such a connection has been studied between fractals and an extended family of subdivision including stationary and non-stationary schemes. This paper aims to move one step further on such a connection and introduce multiple-function systems, which has a set of function systems and choose one for each step of iteration. These multiple-function systems can be obtained by deriving the iterated function systems based on the subdivision operators and applying some modifications, including deleting some transformations, to them. Such multiple-function systems can be arranged in a tree structure and can generate different attractors along different paths in the tree. Several examples are presented to illustrate the performance of these multiple-function systems.
Funder
Scientific Research and Development Program of Hebei University of Economics and Business
Natural Science Foundation of Hebei Province of China
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
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