Generating directional attractors based on multiple subdivision

Baoxing Zhang; Hongchan Zheng; Yuanyuan Xie

doi:10.59400/adecp3054

Generating directional attractors based on multiple subdivision

Baoxing Zhang College of Statistics and Mathematics, Hebei University of Economics and Business
Hongchan Zheng
Yuanyuan Xie

Article ID: 3054

Keywords: Iterated function system; multiple iterated function system; multiple subdivision; iteration process control; directional attractors MSC CLASSIFICATION: 35B41; 39B12

Abstract

The connection between self-similar fractals and subdivision shows that self-similar fractals can be generated as attractors by an extended family of subdivision schemes. This paper aims to equipe these attractors with directions. Such directional attractors in this paper are generated based on a kind of multiple subdivision, which owns several anisotropic subdivision operators and generate surfaces with directions. For the multiple subdivision, we derive an iterated function system for each anisotropic subdivision operator to get a multiple function system, which can be arranged in a tree structure. Then by controlling the paths in the tree, attractors with different directions can be generated. Several examples are given to illustrate these new directional attractors.

Published

2025-06-30

How to Cite

Zhang, B., Zheng, H., & Xie, Y. (2025). Generating directional attractors based on multiple subdivision. Advances in Differential Equations and Control Processes, 32(2). https://doi.org/10.59400/adecp3054

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Issue

Vol. 32 No. 2 (2025)

Section

Article

Supporting Agencies

This research is funded by Science Research Project of Hebei Education Department, NO. QN2024065 and the National Natural Science Foundation of China (12201453).

This work is licensed under a Creative Commons Attribution 4.0 International License.

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