IFS分形的精确凸包
动力系统
2018-02-05 v5
摘要
寻找IFS分形凸包的问题在理论与计算背景下均有意义。现有多种方法对其进行近似，但我们的目标为其精确确定。从IFS参数出发先验地考察极值点的有限性，揭示出凸包问题可解的某些情形。详述了文献中的既有结果，并引入且明确了两种新方法以用于实际适用——一种更通用，另一种更高效。极值点地址中的焦点周期性成为核心思想。
引用
@article{arxiv.1502.03788,
title = {On the Exact Convex Hull of IFS Fractals},
author = {József Vass},
journal= {arXiv preprint arXiv:1502.03788},
year = {2018}
}
备注
Some but not all of these results appeared in the author's doctoral dissertation, and were presented at the 2014 Winter Meeting of the Canadian Mathematical Society. This research was started in Fall 2009, and the results were finalized in Feb. 2015. Some formatting changes were made in 2017. The paper is to appear in Fractals, Vol. 26, No. 1 (2018) 1850002. (Contains 34 pages with 11 figures.)