On the Exact Convex Hull of IFS Fractals
Abstract
The problem of finding the convex hull of an IFS fractal is relevant in both theoretical and computational settings. Various methods exist that approximate it, but our aim is its exact determination. The finiteness of extremal points is examined a priori from the IFS parameters, revealing some cases when the convex hull problem is solvable. Former results are detailed from the literature, and two new methods are introduced and crystallized for practical applicability -- one more general, the other more efficient. Focal periodicity in the address of extremal points emerges as the central idea.
Keywords
Cite
@article{arxiv.1502.03788,
title = {On the Exact Convex Hull of IFS Fractals},
author = {József Vass},
journal= {arXiv preprint arXiv:1502.03788},
year = {2018}
}
Comments
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.)