Blowups and Tops of Overlapping Iterated Function Systems
Dynamical Systems
2023-02-22 v1
Abstract
We review aspects of an important paper by Robert Strichartz concerning reverse iterated function systems (i.f.s.) and fractal blowups. We compare the invariant sets of reverse i.f.s. with those of more standard i.f.s. and with those of inverse i.f.s. We describe Strichartz' fractal blowups and explain how they may be used to construct tilings of even in the case where the i.f.s. is overlapping. We introduce and establish the notion of "tops" of blowups. Our motives are not pure: we seek to show that a simple i.f.s. and an idea of Strichartz, can be used to create complicated tilings that may model natural structures.
Keywords
Cite
@article{arxiv.2302.10372,
title = {Blowups and Tops of Overlapping Iterated Function Systems},
author = {Louisa F. Barnsley and Michael F. Barnsley},
journal= {arXiv preprint arXiv:2302.10372},
year = {2023}
}