Blowups and Tops of Overlapping Iterated Function Systems

TL;DR

This paper reviews Strichartz's work on reverse iterated function systems and fractal blowups, exploring their invariant sets and applications in creating complex tilings of Euclidean space, even with overlapping systems.

Contribution

It introduces the concept of 'tops' of blowups and demonstrates how simple overlapping IFS can generate intricate tilings, connecting fractal theory with natural structure modeling.

Findings

Fractal blowups can be used to construct tilings of ^n.

The notion of 'tops' of blowups is established.

Overlapping IFS can produce complex, natural-like structures.

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 $\mathbb{R}^{n}$ 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.