A Survey on Newhouse Thickness, Fractal Intersections and Patterns

Abstract

In this article, we introduce a notion of size for sets, called the thickness, that can be used to guarantee that two Cantor sets intersect (the Gap Lemma) and show a connection among thickness, Schmidt games and patterns. We work mostly in the real line, but we also introduce the topic in higher dimensions.

Keywords

• thickness
• Gap Lemma
• patterns