IUMJ

Title: Rectifiable curves in Sierpinski carpets

Authors: Estibalitz Durand-Cartagena and Jeremy T. Tyson

Issue: Volume 60 (2011), Issue 1, 285-310

Abstract:

We characterize the slopes of nontrivial line segments contained in self-similar and non-self-similar Sierpi\'nski carpets. The set of slopes is related to Farey sequences and the dynamics of punctured square toral billiards. Our results provide a first step towards a description of the rectifiable curves contained in such carpets.