Rectifiable curves in Sierpiński carpets

Estibalitz Durand-Cartagena, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review

Abstract

We characterize the slopes of nontrivial line segments contained in self-similar and non-self-similar Sierpiński 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.

Original languageEnglish (US)
Pages (from-to)285-309
Number of pages25
JournalIndiana University Mathematics Journal
Volume60
Issue number1
DOIs
StatePublished - 2011

Keywords

  • Farey fraction
  • Fractal
  • Rectifiable curve

ASJC Scopus subject areas

  • Mathematics(all)

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