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 language | English (US) |
|---|---|
| Pages (from-to) | 285-309 |
| Number of pages | 25 |
| Journal | Indiana University Mathematics Journal |
| Volume | 60 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2011 |
Keywords
- Farey fraction
- Fractal
- Rectifiable curve
ASJC Scopus subject areas
- General Mathematics
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