Intersection the twin dragon with rational lines
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909122805366784 |
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| author | Akiyama, Shigeki Grosskopf, Paul Loridant, Benoît Steiner, Wolfgang |
| author_facet | Akiyama, Shigeki Grosskopf, Paul Loridant, Benoît Steiner, Wolfgang |
| contents | The Knuth Twin Dragon is a compact subset of the plane with fractal boundary of Hausdorff dimension $s = (\log λ)/(\log \sqrt{2})$, $λ^3 = λ^2 + 2$. Although the intersection with a generic line has Hausdorff dimension $s-1$, we prove that this does not occur for lines with rational parameters. We further describe the intersection of the Twin Dragon with the two diagonals as well as with various axis parallel lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intersection the twin dragon with rational lines Akiyama, Shigeki Grosskopf, Paul Loridant, Benoît Steiner, Wolfgang Metric Geometry The Knuth Twin Dragon is a compact subset of the plane with fractal boundary of Hausdorff dimension $s = (\log λ)/(\log \sqrt{2})$, $λ^3 = λ^2 + 2$. Although the intersection with a generic line has Hausdorff dimension $s-1$, we prove that this does not occur for lines with rational parameters. We further describe the intersection of the Twin Dragon with the two diagonals as well as with various axis parallel lines. |
| title | Intersection the twin dragon with rational lines |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2402.18371 |