Intersection the twin dragon with rational lines

Fuente: arXiv
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Bibliographic Details
Main Authors: Akiyama, Shigeki, Grosskopf, Paul, Loridant, Benoît, Steiner, Wolfgang
Format: Preprint
Published: 2024
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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