Intersecting the Twin Dragon with rational lines
The Knuth Twin Dragon is a compact subset of the plane with fractal boundary of Hausdorff dimension s = (\log \lambda)/(\log \sqrt{2}) , \lambda^{3} = \lambda^{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.
Authors
- Paul Großkopf
- Benoît Loridant
- Shigeki Akiyama (ORCID: https://orcid.org/0000-0001-7549-6686)
- Wolfgang Steiner (ORCID: https://orcid.org/0000-0002-3329-7213)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Libre de Bruxelles (BE)
- University of Tsukuba (JP)
- Montanuniversität Leoben (AT)
- Université Paris Cité (FR)
Publication Details
- Journal
- Journal of Fractal Geometry Mathematics of Fractals and Related Topics
- Published
- 2024-09-10
- DOI
- https://doi.org/10.4171/jfg/149
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche
- Austrian Science Fund
- Österreichische Agentur für Internationale Mobilität und Kooperation in Bildung, Wissenschaft und Forschung
- Japan Society for the Promotion of Science