Intersecting the Twin Dragon with rational lines

Shigeki Akiyama; Paul Großkopf; Benoit Loridant; Wolfgang Steiner

doi:10.4171/JFG/149

Intersecting the Twin Dragon with rational lines

Shigeki Akiyama, Paul Großkopf, Benoit Loridant, Wolfgang Steiner

Lehrstuhl für Mathematik, Statistik und Geometrie (380)

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Begutachtung

Abstract

The Knuth Twin Dragon is a compact subset of the plane with fractal boundary of Hausdorff dimension s D .log λ/=.log ^p2/, λ ³ D λ ² C 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.

Originalsprache	Englisch
Seiten (von - bis)	205-217
Seitenumfang	13
Fachzeitschrift	Journal of Fractal Geometry
Jahrgang	11.2024
Ausgabenummer	3-4
DOIs	https://doi.org/10.4171/JFG/149
Publikationsstatus	Veröffentlicht - 10 Sept. 2024

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Publisher Copyright:
© 2024 European Mathematical Society.

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10.4171/JFG/149

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