Intersecting the Twin Dragon with rational lines

Shigeki Akiyama, Paul Großkopf, Benoit Loridant, Wolfgang Steiner

Research output: Contribution to journalArticleResearchpeer-review

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.

Original languageEnglish
Pages (from-to)205-217
Number of pages13
JournalJournal of Fractal Geometry
Volume11.2024
Issue number3-4
DOIs
Publication statusPublished - 10 Sept 2024

Bibliographical note

Publisher Copyright: © 2024 European Mathematical Society.

Keywords

  • Hausdorff dimension
  • number system

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