Intersecting the Twin Dragon with rational lines
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In: Journal of Fractal Geometry, Vol. 11.2024, No. 3-4, 10.09.2024, p. 205-217.
Research output: Contribution to journal › Article › Research › peer-review
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TY - JOUR
T1 - Intersecting the Twin Dragon with rational lines
AU - Akiyama, Shigeki
AU - Großkopf, Paul
AU - Loridant, Benoit
AU - Steiner, Wolfgang
N1 - Publisher Copyright: © 2024 European Mathematical Society.
PY - 2024/9/10
Y1 - 2024/9/10
N2 - 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.
AB - 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.
KW - Hausdorff dimension
KW - number system
UR - http://www.scopus.com/inward/record.url?scp=85208658438&partnerID=8YFLogxK
U2 - 10.4171/JFG/149
DO - 10.4171/JFG/149
M3 - Article
VL - 11.2024
SP - 205
EP - 217
JO - Journal of Fractal Geometry
JF - Journal of Fractal Geometry
SN - 2308-1317
IS - 3-4
ER -
