Open Access
2005-2006 On the coordinate functions of Lévy’s dragon curve.
Pieter C. Allaart, Kiko Kawamura
Author Affiliations +
Real Anal. Exchange 31(1): 295-308 (2005-2006).


Lévy's dragon curve [P. Lévy, Les courbes planes ou gauches et les surfaces composées de parties semblables au tout, J. Ecole Polytechn., 227-247, 249-291 (1938)] is a well-known self-similar planar curve with non-empty interior. We derive an arithmetic expression for the coordinate functions of Lévy's dragon curve, and show that the 3/2 -dimensional Hausdorff measure of the graph of each coordinate function is strictly positive and finite. This complements known dimensional results concerning the coordinate functions of space-filling curves of Peano and Hilbert. The proof is based on deriving suitable uniform upper bounds for the sizes of the graphs' level sets.


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Pieter C. Allaart. Kiko Kawamura. "On the coordinate functions of Lévy’s dragon curve.." Real Anal. Exchange 31 (1) 295 - 308, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1111.28006
MathSciNet: MR2218845

Primary: 26A27

Keywords: coordinate function , Hausdorff dimension , Levy's dragon curve

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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