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1998/1999 The Hausdorff Dimension of Hilbertʼs Coordinate Functions
Mark McClure
Real Anal. Exchange 24(2): 875-884 (1998/1999).


We characterize the coordinate functions of Hilbert's space-filling curve using a directed-graph iterated function system and use this to analyze their fractal properties. In particular, we show that both coordinate functions have graphs of Hausdorff dimension $\frac{3}{2}$ and level sets of dimension $\frac{1}{2}$.


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Mark McClure. "The Hausdorff Dimension of Hilbertʼs Coordinate Functions." Real Anal. Exchange 24 (2) 875 - 884, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 28 September 2010

zbMATH: 0937.53500
MathSciNet: MR1704763

Primary: 26A27

Keywords: Hausdorff dimension , self similarity , space filling curves

Rights: Copyright © 1999 Michigan State University Press

Vol.24 • No. 2 • 1998/1999
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