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The Hausdorff Dimension of Hilbertʼs Coordinate Functions
- Source :
- Real Anal. Exchange 24, no. 2 (1999), 875-884
- Publication Year :
- 1999
- Publisher :
- Michigan State University Press, 1999.
-
Abstract
- 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 $\frac{1}{2}$.
- Subjects :
- 26A27
self similarity
Hausdorff dimension
space filling curves
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Real Anal. Exchange 24, no. 2 (1999), 875-884
- Accession number :
- edsair.project.eucl..e24e9d006c7c0d8d9e590290d1b4ea59