The Hausdorff Dimension of Hilbert's Coordinate Functions

@inproceedings{McClure1998TheHD,
  title={The Hausdorff Dimension of Hilbert's Coordinate Functions},
  author={Mark McClure},
  year={1998}
}
We characterize the coordinate functions of Hilbert's spacelling 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 Hausdor dimension 3 2 and level sets of dimension 1 2 . 

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Springer-Verlag

Hans Sagan, Space-Filling Curves
New York, • 1994
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Highly Influenced

On self-a ne functions.

Kon Norio Kono
Japan J. Appl. Math • 1986

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