Fractal dimension of sets induced by bases of imaginary quadratic fields (Q2702763)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fractal dimension of sets induced by bases of imaginary quadratic fields |
scientific article |
Statements
13 March 2001
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canonical number system
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fractal dimension
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Fractal dimension of sets induced by bases of imaginary quadratic fields (English)
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Each base of a canonical number system in an imaginary quadratic field induces the tiling of the plane. One piece of this tiling consists of all complex numbers with fixed integral part. A formula enabling to calculate the fractal dimension of the boundary of a tile is derived. It is a generalisation of the previous result of \textit{W. J. Gilbert} [Can. Math. Bull. 29, 495-500 (1986; Zbl 0564.10007)].
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