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Fractal dimension of sets induced by bases of imaginary quadratic fields. (English) Zbl 0956.11022

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 W. J. Gilbert [Can. Math. Bull. 29, 495-500 (1986; Zbl 0564.10007)].

MSC:

11R11 Quadratic extensions
28A80 Fractals
11A63 Radix representation; digital problems

Citations:

Zbl 0564.10007
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References:

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