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The topological structure of fractal tilings generated by quadratic number systems. (English) Zbl 1123.11004

The authors study topological properties of tilings associated with number systems of \(\mathbb Z[\alpha]\), where \(\alpha\) is a quadratic number: fractal boundary, interior, graphs determining the set of neighbors of a given tile. Their approach is twofold, using both geometry of numbers and automata theory.

MSC:

11A63 Radix representation; digital problems
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
28A80 Fractals
37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010)
05B45 Combinatorial aspects of tessellation and tiling problems
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
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