A sufficient condition for aperiodicity of striped Wang tiles is established via parabola geometry, enabling explicit constructions of aperiodic sets for every pair of quadratic irrationals as vertical and horizontal stripe densities.
Combinatorics, Automata, and Number Theory , volume 135 of Encyclopedia of Mathematics and its Applications
2 Pith papers cite this work. Polarity classification is still indexing.
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Conditions on substitutions are exhibited under which Dumont-Thomas numeration systems derived from them are positional.
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An aperiodic set of Wang tiles for every quadratic irrational
A sufficient condition for aperiodicity of striped Wang tiles is established via parabola geometry, enabling explicit constructions of aperiodic sets for every pair of quadratic irrationals as vertical and horizontal stripe densities.
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Positionality of Dumont--Thomas numeration systems for integers
Conditions on substitutions are exhibited under which Dumont-Thomas numeration systems derived from them are positional.