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arXiv · 1210.3967

Hexagonal inflation tilings and planar monotiles

Michael Baake·Franz Gähler·Uwe Grimm
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Abstract

Aperiodic tilings with a small number of prototiles are of particular interest, both theoretically and for applications in crystallography. In this direction, many people have tried to construct aperiodic tilings that are built from a single prototile with nearest neighbour matching rules, which is then called a monotile. One strand of the search for a planar monotile has focussed on hexagonal analogues of Wang tiles. This led to two inflation tilings with interesting structural details. Both possess aperiodic local rules that define hulls with a model set structure. We review them in comparison, and clarify their relation with the classic half-hex tiling. In particular, we formulate various known results in a more comparative way, and augment them with some new results on the geometry and the topology of the underlying tiling spaces.

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Michael Baake, Franz Gähler, Uwe Grimm. 2012-10-15. Hexagonal inflation tilings and planar monotiles. https://doi.org/10.3390/sym4040581

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