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• W2963943941 abstract "We present a single, connected tile which can tile the plane but only non-periodically. The tile is hexagonal with edge markings, which impose simple rules as to how adjacent tiles are allowed to meet across edges. The first of these rules is a standard matching rule, that certain decorations match across edges. The second condition is a new type of matching rule, which allows tiles to meet only when certain decorations in a particular orientation are given the opposite charge. This forces the tiles to form a hierarchy of triangles, following a central idea of the Socolar--Taylor tilings. However, the new edge-to-edge orientational matching rule forces this structure in a very different way, which allows for a surprisingly simple proof of aperiodicity. We show that the hull of all tilings satisfying our rules is uniquely ergodic and that almost all tilings in the hull belong to a minimal core of tilings generated by substitution. Identifying tilings which are charge-flips of each other, these tilings are shown to have pure point dynamical spectrum and a regular model set structure." @default.
• W2963943941 created "2019-07-30" @default.
• W2963943941 creator A5076810096 @default.
• W2963943941 creator A5086896962 @default.
• W2963943941 date "2021-10-18" @default.
• W2963943941 modified "2023-09-23" @default.
• W2963943941 title "AN APERIODIC TILE WITH EDGE-TO-EDGE ORIENTATIONAL MATCHING RULES" @default.
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• W2963943941 doi "https://doi.org/10.1017/s1474748021000517" @default.
• W2963943941 hasPublicationYear "2021" @default.
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