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- W2918448095 abstract "We introduce a new type of aperiodic hexagonal monotile; a prototile that admits infinitely many tilings of the plane, but any such tiling lacks any translational symmetry. Adding a copy of our monotile to a patch of tiles must satisfy two rules that apply only to adjacent tiles. The first is inspired by the Socolar--Taylor monotile, but can be realised by shape alone. The second is a local growth rule; a direct isometry of our monotile can be added to any patch of tiles provided that a tree on the monotile connects continuously with a tree on one of its neighbouring tiles. This condition forces tilings to grow along dendrites, which ultimately results in nonperiodic tilings. Our local growth rule initiates a new method to produce tilings of the plane." @default.
- W2918448095 created "2019-03-11" @default.
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- W2918448095 date "2019-03-04" @default.
- W2918448095 modified "2023-09-27" @default.
- W2918448095 title "An aperiodic monotile that forces nonperiodicity through a local dendritic growth rule" @default.
- W2918448095 hasPublicationYear "2019" @default.
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