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An aperiodic monotile that forces nonperiodicity through dendrites
Bulletin of the London Mathematical Society ( IF 0.787 ) Pub Date : 2020-06-28 , DOI: 10.1112/blms.12375
Michael Mampusti; Michael F. Whittaker

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 dendrite 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 dendrite rule initiates a new method to produce tilings of the plane.
更新日期:2020-06-29

 

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