Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778861 | Indagationes Mathematicae | 2017 | 19 Pages |
Abstract
We study the topological properties of a class of planar crystallographic replication tiles. Let MâZ2Ã2 be an expanding matrix with characteristic polynomial x2+Ax+B (A,BâZ, Bâ¥2) and vâZ2 such that (v,Mv) are linearly independent. Then the equation MT+Bâ12v=Tâª(T+v)âª(T+2v)âªâ¯âª(T+(Bâ2)v)âª(âT)defines a unique nonempty compact set T satisfying To¯=T. Moreover, T tiles the plane by the crystallographic group p2 generated by the Ï-rotation and the translations by integer vectors. It was proved by Leung and Lau in the context of self-affine lattice tiles with collinear digit set that Tâª(âT) is homeomorphic to a closed disk if and only if 2|A|
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Benoît Loridant, Shu-Qin Zhang,