Classification of Self-Affine Lattice Tilings
Classification of Self-Affine Lattice Tilings
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DOI：
10.1112/jlms/50.3.581
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发表时间：
1994-12
影响因子：
1.2
通讯作者：
C. Bandt;G. Gelbrich
中科院分区：
文献类型：
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作者：
C. Bandt;G. Gelbrich
我们通过一些紧凑集 A 的平移格子来考虑平面的平铺，使得 k 适当选择的平铺的并集类似于 A。定义了这种“k-爬行动物”的仿射和度量等价。我们证明，对于每一个 k⩾ 2 ，都有有限数量的等价类，其中 A 与圆盘同构。两块瓷砖有 3 种仿射类型，k= 3 的瓷砖有 7 种类型。
We consider tilings of the plane by a lattice of translates of some compact setAsuch that the union ofksuitably chosen tiles is similar toA. Affine and metric equivalence of such ‘k‐reptiles’ are defined. We show that for everyk⩾ 2 there is a finite number of equivalence classes for whichAis homeomorphic to a disk. There are three affine types of tiles with two pieces, and seven types withk= 3.