Tiling Spaces of Taylor-Socolar Tilings
Tiling Spaces of Taylor-Socolar Tilings
复制标题
Taylor-Socolar 平铺的平铺空间
DOI：
10.12693/aphyspola.126.508
复制
发表时间：
2014
影响因子：
0.7
通讯作者：
J.
中科院分区：
文献类型：
--
作者：
J.
泰勒太阳能瓷砖作为一种非周期性的单瓦瓷砖被引入。我们考虑了一个平铺空间，它由所有的平铺组成，这些平铺在局部上与Taylor Socolar平铺没有区别，并研究了它的结构。结果表明，除了在Q中测度为0的密集点集上，Taylor Socolar平铺空间与Q进空间(Q)的紧阿贝尔群之间存在一个双射映射，由此我们可以推导出Taylor Socolar平铺具有准晶体结构。我们从Taylor Socolar平铺中制作奇偶平铺，通过白色瓷砖识别Taylor Socolar平铺中所有旋转版本的瓷砖，并通过灰色瓷砖识别所有反向版本的瓷砖。证明了泰勒索克拉平铺是由这个宇称平铺相互局部可导的。
The Taylor Socolar tiling has been introduced as an aperiodic mono-tile tiling. We consider a tiling space which consists of all the tilings that are locally indistinguishable from a Taylor Socolar tiling and study its structure. It turns out that there is a bijective map between the space of the Taylor Socolar tilings and a compact Abelian group of a Q-adic space (Q) except at a dense set of points of measure 0 in Q. From this we can derive that the Taylor Socolar tilings have quasicrystalline structures. We make a parity tiling from the Taylor Socolar tiling identifying all the rotated versions of a tile in the Taylor Socolar tiling by white tiles and all the re ected versions of the tile by gray tiles. It turns out that the Taylor Socolar tiling is mutually locally derivable from this parity tiling.