Forcing Nonperiodicity with a Single Tile
Forcing Nonperiodicity
with a Single Tile
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使用单个图块强制非周期性
DOI：
10.1007/s00283-011-9255-y
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Joan M. Taylor
中科院分区：
文献类型：
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作者：
J. Socolar;Joan M. Taylor
非周期性原型是一种形状，可以安排无限多个副本完全填充欧几里得空间，没有重叠，但不是周期性模式。瓷砖理论家称这样的原型为“爱因斯坦”（德语双关语，意为“一块石头”）。自从伯杰发现了大量的原粒子组合在一起只能以非周期性的方式使平面倾斜以来，人们一直在思考爱因斯坦的可能存在。在本文中，我们回顾并澄清了我们最近引入的一个原型的一些特征，根据合理的定义，该原型是爱因斯坦。[This摘要未出现在已发表的文章中。
An aperiodic prototile is a shape for which infinitely many copies can be arranged to fill Euclidean space completely with no overlaps, but not in a periodic pattern. Tiling theorists refer to such a prototile as an "einstein" (a German pun on "one stone"). The possible existence of an einstein has been pondered ever since Berger's discovery of large set of prototiles that in combination can tile the plane only in a nonperiodic way. In this article we review and clarify some features of a prototile we recently introduced that is an einstein according to a reasonable definition. [This abstract does not appear in the published article.]