不动点定理与非周期平铺
Fixed point theorem and aperiodic tilings
摘要：
我们提出了一个新的简单的建设的非周期瓦片集的基础上自引用（不动点）的论点。人们经常说，一些发现，它出现“提前”，这意味着它可以完全理解的背景下，只有思想发展后。对于本说明的主题，基于定点（自引用）方法构建非周期性瓦片集，情况正好相反。应该是在20世纪60年代第一次提出关于非周期性瓷砖集的问题时发现的：当时所有的工具都相当标准和广泛使用。然而，历史选择了一条不同的道路，许多不错的几何特设建设，而不是开发（由伯杰，罗宾逊，彭罗斯，阿曼和许多其他人。在这篇笔记中，我们试图纠正这个错误，并提出一个应该首先被发现的结构，但似乎被忽视了四十多年。
英文摘要：
We propose a new simple construction of an aperiodic tile set based on self-referential (fixed point) argument. People often say about some discovery that it appeared "ahead of time", meaning that it could be fully understood only in the context of ideas developed later. For the topic of this note, the construction of an aperiodic tile set based on the fixed-point (self-referential) approach, the situation is exactly the opposite. It should have been found in 1960s when the question about aperiodic tile sets was first asked: all the tools were quite standard and widely used at that time. However, the history had chosen a different path and many nice geometric ad hoc constructions were developed instead (by Berger, Robinson, Penrose, Ammann and many others. In this note we try to correct this error and present a construction that should have been discovered first but seemed to be unnoticed for more that forty years.
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