论文标题
一个自我施加的单一单位式瓷砖
A self-ruling monotile for aperiodic tiling
论文作者
论文摘要
整个平面可以用一个迫使大气线的单个瓷砖铺设吗？这被称为EIN Stein问题（在德语中，Ein Stein的意思是一个瓷砖）。本文提出了一种单电动物，该单位词通过设计提供了较高的瓷砖。它基于泰勒和社交（通过主要是六边形的非连接瓷砖强迫其多个神经性）和基于基序的六边形瓷砖而开发的单托动物。相反，在这里，单个替代规则会形成其形状，并且在应用时，迫使瓷砖具有多个。拟议的单电动物称为己sed，是自施加的。它由16个相同的六角形组成，称为枯萎，所有的都具有代表相同二进制标记的前卫边界。在枯竭的情况下，不需要图案才能使其起作用。可以将其他图案添加到单托动物中，以提供一些见解。使用此类基序以使用这种图案证明。
Can the entire plane be paved with a single tile that forces aperiodicity? This is known as the ein Stein problem (in German, ein Stein means one tile). This paper presents a monotile that delivers aperiodic tiling by design. It is based on the monotile developed by Taylor and Socolar (whose aperiodicity is forced by means of a non-connected tile that is mainly hexagonal) and motif-based hexagonal tilings that followed this major discovery. Here instead, a single substitution rule makes its shape, and when applying it, forces the tiling to be aperiodic. The proposed monotile, called HexSeed, is self-ruling. It consists of 16 identical hexagons, called subtiles, all with edgy borders representing the same binary marking. No motif is needed on the subtiles to make it work. Additional motifs can be added to the monotile to provide some insights. The proof of aperiodicity is presented with the use of such motifs.
