The Finite Number of Interior Component Shapes of the Levy Dragon
The Finite Number of Interior Component Shapes of the Levy Dragon
复制标题
Levy Dragon 的有限数量的内部组件形状
DOI：
10.1007/s00454-009-9211-1
复制
发表时间：
2010
影响因子：
0.8
通讯作者：
E. Alster
中科院分区：
文献类型：
--
作者：
E. Alster
利维龙是一个相连的自相似瓷砖，内部不相连。此前已知其内部部件至少有16种不同形状。利用汇聚成 Levy 龙的无限曲线序列的简单性质，证明了内部组件的不同形状的数量是有限的。给出了将这些形状构建为三个凸多边形形状的各种收缩的并集的详细描述，并确定了形状的数量。
The Levy dragon is a connected self-similar tile with disconnected interior. It was previously known that there are at least 16 different shapes of its interior components. Using simple properties of an infinite sequence of curves which converge into the Levy dragon, it is proved that the number of different shapes of the interior components is finite. A detailed description of the buildup of those shapes as unions of various contractions of three convex polygonal shapes is given, and the number of shapes is determined.