Space-filling curves and infinite graphs
Space-filling curves and infinite graphs
复制标题
空间填充曲线和无限图
DOI：
10.1007/bfb0000120
复制
发表时间：
1982
期刊：
影响因子：
--
通讯作者：
K. Subramanian
中科院分区：
文献类型：
--
作者：
R. Siromoney;K. Subramanian
皮亚诺和希尔伯特空间填充曲线形式的二维几何图案被表示为字符串、数组和图形。模式序列使得每条曲线都是后续曲线的前缀，因此我们得到保留前缀的 WDOL 来生成相应的字符串表示形式。极限语言可由 CDOL 系统生成，并由对应于皮亚诺曲线的单个无限字和对应于希尔伯特曲线的两个无限字组成。序列中每条曲线都是后续曲线的前缀的属性有助于定义表示无限曲线模式的无限数组和无限图，我们构造了上下文无关括号 Kolam 数组语法和图 DOL 系统的编码来生成序列和极限。
Two-dimensional geometric patterns in the form of the space filling curves of Peano and Hilbert are represented as a string, an array and a graph. The sequence of patterns is such that each curve is a prefix of the succeeding one and hence we get prefix preserving WDOL to generate the corresponding string representation. The limit language is generable by a CDOL system and consists of a single infinite word corresponding to the Peano curve and two infinite words for the Hilbert curve. The property that in the sequence each curve is a prefix of the succeeding one helps in the definition of the infinite arrays and infinite graphs representing the infinite curve patterns and we construct a Context-free Parentheses Kolam array grammar and a coding of a graph DOL system to generate the sequence as well as the limit.