Fractal Structure of a Class of Two-Dimensional Two-State Cellular Automata
Fractal Structure of a Class of Two-Dimensional Two-State Cellular Automata
复制标题
一类二维二态元胞自动机的分形结构
DOI：
10.1109/candar.2017.89
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Namiki Takao
中科院分区：
文献类型：
--
作者：
Kawaharada Akane;Namiki Takao
众所周知，每一个符号数为素数的线性元胞自动机规则在适当的尺度下都有其极限集，然而，对于非线性元胞自动机规则，极限集的存在性即使在案例研究中也未见报道。本文研究了一类具有极限集的非线性二维元胞自动机规则的存在性及其极限集边界的盒维数。
It is well known that each linear cellular automaton rule with prime number of symbols has its limit set under suitable scaling, however, in case of nonlinear rules, the existence of limit set has not been reported even if case study. In the present paper the authors report on existence of a nonlinear two-dimensional cellular automaton rule which has limit set and on the box dimension of the boundary of its limit set.