中国邮电高校学报(英文) ›› 2010, Vol. 17 ›› Issue (1): 67-72.doi: 10.1016/S1005-8885(09)60426-X

• Artificial Intelligence • 上一篇    下一篇

On behavior of two-dimensional cellular automata with
an exceptional rule under periodic boundary condition

翟莹,易忠,邓培民   

  1. Department of Mathematics, Guangxi Normal University, Guilin 541004, China
  • 收稿日期:2009-03-30 修回日期:1900-01-01 出版日期:2010-02-28
  • 通讯作者: 翟莹

On behavior of two-dimensional cellular automata with
an exceptional rule under periodic boundary condition

ZHAI Ying, YI Zhong, DENG Pei-min   

  1. Department of Mathematics, Guangxi Normal University, Guilin 541004, China
  • Received:2009-03-30 Revised:1900-01-01 Online:2010-02-28
  • Contact: ZHAI Ying

摘要:

This article deals with the behavior of two-dimensional (2-D) cellular automata (CA) with a special rule under periodic boundary condition by using matrix algebra. The important characteristics of CA have been studied, such as Garden of Eden (GOE), maximal transient length, maximal cycle length and so forth. Several necessary and sufficient conditions are provided, which guarantee a given configuration of being a GOE in different cases. Besides, algorithms are proposed to obtain the number of GOEs, the maximal transient length, and the maximal cycle length in such a CA with the rule mentioned above under periodic condition.

关键词:

cellular;automata,;GOE,;maximal;transient;length,;maximal;cycle;length

Abstract:

This article deals with the behavior of two-dimensional (2-D) cellular automata (CA) with a special rule under periodic boundary condition by using matrix algebra. The important characteristics of CA have been studied, such as Garden of Eden (GOE), maximal transient length, maximal cycle length and so forth. Several necessary and sufficient conditions are provided, which guarantee a given configuration of being a GOE in different cases. Besides, algorithms are proposed to obtain the number of GOEs, the maximal transient length, and the maximal cycle length in such a CA with the rule mentioned above under periodic condition.

Key words:

cellular automata;GOE;maximal transient length;maximal cycle length