The Study of one-dimensional cellular automata with nearest-nearest neighborhoods
In this paper, we deal with the global equivalence classification of one-dimensional cellular automata (CA) with nearest-nearest neighborhoods. We present a theoretical classification of all rules through the two homeomorphisms identified in 1. we demonstrate the 30 global equivalence classes of 64 additive rules, and show that in the same equivalence class they have the same number of independent connected component(s) for any L (number of cells). Furthermore, basing on this platform, we also explore the global equivalence class of totalistic rule 20 and 52, which are reputedly capable of highly complex dynamical behaviors and belong to Wolframs class IV. It is worth mentioning that the classification method we have presented are actually applicable to one-dimensional CA with any neighborhood radius.
Shaowei Shen Junbiao Guan
College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou, Zhejiang, 310018, P.R. School of Science Hangzhou Dianzi University Hangzhou, Zhejiang, 310018, P.R.China
国际会议
2010国际混沌、分形理论与应用研讨会(IWCFTA 2010)
昆明
英文
232-236
2010-10-29（万方平台首次上网日期，不代表论文的发表时间）