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J. von Neumann, “Theory of Self-Reproducing Automata,” University of Illinois Press, Urbana and London, 1966.

has been cited by the following article:

• TITLE: Transitivity and Chaoticity in 1-D Cellular Automata

  AUTHORS: Fangyue Chen, Guanrong Chen, Weifeng Jin

  KEYWORDS: Bernoulli Subshift of Finite Type; Cellular Automata; Devaney Chaos; Symbolic Dynamics; Topological Transitivity

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.2 No.1A, March 29, 2013

  ABSTRACT: Recent progress in symbolic dynamics of cellular automata (CA) shows that many CA exhibit rich and complicated Bernoulli-shift properties, such as positive topological entropy, topological transitivity and even mixing. Noticeably, some CA are only transitive, but not mixing on their subsystems. Yet, for one-dimensional CA, this paper proves that not only the shift transitivity guarantees the CA transitivity but also the CA with transitive non-trivial Bernoulli subshift of finite type have dense periodic points. It is concluded that, for one-dimensional CA, the transitivity implies chaos in the sense of Devaney on the non-trivial Bernoulli subshift of finite types.