Transitivity and Chaoticity in 1-D Cellular Automata

Fangyue Chen, Guanrong Chen, Weifeng Jin
2013 International Journal of Modern Nonlinear Theory and Application  
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
more » ... ite 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.
doi:10.4236/ijmnta.2013.21a008 fatcat:v352f2dehndvfb5ji2zmyq35yu