Topological Dynamics of 2D Cellular Automata
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more complex. The main results are the existence of non sensitive CA without equicontinuous points, the non-recursivity of sensitivity constants and the existence of CA having only non-recursive equicontinuous points. They all show a difference between the 1D and the 2D case. Thanks to these new constructions, we also extend undecidability results concerning topological classification previously obtained in the 1D case.
KeywordsCellular Automaton Turing Machine Cellular Automaton Recursive Function Topological Dynamics
Unable to display preview. Download preview PDF.
- 2.Blanchard, F., Maass, A.: Dynamical properties of expansive one-sided cellular automata. Israel J. Math. 99 (1997)Google Scholar
- 5.Durand, B., Formenti, E., Varouchas, G.: On undecidability of equicontinuity classification for cellular automata. In: Morvan, M., Rémila, É. (eds.) DMCS 2003. Volume AB of DMTCS Proceedings, pp. 117–128 (2003)Google Scholar
- 7.Bernardi, V., Durand, B., Formenti, E., Kari, J.: A new dimension sensitive property for cellular automata. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 416–426. Springer, Heidelberg (2004)Google Scholar
- 8.Berger, R.: The undecidability of the domino problem. Mem. Amer. Math Soc. 66 (1966)Google Scholar
- 10.Wang, H.: Proving theorems by pattern recognition ii. Bell System Tech. Journal 40(2) (1961)Google Scholar