Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 258309, 12 pages
Research Article

Complex Dynamic Behaviors in Cellular Automata Rule 14

State Key Laboratory of Power Transmission Equipment and System Security, College of Computer Science, Chongqing University, Chongqing 400030, China

Received 2 November 2011; Revised 1 February 2012; Accepted 1 February 2012

Academic Editor: Vimal Singh

Copyright © 2012 Qi Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Wolfram divided the 256 elementary cellular automata rules informally into four classes using dynamical concepts like periodicity, stability, and chaos. Rule 14, which is Bernoulli στ-shift rule and is a member of Wolfram’s class II, is said to be simple as periodic before. Therefore, it is worthwhile studying dynamical behaviors of rule 14, whether it possesses chaotic attractors or not. In this paper, the complex dynamical behaviors of rule 14 of one-dimensional cellular automata are investigated from the viewpoint of symbolic dynamics. We find that rule 14 is chaotic in the sense of both Li-Yorke and Devaney on its attractor. Then, we prove that there exist fixed points in rule 14. Finally, we use diagrams to explain the attractor of rule 14, where characteristic function is used to describe that all points fall into Bernoulli-shift map after two iterations under rule 14.