Complex Dynamic Behaviors in Cellular Automata Rule 14. (22nd April 2012)

• Record Type: Journal Article
• Authors: Han, Qi; Liao, Xiaofeng; Li, Chuandong
• Other Names: Singh Vimal Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2012(2012)
• Publication Date: 2012-04-22
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2012/258309
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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 σ τ -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.