Next Article in Journal
Non-Extensivity of the Configurational Density Distribution in the Classical Microcanonical Ensemble
Previous Article in Journal
Generalised Entropy of Curves for the Analysis and Classification of Dynamical Systems
Article Menu

Export Article

Open AccessArticle

The Topological Pressure of Linear Cellular Automata

Department of Applied Mathematics, National Dong Hwa University, 97063, Hualian, Taiwan, R.O.C.
Taida Institute for Mathematical Sciences, National Taiwan University, 10617, Taipei, Taiwan, R.O.C.
National Center for Theoretical Sciences, Mathematics Division, National Tsing Hua University, 30043, Hsinchu, Taiwan, R.O.C.
Author to whom correspondence should be addressed.
Entropy 2009, 11(2), 271-284;
Received: 13 April 2009 / Accepted: 6 May 2009 / Published: 11 May 2009
PDF [241 KB, uploaded 24 February 2015]


This elucidation studies ergodicity and equilibrium measures for additive cellular automata with prime states. Additive cellular automata are ergodic with respect to Bernoulli measure unless it is either an identity map or constant. The formulae of measure-theoretic and topological entropies can be expressed in closed forms and the topological pressure is demonstrated explicitly for potential functions that depend on finitely many coordinates. According to these results, Parry measure is inferred to be an equilibrium measure. View Full-Text
Keywords: Cellular automata; additive; equilibrium measure Cellular automata; additive; equilibrium measure
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

Ban, J.-C.; Chang, C.-H. The Topological Pressure of Linear Cellular Automata. Entropy 2009, 11, 271-284.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top