# Automata and ComplexityPeriods in the Q2R, X2R and Kawasaki-Q2R Cellular Automata

Automata and Complexity: Periods in the Q2R, X2R and Kawasaki-Q2R Cellular Automata [We study global and local periods of the cellular automaton Q2R, the equivalent model on a triangular grid (X2R) and a Kawasaki-Q2R update. The first two show similar results in both the global and local periods. We find a critical energy Ecp=-0.8700±0.0006\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{cp}=-0.8700 \pm 0.0006$$\end{document} for Q2R and Ecp=-0.88408±0.0004\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{cp} = -0.88408 \pm 0.0004$$\end{document} for X2R. In the Kawasaki-Q2R automaton dynamics finite global periods are present exclusively at very low energies and no critical energy is found. However, in all three cellular automata there is an evident formation of clusters of finite cycles. Ergodicity is violated.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Automata and ComplexityPeriods in the Q2R, X2R and Kawasaki-Q2R Cellular Automata

Part of the Emergence, Complexity and Computation Book Series (volume 42)
Automata and Complexity — Apr 20, 2022
12 pages      /lp/springer-journals/automata-and-complexity-periods-in-the-q2r-x2r-and-kawasaki-q2r-5dq10PdMcl
Publisher
Springer International Publishing
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-030-92550-5
Pages
43 –55
DOI
10.1007/978-3-030-92551-2_4
Publisher site
See Chapter on Publisher Site

### Abstract

[We study global and local periods of the cellular automaton Q2R, the equivalent model on a triangular grid (X2R) and a Kawasaki-Q2R update. The first two show similar results in both the global and local periods. We find a critical energy Ecp=-0.8700±0.0006\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{cp}=-0.8700 \pm 0.0006$$\end{document} for Q2R and Ecp=-0.88408±0.0004\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_{cp} = -0.88408 \pm 0.0004$$\end{document} for X2R. In the Kawasaki-Q2R automaton dynamics finite global periods are present exclusively at very low energies and no critical energy is found. However, in all three cellular automata there is an evident formation of clusters of finite cycles. Ergodicity is violated.]

Published: Apr 20, 2022