Abstract
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both configurations become identical after a reasonable time. We prove coalescence for two elementary rules and show that there exists infinitely many coalescing CA. We then conduct an experimental study on all elementary CA and show that some rules exhibit a phase transition, which belongs to the universality class of directed percolation.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Fatès, N., Morvan, M.: An experimental study of robustness to asynchronism for elementary cellular automata. Complex Systems 16 (2005) (to appear)
Kaulakys, B., Ivanauskas, F., Mekauskas, T.: Synchronization of chaotic systems driven by identical noise. International Journal of Bifurcation and Chaos 9(3), 533–539 (1999)
Fates, N., Regnault, D., Schabanel, N., Thierry, E.: Asynchronous behavior of double-quiescent elementary cellular automata. In: LATIN (2006) (to appear)
Hinrichsen, H.: Nonequilibrium critical phenomena and phase transitions into absorbing states. Advances in Physics, 815 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rouquier, JB., Morvan, M. (2006). Coalescing Cellular Automata. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758532_44
Download citation
DOI: https://doi.org/10.1007/11758532_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34383-7
Online ISBN: 978-3-540-34384-4
eBook Packages: Computer ScienceComputer Science (R0)