Approximating dynamics of a number-conserving cellular automaton by a finite-dimensional dynamical system

Henryk Fukś and Yucen Jin ()
Additional contact information
Henryk Fukś: Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S3A1, Canada
Yucen Jin: Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S3A1, Canada

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 12, 1-18

Abstract: The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely dimensional system. While it is well known that this approximation works surprisingly well for some CA, it is still not clear why it is the case, and which CA rules have this property. In order to shed some light on this problem, we present an example of a four input CA for which probabilities of occurrence of short blocks of symbols can be computed exactly. This rule is number conserving and possesses a blocking word. Its local structure approximation correctly predicts steady-state probabilities of small length blocks, and we present a rigorous proof of this fact, without resorting to numerical simulations. We conjecture that the number-conserving property together with the existence of the blocking word are responsible for the observed perfect agreement between the finite-dimensional approximation and the actual infinite-dimensional dynamical system.

Keywords: Cellular automata; mean field; local structure; additive invariants (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183120501727
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:31:y:2020:i:12:n:s0129183120501727

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183120501727

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().