Dynamics of Cellular Automata in Noncompact Spaces

Formenti, Enrico; Kůrka, Petr

doi:10.1007/978-1-4939-8700-9_138

Enrico Formenti³ &
Petr Kůrka^4,5

Part of the book series: Encyclopedia of Complexity and Systems Science Series ((ECSSS))

1232 Accesses

Originally published in

R. A. Meyers (ed.), Encyclopedia of Complexity and Systems Science, © Springer-Verlag 2009

https://doi.org/10.1007/978-0-387-30440-3_138

Glossary

Almost equicontinuous CA:: A CA which has at least one equicontinuous configuration.
Attraction basin:: The set of configurations whose orbit is eventually attracted by an attractor.
Attractor:: A closed invariant set which attracts all orbits in some of its neighborhood.
Besicovitch pseudometrics:: A pseudometric that quantifies the upper-density of differences.
Blocking word:: A word that interrupts the information flow. A configuration containing an infinite number of blocking words both to the right and to the is equicontinuous in the Cantor topology.
Equicontinuous CA:: A CA in which all configurations are equicontinuous.
Equicontinuous configuration:: A configuration for which nearby configurations remain close.
Expansive CA:: Two distinct configurations, no matter how close, eventually separate during the evolution.
Generic space:: The space of configurations for which upper-density and lower-density coincide.
Sensitive CA:: In any neighborhood of any configuration there exists a...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 549.99; Price excludes VAT (USA)

Hardcover Book: USD 799.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

Primary Literature

Besicovitch AS (1954) Almost periodic functions. Dover, New York
Google Scholar
Blanchard F, Formenti E, Kůrka P (1999) Cellular automata in the Cantor, Besicovitch and Weyl spaces. Complex Syst 11(2):107–123
MathSciNet MATH Google Scholar
Blanchard F, Cervelle J, Formenti E (2005) Some results about the chaotic behaviour of cellular automata. Theor Comput Sci 349(3):318–336
Article Google Scholar
Cattaneo G, Formenti E, Margara L, Mazoyer J (1997) A shiftinvariant metric on S^ℤ inducing a nontrivial topology, Lecture notes in computer science, vol 1295. Springer, Berlin
MATH Google Scholar
Formenti E, Kůrka P (2007) Subshift attractors of cellular automata. Nonlinearity 20:105–117
Article MathSciNet Google Scholar
Hedlund GA (1969) Endomorphisms and automorphisms of the shift dynamical system. Math Syst Theory 3:320–375
Article MathSciNet Google Scholar
Hurd LP (1990) Recursive cellular automata invariant sets. Complex Syst 4:119–129
MathSciNet MATH Google Scholar
Iwanik A (1988) Weyl almost periodic points in topological dynamics. Colloquium Mathematicum 56:107–119
Article MathSciNet Google Scholar
Kamae J (1973) Subsequences of normal sequences. Isr J Math 16(2):121–149
Article MathSciNet Google Scholar
Knudsen C (1994) Chaos without nonperiodicity. Am Math Mon 101:563–565
Article MathSciNet Google Scholar
Kůrka P (1997) Languages, equicontinuity and attractors in cellular automata. Ergod Theory Dyn Syst 17:417–433
Article MathSciNet Google Scholar
Kůrka P (2003) Cellular automata with vanishing particles. Fundamenta Informaticae 58:1–19
MathSciNet Google Scholar
Kůrka P (2005) On the measure attractor of a cellular automaton. Discret Continuous Dyn Syst 2005(suppl):524–535
MathSciNet Google Scholar
Marcinkiewicz J (1939) Une remarque sur les espaces de a.s. Besicovitch, vol 208. C R Acad Sci, Paris, pp 157–159
MATH Google Scholar
Sablik M (2006) étude de l’action conjointe d’un automate cellulaire et du décalage: une approche topologique et ergodique. Université de la Mediterranée, PhD thesis
Google Scholar

Books and Reviews

Besicovitch AS (1954) Almost periodic functions. Dover, New York
Google Scholar
Kitchens BP (1998) Symbolic dynamics. Springer, Berlin
Book Google Scholar
Kůrka P (2003) Topological and symbolic dynamics, Cours spécialisés, vol 11. Société Mathématique de France, Paris
Google Scholar
Lind D, Marcus B (1995) An introduction to symbolic dynamics and coding. Cambridge University Press, Cambridge
Book Google Scholar

Download references

Acknowledgments

We thank Marcus Pivato and Francois Blanchard for careful reading of the paper and many valuable suggestions. The research was partially supported by the Research Program Project “Sycomore” (ANR-05-BLAN-0374).

Author information

Authors and Affiliations

Laboratoire I3S – UNSA/CNRS UMR 6070, Université de Nice Sophia Antipolis, Sophia Antipolis, France
Enrico Formenti
Département d’Informatique, Université de Nice Sophia Antipolis, Nice, France
Petr Kůrka
Center for Theoretical Study, Academy of Sciences and Charles University, Prague, Czechia
Petr Kůrka

Authors

Enrico Formenti
View author publications
You can also search for this author in PubMed Google Scholar
Petr Kůrka
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Enrico Formenti .

Editor information

Editors and Affiliations

Unconventional Computing Centre, University of the West of England, Bristol, UK
Andrew Adamatzky

Rights and permissions

Reprints and permissions

Copyright information

About this entry

Cite this entry

Formenti, E., Kůrka, P. (2009). Dynamics of Cellular Automata in Noncompact Spaces. In: Adamatzky, A. (eds) Cellular Automata. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8700-9_138

Download citation

DOI: https://doi.org/10.1007/978-1-4939-8700-9_138
Published: 28 November 2018
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-8699-6
Online ISBN: 978-1-4939-8700-9
eBook Packages: Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

Publish with us

Policies and ethics