The number of orbits of periodic box-ball systems

Akihiro Mikoda, Shuichi Inokuchi, Yoshihiro Mizoguchi, Mitsuhiko Fujio

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

A box-ball system is a kind of cellular automata obtained by the ultradiscrete Lotka-Volterra equation. Similarities and differences between behavious of discrete systems (cellular automata) and continuous systems (differential equations) are investigated using techniques of ultradiscretizations. Our motivations is to take advantage of behavious of box-ball systems for new kinds of computations. Especially, we tried to find out useful periodic box-ball systems(pBBS) for random number generations. Applicable pBBS systems should have long fundamental cycles. We focus on pBBS with at most two kinds of solitons and investigate their behaviours, especially, the length of cycles and the number of orbits. We showed some relational equations of soliton sizes, a box size and the number of orbits. Varying a box size, we also found out some simulation results of the periodicity of orbits of pBBS with same kinds of solitons.

Original languageEnglish
Title of host publicationUnconventional Computation - 5th International Conference, UC 2006, Proceedings
PublisherSpringer Verlag
Pages181-194
Number of pages14
ISBN (Print)3540385932, 9783540385936
Publication statusPublished - Jan 1 2006
Event5th International Conference on Unconventional Computation, UC 2006 - York, United Kingdom
Duration: Sep 4 2006Sep 8 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4135 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th International Conference on Unconventional Computation, UC 2006
CountryUnited Kingdom
CityYork
Period9/4/069/8/06

Fingerprint

Solitons
Orbits
Ball
Orbit
Cellular automata
Random number generation
Cellular Automata
Differential equations
Lotka-Volterra Equations
Random number Generation
Cycle
Continuous System
Discrete Systems
Periodicity
Differential equation
Simulation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Mikoda, A., Inokuchi, S., Mizoguchi, Y., & Fujio, M. (2006). The number of orbits of periodic box-ball systems. In Unconventional Computation - 5th International Conference, UC 2006, Proceedings (pp. 181-194). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4135 LNCS). Springer Verlag.

The number of orbits of periodic box-ball systems. / Mikoda, Akihiro; Inokuchi, Shuichi; Mizoguchi, Yoshihiro; Fujio, Mitsuhiko.

Unconventional Computation - 5th International Conference, UC 2006, Proceedings. Springer Verlag, 2006. p. 181-194 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4135 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mikoda, A, Inokuchi, S, Mizoguchi, Y & Fujio, M 2006, The number of orbits of periodic box-ball systems. in Unconventional Computation - 5th International Conference, UC 2006, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4135 LNCS, Springer Verlag, pp. 181-194, 5th International Conference on Unconventional Computation, UC 2006, York, United Kingdom, 9/4/06.
Mikoda A, Inokuchi S, Mizoguchi Y, Fujio M. The number of orbits of periodic box-ball systems. In Unconventional Computation - 5th International Conference, UC 2006, Proceedings. Springer Verlag. 2006. p. 181-194. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Mikoda, Akihiro ; Inokuchi, Shuichi ; Mizoguchi, Yoshihiro ; Fujio, Mitsuhiko. / The number of orbits of periodic box-ball systems. Unconventional Computation - 5th International Conference, UC 2006, Proceedings. Springer Verlag, 2006. pp. 181-194 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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