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

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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  • 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.