The Number of Orbits of Periodic Box-Ball Systems

  • Akihiro Mikoda
  • Shuichi Inokuchi
  • Yoshihiro Mizoguchi
  • Mitsuhiko Fujio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4135)


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.


Cellular Automaton Random Number Generation Ball System Fundamental Cycle Kyushu Institute 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Akihiro Mikoda
    • 1
  • Shuichi Inokuchi
    • 2
  • Yoshihiro Mizoguchi
    • 2
  • Mitsuhiko Fujio
    • 3
  1. 1.Graduate School of MathematicsKyushu UniversityJapan
  2. 2.Faculty of MathematicsKyushu UniversityJapan
  3. 3.Department of Systems Innovation and InformaticsKyushu Institute of TechnologyJapan

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