### 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 language | English |
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Title of host publication | Unconventional Computation - 5th International Conference, UC 2006, Proceedings |

Publisher | Springer Verlag |

Pages | 181-194 |

Number of pages | 14 |

ISBN (Print) | 3540385932, 9783540385936 |

Publication status | Published - Jan 1 2006 |

Event | 5th International Conference on Unconventional Computation, UC 2006 - York, United Kingdom Duration: Sep 4 2006 → Sep 8 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4135 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 5th International Conference on Unconventional Computation, UC 2006 |
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Country | United Kingdom |

City | York |

Period | 9/4/06 → 9/8/06 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - The number of orbits of periodic box-ball systems

AU - Mikoda, Akihiro

AU - Inokuchi, Shuichi

AU - Mizoguchi, Yoshihiro

AU - Fujio, Mitsuhiko

PY - 2006/1/1

Y1 - 2006/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33749987008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749987008&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33749987008

SN - 3540385932

SN - 9783540385936

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 181

EP - 194

BT - Unconventional Computation - 5th International Conference, UC 2006, Proceedings

PB - Springer Verlag

ER -