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
Y1 - 2006
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.
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U2 - 10.1007/11839132_15
DO - 10.1007/11839132_15
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
T2 - 5th International Conference on Unconventional Computation, UC 2006
Y2 - 4 September 2006 through 8 September 2006
ER -