Fundamental Cycle of a Periodic Box-Ball System
  We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state. 
Daisuke Yoshihara, Fumitaka Yura and Tetsuji Tokihiro