On Oscillations in Cellular Automata
  We investigate cellular automata where some global quantity varies periodically or quasiperiodically with time. We find that these systems are highly predictable, and can be rather well described by a set of mean-field variables. We conclude that this is not a collective phenomenon - where different subsystems are supposed to synchronize - but rather like many very weakly coupled oscillators fluctuating around one exact frequency. The global quantity measured is a mean taken over all these subsystems, and gets more precise the larger the system is. 
Jan Hemmingsson and Hans J. Herrmann