Noisy collective behaviour in deterministic cellular automata

We investigate cellular automata in four and five dimensions for which Chaté and Manneville recently have found nontrivial collective behaviour. More precisely, though being fully deterministic, the average magnetization seems to be periodic respectively quasiperiodic, with superimposed noise whose amplitude decreases with system size. We confirm this behaviour on very large systems and over very large times. We analyse in detail the statistical properties of the “noise”. Systems on small lattices and/or subject to additional external noise are metastable. Arguments by Grinstein et al. suggest that in the periodic case the infinite deterministic systems should be metastable too. These arguments are generalized to quasiperiodic systems. We find evidence that they do indeed apply, but we find no direct evidence for metastability of large systems.