Non-trivial collective behavior in three-dimensional totalistic illegal cellular automata with high connectivity

The collective behavior of totalistic illegal cellular automata rules in d = 3 with high connectivity is studied. Around 90 new rules show the non-trivial collective behavior P3 and QP3. Also a type-III intermittent behavior is found with scaling exponents -1 for the average transient time and -3/2 for the distribution of the laminar phases. The space of the rules is located obtaining the Shannon information function and using a mean-field approximation. The time autocorrelation function decays as a power law with an exponent of -1/2 for the quasiperiod-3 and with non-universal exponents for amplitude intermittent P2 and for some P2. (C) 1998 Elsevier Science B.V.