  The cellular automata with local permutation invariance are considered. We
show that in the two-state case the set of such automata coincides with the
generalized Game of Life family. We count the number of equivalence classes of
the rules under consideration with respect to permutations of states. This
reduced number of rules can be efficiently generated in many practical cases by
our C program. Since a cellular automaton is a combination of a local rule and
a lattice, we consider also maximally symmetric two-dimensional lattices. In
addition, we present the results of compatibility analysis of several rules
from the Life family.
