  Cellular automata (CA) are dynamical systems defined by a finite local rule
but they are studied for their global dynamics. They can exhibit a wide range
of complex behaviours and a celebrated result is the existence of
(intrinsically) universal CA, that is CA able to fully simulate any other CA.
In this paper, we show that the asymptotic density of universal cellular
automata is 1 in several families of CA defined by local symmetries. We extend
results previously established for captive cellular automata in two significant
ways. First, our results apply to well-known families of CA (e.g. the family of
outer-totalistic CA containing the Game of Life) and, second, we obtain such
density results with both increasing number of states and increasing
neighbourhood. Moreover, thanks to universality-preserving encodings, we show
that the universality problem remains undecidable in some of those families.
