On Local Symmetries and Universality in Cellular Automata

Laurent Boyer & Guillaume Theyssier
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...