ABSTRACT
Cellular automata are automata distributed on the nodes of a periodic lattice, a discrete geometrical structure invariant under certain translation and rotation operations. Historically, the first cellular automata proposed by von Neumann were on the nodes of a two-dimensional square grid. The first studies on automata networks, in particular on von Neumann's self-reproducing automata, dealt with cellular automata. One-dimensional cellular automata lattices are textbook models which, despite very simple structures, exhibit a variety of behaviors. Symmetric boolean functions with three inputs, that is to say functions for which the inputs on the right and the left behave symmetrically, belong to one of these three classes. Since there are only 16 boolean functions with two inputs, it does not take long to study all of them completely. The function with code 0 always converges in one iteration to the configuration in which all automata are in state 0, regardless of the initial state.
