Converging properties of one-dimensionnal monotonous cellular automa
A cellular automaton is monotonous if it preserves the order on configurations inherited from an order on
states. If at first sight, the significantly sparse aspect of that product order lead us to believe that mono-
tonicity would not be that restrictive, the fact that cellular automata are characterised by a local rule
applied shift-invariantly makes the impact of this constraint more remarkable than expected. After intro-
ducing the basic concepts of our work, we first state general results about monotonous cellular automata