Eventually Number-Conserving Cellular Automata

We present a preliminary study of a new class of two-input cellular automaton rules called eventually number-conserving rules characterized by the property of evolving after a finite number of time steps to states whose number of active sites remains constant. Viewed as models of systems of interacting particles, these rules obey a kind of Darwinian principle by either annihilating unnecessary particles or creating necessary ones. Our main objective is to discuss possible characterizations and show how to determine such rules possessing a given limit set.