DIMER AUTOMATA AND CELLULAR-AUTOMATA

We define a class of discrete dynamical systems which we call dimer au tomata. Whereas in a cellular automaton the new state of one cell is a function of the states in the neighborhood, in a dimer automaton the new states of two neighboring cells are functions of the states of the se two cells. Dimer automata with synchronous dynamics seem artificial , but with asynchronous dynamics such systems are very natural. They a re as simple as cellular automata; they have some advantages in modeli ng spatial spread. We present the definition, some easy consequences, a classification of one-dimensional dimer automata, a first approach t o determine a characteristic equation and a formula for an approximate asymptotic density as well as a comparison to computer simulations. F inally we compare synchronous and asynchronous cellular automata.