Dimer automata and cellular automata

Abstract We define a class of discrete dynamical systems which we call dimer automata. 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 these two cells. Dimer automata with synchronous dynamics seem artificial, but with asynchronous dynamics such systems are very natural. They are as simple as cellular automata; they have some advantages in modeling spatial spread. We present the definition, some easy consequences, a classification of one-dimensional dimer automata, a first approach to determine a characteristic equation and a formula for an approximate asymptotic density as well as a comparison to computer simulations. Finally we compare synchronous and asynchronous cellular automata.

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