Spectrum of Elementary Cellular Automata and Closed Chains of Contours ^†

In this paper, we study the properties of some elementary automata. We have obtained the characteristics of these cellular automata. The concept of the spectrum for a more general class than the class of elementary automata is introduced. We introduce and study discrete dynamical systems which represents the transport of mass on closed chains of contours. Particles on contours move in accordance with given rules. These dynamical systems can be interpreted as cellular automata. Contributions towards this study are as follows. The characteristics of some elementary cellular automata have been obtained. A theorem about the velocity of particles’ movement on the closed chain has been proved. It has been proved that, for any ε > 0 , there exists a chain with flow density ρ < ε such that the average flow particle velocity is less than the velocity of free movement. An interpretation of this system as a transport model is given. The spectrum of a binary closed chain with some conflict resolution rule is studied