Some Parameters Characterizing Cellular Automata Rules

Three parameters that can be used to characterize aspects of cellular automata behavior are considered for binary valued one-dimensional rules. These are the λ parameter, the Z parameter, and the obstruction (Θ) parameter. After a brief review of the λ and Z parameters, the Θ parameter is defined and shown to characterize the degree of nonadditivity of a rule. A derivation of the Z parameter in terms of rule table entries is given. It is shown that the λ parameter and Θ parameter are equal respectively to the area and volume under certain graphs. Finally, the nongenerative 3-site rules are listed in terms of these parameters and their decomposition into additive and nonadditive parts and certain regularities are noted.