Characteristic Dynamics of Elementary Cellular Automata with a Single Conserved Quantity
We show that several rules in Wolfram’s elementary cellular automata have a single conserved quantity and that they commonly show two kinds of characteristic dynamical behavior. One is the density classification. Each rule classifies the density of its conserved quantity in the same sense that Capcarrère and Sipper proved for rule 184. The other is the nonequilibrium phase transition similar to that shown by the TASEP. Possible relations between the number of conserved quantities and the dynamical behavior is discussed.