Characterization of cellular automata rules using quantitative lattice properties

Abstract

The properties of the one-dimensional cellular automata are quantified using the concepts of kinetic energy K and the entropy S. Upon imposing that the system is isolated, it was shown that the total energy E is conserved. Using the randomly-initialized CA system as reference, it is observed that a sense of order produced by self-organization (rule) translate to a decrease in kinetic energy ΔK < 0 and entropy ΔS . Using the deviation of the kinetic energy and entropy values of the system from the random case, the dynamics of different CA rule are characterized. A resulting phase space of the resulting dynamics is shown to lie into different distinct regions of the K − S phase plot.