An Equivalent of XOR Operator and Its Application in One-Dimensional CA Model

Abstract

In this paper, we study the probabilistic characterization of one dimensional cellular automaton model based on two values {0,1}. We propose a complex metric in order to characterize a one dimensional lattice with respect to the occupation probability also known as density. Based on numerical results, the proposed function is equivalent to XOR operator for two dimensional vector and for large system, it characterizes two phases with critical probability of p=0.5 which is the same result obtained using the information entropy function. In the second part, we study the variation of the proposed metric and the information entropy with respect to the repartition of the binary sequence that is generated using an optimal transformation of the logarithmic logistic map which is a non linear model of discrete dynamical system, numerical results illustrate the equivalence of the variations between both functions.