Cellular automata and random field: Statistical analysis of complex space-time systems

Abstract

In the classical approach to the mathematical model specification, for space-time complex system, the usual framework is the Partial Difference-Differential Equations system (PDEs). This approach is very hard from a mathematical point of view, and the search for the (PDEs) solutions, almost in the practical applications, often it is impossible. Our approach is based, on the contrary, on Cellular Automata methodology in the framework of Random Field models. The statistical model building methodology for the Random Fields, is based on very simple statistical and probabilistic reasoning that utilize the concept of divisible distributions and logistic non-linear model. The interaction rules for the Cellular Automata mechanism, are built thorough inferential statistics and data analysis. © 2012 Springer-Verlag Berlin Heidelberg.