Three-level description of the domino cellular automaton
Zbigniew Czechowski, Mariusz Białecki · Journal of Physics A Mathematical and Theoretical · 2012
Motivated by the approach of kinetic theory of gases, a three-level description (microscopic, mesoscopic and macroscopic) of cellular automaton is presented. To provide an analytical treatment, a simple domino cellular automaton with avalanches is constructed. Formulas concerning exact relations for density, clusters, avalanches and other parameters in a stationary state are derived. Some relations approximately valid for deviations from the stationary state are found, and the adequate Ito equation is constructed. It provides the time evolution description of the density on the macroscopic level. The results support an idea of application of the Ito equation to some natural time series.