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Inspired by the approach of kinetic theory of gases, a three-leveldescription (microscopic, mesoscopic and macroscopic) of cellular automaton ispresented. To provide an analytical treatment a simple domino cellularautomaton with avalanches was constructed. Formulas concerning exact relationsfor density, clusters, avalanches and other parameters in an equilibrium statewere derived. It appears that some relations are approximately valid fordeviations from the equilibrium, so the adequate Ito equation could beconstructed. The equation provides the time evolution description of somevariable on the macroscopic level. The results also suggest a motive forapplying of the procedure of construction of the Ito equation (from time seriesdata) to natural time series.

Three-level description of the domino cellular automaton