CELLULAR AUTOMATON WITH PERCOLATION AS A DYNAMIC SYSTEM: ENTROPY APPROACH

A model of information confrontation based on a two-dimensional percolation-cellular automaton on a closed oriented surface is constructed and implemented programmatically. Numerical experiments were performed. A theorem on the finiteness of a completely positive topological entropy of a given cellular automaton is formulated and proved. As an applied application of the constructed automaton, a retrospective forecast of the results of the Russian Presidential election in 2018 was made both in Russia as a whole and in two regions of Russia. The General logic of using the automaton was as follows. At the preparatory stage, a model of the region was built, which is a field of a cellular automaton. In the case of regions, anamorphic mapping was used, in which each territorial-administrative unit is represented by a certain number of cells that occupy a connected area of the field of the automaton; the areas of these areas are proportional to the number of voters, and if possible, geographical neighbors are preserved. The color of the cell corresponds to a certain political position; for example, if a certain city has 60% support for the President, then this percentage of cells in that city is red. As initial data for the calculation, the results of sociological surveys on support for the current President conducted 6-12 months before the election were taken; the dynamics of the system is modeled using a cellular automaton; for the formed stationary solution, the shares of cells corresponding to the number of supporters and opponents of the President, as well as non-appearance, are calculated; these shares are taken as a forecast of election results. Those constructed in this way showed significantly lower accuracy than forecasts made using standard sociological methods in the last days before the election. However, they can be used for early forecasting. The reason for this difference is that the opinions of voters immediately prior to elections are determined by campaign, and long before the election - the prevalence and embeddedness of value orientations, which is incorporated in the model.

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