The article “A generalized neighborhood for cellular automata”, published by professor Dmitry Zaitsev in 2017 in the journal Theoretical Computer Science, was included in the rating list PlumX Metrics – Top Social Media Articles.
Cellular automata are a promising area of computer science for the organization of massively parallel computations and breakthroughs in many fields of science and technology due to the solution in an acceptable time of previously unsolvable tasks. A two-dimensional cellular automaton can be represented as a sheet of an ordinary grid notebook with cells of different colors that simultaneously change their color depending on the colors of the neighbors. Multidimensional cellular automata are the most suitable for solving problems of nuclear physics, new research in chemistry, biology, and the study of the human brain. Traditionally, two types of cell neighborhoods were used: von-Neumann and Moore. However, in multi-dimensional automata, the von-Neumann neighborhood (a “cross” for two dimensions) is too sparse, while the Moore neighborhood (a “three-cell square” for two dimensions) is too dense. A generalized neighborhood of Zaitsev, proposed and studied in the article, is a set of neighborhoods obtained by means of one or two parameters whose extreme values give the above classical neighborhoods. The computer program hmn provided by the author for public use generates the canvas of the cellular automaton model for the specified parameter values. During the publication of the article, two new numerical sequences A265014 and A266213 were proposed and adopted by the Online Encyclopedia of Integer Sequences to calculate the number of neighbors in different types of automata. New generalized neighborhoods allow building more accurate models for different applications of cellular automata. Currently, Zaitsev’s neighborhoods have been used to investigate cracks in the wear of materials by the laboratory of one of the well-known aircraft manufacturers, as well as in advanced virology studies.
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