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Shape of Diamond Pushes Forward Computer Science

A new sequence, submitted by Professor Dmitry Zaitsev from International Humanitarian University, Odessa, Ukraine to "The On-Line Encyclopedia of Integer Sequences" on 24 December 2015, has been recently approved. 
Von Neumann studied self-reproducing cellular automata with a “cross shaped” neighborhood on a plane. A diamond-shaped neighborhood generalizes it on multidimensional space and radius greater than one. Zaitsev numbers specify the number of cells on a surface of a diamond-shaped neighborhood while Delannoy numbers specify the total number of cells in this neighborhood. Besides, Professor Zaitsev offered a generalized neighborhood which spans the range between von Neumann's and Moore's neighborhoods using a parameter to adjust the number and location of neighboring cells. Moore's neighborhood represents a hypercube in a multidimensional lattice and the parameter specifies dimension of facets which connect a cell to its neighbors. 
program generates canvas of the cellular structure represented with connections between neighboring cells in the form of a Petri net. A simple cell model of the canvas can be replaced by cell models from computing, networking, systems biology, and other applications. Massively parallel computing on cellular automata breaks through the obstacle of intractable tasks on which scientists work since the middle of twentieth century.