Ostapkevich M.  

Using Hexagonal Grid in Cellular Automata and CNN Models for Pattern Formation.

The simulation of pattern formation is an essential part of research into a wide variety of natural phenomena and artificial systems. One of the promising approaches to their simulation is based upon the notions of cellular automata and cellular-neural networks. The existing discrete models use the rectangular grid. A hexagonal grid offers some advantages over the rectangular one. Particularly, these are the equal distances between all the neighbor cells and more axes of symmetry. These qualities would allow to generate patterns, which correspond to the real world configurations within versatile complex systems to a greater extent. A cellular-automata model and a cellular neural network with hexagonal grid and templates of various radii are presented and their properties are investigated. An application library for cellular-neural network model construction and simulation with rectangular and hexagonal grids of arbitrary template radii as well as a visualization tool were implemented as a by-product of the research.

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