Abstract
One can study geometrical models of image patterns generated by CA evolution. For this, the present paper has investigated theoretical and imaginary investigation of two-dimensional (2D) linear and uniform cellular automata (CA). We study 2D linear CA under special boundary (reflexive and adiabatic) conditions over the binary field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbb{Z}_{2}$</tex> , i.e. two states case. We investigate the evolution of image patterns corresponding to the uniform linear rules of 2D CA with the reflexive and adiabatic boundary conditions over <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbb{Z}_{2}$</tex> . The linear rules of CA can be found to be some image copies of a given first image depending on the special boundary types.
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