Two states uniform 2D linear cellular automata and some replicating patterns

This paper has presented theoretical and imaginary investigation of 2D (two-dimensional) additive (linear) and uniform CA (cellular automata). Regarding some important properties, one can consider geometrical models of motifs (image model) generated by CA finite iterations. In the present paper, we study 2D linear CA under null and periodic boundary conditions over the binary or two states field ℤ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> i.e. two spin states case. It is studied the applications of replicating patterns corresponding to the uniform linear rules of 2D CA with these special boundary conditions over ℤ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . All the linear null and periodic rules can be found to be multiple replicating copies of a given image depending on the special types.

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