In this paper the theory of 2-Variable Boolean Operation (2-VBO) has been discussed on a pair of n-bit strings. 2-VBO serves to bring out the relation between numbers which when plot on a 2-D surface form interesting patterns; patterns that may be fixed, periodic, chaotic or complex. Some of these patterns represent natural fractals. This paper also provides mathematical analysis corresponding to each of the obtained patterns, which would aid to understanding their formation. 2-VBO is an attempt towards the production and classification of patterns which represent various mathematical models and naturally occurring phenomena.
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