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In this paper the theory of Carry Value Transformation (CVT) is designed anddeveloped on a pair of n-bit strings and is used to produce many interestingpatterns. One of them is found to be a self-similar fractal whose dimension issame as the dimension of the Sierpinski triangle. Different constructionprocedures like L-system, Cellular Automata rule, Tilling for this fractal areobtained which signifies that like other tools CVT can also be used for theformation of self-similar fractals. It is shown that CVT can be used for theproduction of periodic as well as chaotic patterns. Also, the analytical andalgebraic properties of CVT are discussed. The definition of CVT intwo-dimension is slightly modified and its mathematical properties arehighlighted. Finally, the extension of CVT and modified CVT (MCVT) are done inhigher dimensions.

Theory of Carry Value Transformation (CVT) and its Application in Fractal formation