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

Abstract: In this paper the theory of Carry Value Transformation (CVT) is designed and developed on a pair of n-bit strings and is used to produce many interesting patterns. One of them is found to be a self-similar fractal whose dimension is same as the dimension of the Sierpinski triangle. Different construction procedures like L-system, Cellular Automata rule, Tilling for this fractal are obtained which signifies that like other tools CVT can also be used for the formation of self-similar fractals. It is shown that CVT can be used for the production of periodic as well as chaotic patterns. Also, the analytical and algebraic properties of CVT are discussed. The definition of CVT in two-dimension is slightly modified and its mathematical properties are highlighted. Finally, the extension of CVT and modified CVT (MCVT) are done in higher dimensions.