  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.
