Act of CVT and EVT In The Formation of Number-Theoretic Fractals

In this paper we have defined two functions that have been used to construct different fractals having fractal dimensions between 1 and 2. More precisely, we can say that one of our defined functions produce the fractals whose fractal dimension lies in [1.58, 2) and rest function produce the fractals whose fractal dimension lies in (1, 1.58]. Also we tried to calculate the amount of increment of fractal dimension in accordance with base of the number systems. And in switching of fractals from one base to another, the increment of fractal dimension is constant, which is 1.58, it’s quite surprising! Keywords-Carry Value Transformation, Extreme Value Transformation, Fractals, Fractal dimension. We have constructed two functions namely Carry Value transformation and Extreme Value Transformation; and on using these we have generated different fractals of fractal dimension lying between the interval (1, 2). Indeed, for any given number in between (1, 2) this functions could give one fractal having fractal dimension nearer to the given number. The maximum error could be 0.12 in approximating fractal dimension. Finally our observation centers on the fact that when we switch from one fractal to another fractal on using our said methodology, the amount of fractal dimension (amount of chaos) is remaining unaltered as 1.58.