This Book discusses the Applications of Fractal and Dynamical System using fixed point and Iterative function system. We have opted the approach of superior iterates in analyzing the complex dynamics of various functions. In this Book we have introduced two new fractals based on new functions named as newbie fractal and initial controlled fractals. These functions are the variant of Mandelbrot function. The second function is initial controlled fractal. These fractals are governed by initial controlled functions such as sin, cos, log, tan, conj, abs etc. Finally, complex dynamics of this function using Superior iterates. Finally, A new approach to Barsnley Fractals using superior iterates is presented in the Book generate new escape time fractals which gives a new approach to the study of IFS.