Associated with Mandelbrot's fractal geometry the method of Iterated Function System (IFS) is an important technique for generating, classification, and communication of fractal patterns. Such systems were originally studied by Hutchinson and popularized by-Barnsley in 1982. In this work, a review of literatures and clarifying the most important notions and theorems of this subject, which clear up the way of applying the IPS on complete metric space whose elements are compact sets and theorem ensure the existence and uniqueness of an attractor of the IFS. The purpose of this thesis is to formulate and solve the inverse problem of fractal set using a new approach in minimization theory. This can be made by finding and generating parameters of a set of affine maps, contractive mapping; which is iterated function system (IFS); that repeatedly iterative numerically by using the random iteration algorithm. Moreover, in this work we consider the attractor of IFS is given. Those structures have important useful applications in the modeling of, natural phenomena in computer graphics.