Orbit of an image under iterated system

An orbital picture depicts the path of an object under semi-group of transformations. The concept initially given by Barnsley [3] has utmost importance in image compression, biological modeling and other areas of fractal geometry. In this paper, we introduce superior iterations to study the role of linear and nonlinear transformations on the orbit of an object. Various characteristics of the computed figures have been discussed to indicate the usefulness of study in mathematical analysis. Modified algorithms are given to compute the orbital picture and V-variable orbital picture. An algorithm to calculate the distance between images makes the study motivating. A brief discussion about the proof of the Cauchy sequence of images is also given.