S-iteration scheme and polynomiography

The aim of this paper is to present a modification of the visualization process of finding the roots of a given complex polynomial. In this paper S-iteration scheme is used instead of standard Picard iteration. The word “polynomiography coined by Kalantari for that visualization process. The images obtained are called polynomiographs. Polynomiographs have importance for both the art and science aspects. By using S-iteration scheme we obtain quite new nicely looking polynomiographs that are different from standard Picard iteration. Presented examples show that we obtain very interesting patterns for complex polynomial equations, permutation and doubly stochastic matrices. We believe that the results of this paper enrich the functionality of the existing polynomiography software.