Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography

Abstract

In this paper, we propose some modifications of the basic family of iterations with a new four-step iteration called RK iteration and its s-convexity. We present some graphical examples showing the dynamics of the new iteration in the colouring and shapes of the obtained polynomiographs compared to the ones from the basic family only. Moreover, the computational results reveal that the value of s in the s-convex combination of the RK iteration has a significant impact on the time taken by the iteration process for approximating the roots of the polynomials. The obtained results are interesting from an artistic and computational point of view.