Polynomiography and various convergence tests

Abstract

The aim of this paper is to present a modification of the visualization process of finding the roots of a given complex polynomial which is called polynomiography. The name polynomiography was introduced by Kalantari. The polynomiographs are very interesting both from educational and artistic points of view. In this paper we are interested in the artistic values of the polynomiography. The proposed modification is based on the change of the usual convergence test used in the polynomiography, i.e. using the modulus of a difference between two successive elements obtained in an iteration process, with the tests based on distance and non-distance conditions. Presented examples show that using various convergence tests we are able to obtain very interesting and diverse patterns. We believe that the results of this paper can enrich the functionality of the existing polynomiography software.