New Fixed Points Outcomes for Fractal Creation by Applying Different Fixed Point Technique

Abstract

Fractal like Julia set is regarded as one of the striking and significant mathematical fractals in the field of science and technology. There are different numerical iterative techniques which generate these fractals and in fact these numerical iterative techniques are the strength of fractal geometry. In recent past, Julia sets have been studied through numerical techniques like Picard, Mann, and Ishikawa
etc. which are the examples of one-step, two-step, and three-step iterative techniques respectively. In this article, we have concentrated our research work on the computation as well as the different features of cubic Julia sets for the complex polynomial Pm,n(z) = z 3 +mz+n. This generation process has been carried-over through a new numerical four-step iterative technique. We have generated new and ever seen cubic Julia sets for the above complex polynomial. The cubic Julia sets generated through above polynomial have important mathematical properties. It is also fascinating that some of the generated cubic Julia sets are analogous to fractal shaped antennas, butterfly and some categories of ants. Some of the generated cubic Julia sets can also be categorized as wall-decorated pictures