New escape conditions with general complex polynomial for fractals via new fixed point iteration

The aim of this paper is to generalize the results regarding fractals and prove escape conditions for general complex polynomial. In this paper we state the orbit of a newly defined iterative scheme and establish the escape criteria in fractal generation for general complex polynomial. We use established escape criteria in algorithms to generate Mandelbrot and Multi-corns sets. In addition, we present some graphs of quadratic, cubic and higher Mandelbrot and Multi-corns sets and discuss how the alteration in parameters make changes in graphs.

Automated summary

This paper generalizes results on fractals and proves escape conditions for general complex polynomials. A newly defined iterative scheme is used to establish escape criteria in fractal generation for general complex polynomials, and the criteria are applied in algorithms to generate Mandelbrot and Multi-corns sets. Additionally, graphs of quadratic, cubic, and higher Mandelbrot and Multi-corns sets are presented, with a discussion on how changes in parameters affect the graphs.