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

Muhammad Tanveer; Imran Ahmed; Ali Raza; Sumaira Nawaz; Yu-Pei Lv; Muhammad Tanveer; Imran Ahmed; Ali Raza; Sumaira Nawaz; Yu-Pei Lv

doi:10.3934/math.2021329

AIMS Mathematics

2021, Volume 6, Issue 6: 5563-5580. doi: 10.3934/math.2021329

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Research article

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

1.
Department of Mathematics and Statistics, The University of Lahore, Lahore 54000, Pakistan
2.
COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road, Lahore, Pakistan
3.
Department of Mathematics, The University of Lahore, Gujrat campus, Gujrat, Pakistan
4.
Department of Mathematics, Huzhou University, Huzhou 313000, China

Received: 19 December 2020 Accepted: 08 March 2021 Published: 19 March 2021
MSC : 47H10, 54H25

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.
- Mandelbrot set,
- Multi-corns set,
- general polynomial,
- fractal,
- fixed point
Citation: Muhammad Tanveer, Imran Ahmed, Ali Raza, Sumaira Nawaz, Yu-Pei Lv. New escape conditions with general complex polynomial for fractals via new fixed point iteration[J]. AIMS Mathematics, 2021, 6(6): 5563-5580. doi: 10.3934/math.2021329

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Abstract

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.

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