Generalized Mandelbrot Sets of a Family of Polynomials Pnz=zn+z+c;n≥2

Generalized Mandelbrot Sets of a Family of Polynomials Pnz=zn+z+c;n≥2

In this paper, we study the general Mandelbrot set of the family of polynomials Pnz=zn+z+c;n≥2, denoted by GM(Pn). We construct the general Mandelbrot set for these polynomials by the escaping method. We determine the boundaries, areas, fractals, and symmetry of the previous polynomials. On the othe...

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Bibliographic Details
Published in:International journal of mathematics and mathematical sciences Vol. 2022
Main Author: Farris, Salma M.
Format: Journal Article
Language:English
Published: New York Hindawi 2022
Hindawi Limited
Subjects:
Fractals
Polynomials
Online Access:Get full text
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Summary:In this paper, we study the general Mandelbrot set of the family of polynomials Pnz=zn+z+c;n≥2, denoted by GM(Pn). We construct the general Mandelbrot set for these polynomials by the escaping method. We determine the boundaries, areas, fractals, and symmetry of the previous polynomials. On the other hand, we study some topological properties of GMPn. We prove that GMPn is bounded and closed; hence, it is compact. Also, we characterize the general Mandelbrot set as a union of basins of attraction. Finally, we make a comparison between the properties of famous Mandelbrot set Mz2+c and our general Mandelbrot sets.
ISSN:0161-1712
1687-0425
DOI:10.1155/2022/4510088