IJPAM: Volume 107, No. 1 (2016)

NEW JULIA AND MANDELBROT SETS FOR
A NEW FASTER ITERATIVE PROCESS

Mandeep Kumari$^1$, Ashish$^2$, Renu Chugh$^3$
$^{1,3}$Department of Mathematics
Maharshi Dayanand University
Rohtak, 124001, INDIA
$^2$Department of Mathematics
RPS Degree College, Balana
Mahendergarh, 123029, INDIA


Abstract. Fixed point iterative procedures are the backbones of fractal geometry. In existing literature Julia sets, Mandelbrot sets and their variants have been studied using one - step, two - step, three - step and four - step iterative process. Recently, M. Abbas and T. Nazir [#!1!#] introduced a new iterative process (a four-step iterative process) which is faster than all of Picard, Mann and Agarwal processes. In this paper, we obtain further generalizations of Julia and Mandelbrot sets using this faster iterative process for quadratic, cubic and higher degree polynomials. Further, we analyze that few Julia and Mandelbrot sets took the shape of Lord Ganesha (name of Hindu God), Dragon and Urn.

Received: December 29, 2015

AMS Subject Classification: 37F45, 37F50

Key Words and Phrases: Julia set, Mandelbrot set, four-step feedback process, escape criterion, complex polynomials.

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DOI: 10.12732/ijpam.v107i1.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 1
Pages: 161 - 177


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