Julia sets and Mandelbrot sets in Noor orbit

被引：51
作者：
Ashish [1 ]
Rani, Mamta [2 ]
Chugh, Renu [1 ]
机构：
[1] Maharshi Dayanand Univ, Dept Math, Rohtak 124001, Haryana, India
[2] Cent Univ Rajasthan, Dept Comp Sci, Kishangarh 305801, India
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 228卷
关键词：
Julia set; Mandelbrot set; Four-step feedback process; Noor orbit; TOPOLOGICAL CLOSENESS; CUBIC POLYNOMIALS; NOISE; ITERATION;
D O I：
10.1016/j.amc.2013.11.077
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In recent literature, researchers have generated Julia sets and Mandelbrot sets in Mann and Ishikawa orbits that are examples of two-step and three-step feedback processes respectively. This paper presents further generalization of Julia and Mandelbrot sets for complex-valued polynomials such as quadratic, cubic and higher degree polynomials using a Noor orbit, which is a four-step iterative procedure. The graphical images of Julia and Mandelbrot sets have been visualized and certain patterns in Mandelbrot sets have been recognized. It is fascinating to see that a few Mandelbrot sets are akin to a butterfly or a coupled urn or a coupled trident. (C) 2013 Elsevier Inc. All rights reserved.
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收藏
页码：615 / 631
页数：17
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