Superior Julia Sets and Superior Mandelbrot Sets in SP Orbit


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Authors

  • Mandeep Kumari Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, India
  • Sudesh Kumari Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, India
  • Renu Chugh Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, India

Keywords:

Superior Julia set, Superior Mandelbrot set, Superior escape criterion, SP orbit, complex polynomials

Abstract

The aim of this paper is to generate new Superior Julia and Superior Mandelbrot sets for complex-valued polynomials such as quadratic, cubic and higher degree polynomials using SP orbit, which is an example of four-step iterative procedure. In this paper, we visualize the graphical images of Superior Julia sets and Superior Mandelbrot sets and analyze their patterns. It is surprising to see that a few Superior Mandelbrot sets take the shape of decorated coupled Urns (Kalash in Hindi language), a decorated coupled Lightening lamp (Diya in Hindi language) and beautiful scared patterns (Rangolies in Hindi language). We believe that our results generalize and extend the existing results in the literature of Fractal theory.

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Published

15-04-2017

How to Cite

Mandeep Kumari, Sudesh Kumari, & Renu Chugh. (2017). Superior Julia Sets and Superior Mandelbrot Sets in SP Orbit. International Journal of Mathematics And Its Applications, 5(2 - A), 67–83. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/797

Issue

Vol. 5 No. 2 - A (2017)

Section

Research Article

License

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.