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A Study of New Fractals Complex Dynamics for Inverse and Logarithmic Functions

by Shashank Lingwal, Ashish Negi, Sumiti Kapoor
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 43 - Number 5
Year of Publication: 2012
Authors: Shashank Lingwal, Ashish Negi, Sumiti Kapoor
10.5120/6099-8293

Shashank Lingwal, Ashish Negi, Sumiti Kapoor . A Study of New Fractals Complex Dynamics for Inverse and Logarithmic Functions. International Journal of Computer Applications. 43, 5 ( April 2012), 20-26. DOI=10.5120/6099-8293

@article{ 10.5120/6099-8293,
author = { Shashank Lingwal, Ashish Negi, Sumiti Kapoor },
title = { A Study of New Fractals Complex Dynamics for Inverse and Logarithmic Functions },
journal = { International Journal of Computer Applications },
issue_date = { April 2012 },
volume = { 43 },
number = { 5 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 20-26 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume43/number5/6099-8293/ },
doi = { 10.5120/6099-8293 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:34:22.861347+05:30
%A Shashank Lingwal
%A Ashish Negi
%A Sumiti Kapoor
%T A Study of New Fractals Complex Dynamics for Inverse and Logarithmic Functions
%J International Journal of Computer Applications
%@ 0975-8887
%V 43
%N 5
%P 20-26
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The object Mandelbrot set given by Mandelbrot in 1979 and its relative object Julia set have become a wide and elite area of research nowadays due to their beauty and complexity of their nature. Many researchers and authors have worked to study and reveal the new concepts unexplored in the complexities of these two most popular sets of fractal geometry. In this paper we review the recently done work on complex functions for producing beautiful fractal graphics, by few eminent researchers contributing a lot to the field of fractal geometry. The reviewed work mainly emphasizes on the complex functional dynamics of Ishikawa iterates for inverse and logarithmic function and existence of relative superior Mandel-bar set.

References
  1. B. Branner, "The Mandelbrot Set", Proceedings of Symposia in Applied Mathematics 39 (1989), 75-105
  2. Yashwant S Chauhan, Rajeshri Rana, and Ashish Negi, "New Tricorn & Multicorns of Ishikawa Iterates", International Journal of Computer Applications (0975-8887) Volume 7- No. 13,October 2010
  3. Yashwant S. Chauhan, Rajeshri Rana, Ashish Negi, "Mandel-Bar Sets of Inverse Complex Function", International Journal of Computer Applications (0975-8887) Volume 9- No. 2, November 2010
  4. W. D. Crowe, R. Hasson, P. J. Rippon, and P. E. D. Strain-Clark, "On the structure of the Mandel-bar set", Nonlinearity(2)(4)(1989), 541-553. MR1020441
  5. Robert L. Devaney, "A First Course in Chaotic Dynamical System: Theory and Experiment", Addison-Wesley, 1992. MR1202237
  6. S. Dhurandar, V. C. Bhavsar and U. G. Gujar, "Analysis of z-plane fractal images from for " Computers and Graphics 17,1(1993), 89-94
  7. U. G. Gujar and V. C. Bhavsar, "Fractals from in complex c-Plane", Computers and Graphics 15, 3 (1991), 441-449
  8. U. G. Gujar, V. C. Bhavsar and N. Vangala, "Fractals from in complex z-Plane", Computers and Graphics 15, 4 (1991), 45-49
  9. S. Ishikawa, "Fixed Points by a new iteration method", Proc. Amer. Math. Soc. 44 (1974), 147-150
  10. Ashish Negi, Shashank Lingwal and Yashwant Singh Chauhan, "Complex and Inverse Complex Dynamics of Fractals using Ishikawa Iteration", International Journal of Computer Applications (0975- 8887) Volume 40-No. 12, February 2012
  11. Rajeshri Rana, Yashwant S Chauhan, and Ashish Negi, "Non Linear Dynamics of Ishikawa Iterates", International Journal of Computer Applications (0975-8887) Volume 7- No. 13,October 2010
  12. Rajeshri Rana, Yashwant S. Chauhan, Ashish Negi, "Inverse Complex Function Dynamics of Ishikawa Iterates", International Journal of Computer Applications (0975-8887) Volume 9- No. 1, November 2010
  13. K. W. Shirriff, "An investigation of fractals generated by ", Computers and Graphics 13, 4 (1993), 603-607
  14. N. Shizuo and DierkSchleicher, "Non-local connectivity of the Tricorn and Multicorns", Dynamical system and chaos (1) (Hachioji, 1994), 200-203, World Sci. Publ. , River Edge, NJ, 1995 MR1479931
Index Terms

Computer Science
Information Sciences

Keywords

Fractals Complex Dynamics Relative Superior Mandelbrot Set Relative Superior Julia Set Ishikawa Iteration Relative Superior Mandel-bar Set Midgets

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