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Reseach Article

A Combined Study of New Escape Time Fractal for Sine and Inverse Tangent Functions

by Shashank Lingwal, Ashish Negi, Y. S. Chauhan
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 89 - Number 1
Year of Publication: 2014
Authors: Shashank Lingwal, Ashish Negi, Y. S. Chauhan
10.5120/15469-4087

Shashank Lingwal, Ashish Negi, Y. S. Chauhan . A Combined Study of New Escape Time Fractal for Sine and Inverse Tangent Functions. International Journal of Computer Applications. 89, 1 ( March 2014), 35-40. DOI=10.5120/15469-4087

@article{ 10.5120/15469-4087,
author = { Shashank Lingwal, Ashish Negi, Y. S. Chauhan },
title = { A Combined Study of New Escape Time Fractal for Sine and Inverse Tangent Functions },
journal = { International Journal of Computer Applications },
issue_date = { March 2014 },
volume = { 89 },
number = { 1 },
month = { March },
year = { 2014 },
issn = { 0975-8887 },
pages = { 35-40 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume89/number1/15469-4087/ },
doi = { 10.5120/15469-4087 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:08:09.263007+05:30
%A Shashank Lingwal
%A Ashish Negi
%A Y. S. Chauhan
%T A Combined Study of New Escape Time Fractal for Sine and Inverse Tangent Functions
%J International Journal of Computer Applications
%@ 0975-8887
%V 89
%N 1
%P 35-40
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Complex graphics of dynamical system have been a subject of intense research nowadays. The fractal geometry is the base of these beautiful graphical images. Many researchers and authors have worked to study the complex nature of the two most popular sets in fractal geometry, the Julia set and the Mandelbrot set, and proposed their work in various forms using existing tools and techniques. The generation of fractals and study of the dynamics of transcendental function is one of the emerging and interesting fields of research nowadays. Recently, Ashish Negi, Rajeshri Rana and Yashwant S. Chauhan are among those researchers who have contributed a lot in the area of Fractal Geometry applications. In this paper we review the recently done work on sine and inverse tangent functions.

References
  1. W. Bergweiler, Iteration of meromorphic functions. Bull. Amer. Math. Soc. (N. S. ) 29 (1993), 151–188.
  2. W. Bergweiler and A Ereneko, "Dynamics of a higher dimensional analog of the trigonometric functions", Bull. Amer. Math. Soc. (N. S. )1 (2010), 35-38.
  3. B. Branner, The Mandelbrot Set, Proceedings of Symposia in Applied Mathematics39 (1989), 75-105. Published as Chaos and Fractals: The Mathematics Behind the Computer Graphics.
  4. Yashwant S Chauhan, Rajeshri Rana and Ashish Negi. "New Julia Sets of Ishikawa Iterates", International Journal of Computer Applications 7(13):34–42, October 2010. Published By Foundation of Computer Science. ISBN: 978-93-80746-97-5.
  5. R. L. Devaney and M. Krych, "Dynamics of exp(z)", Ergodic Theory Dynam. Systems4 (1984), 35–52.
  6. R. L. Devaney and F. Tangerman, "Dynamics of entire functions near the essential Singularity", Ergodic Theory Dynam. Systems 6 (1986), 489–503.
  7. Robert L. Devaney, "An Introduction to Chaotic Dynamical Systems", Second Edition, 1989, Perseus Books Publishing, Reading, MA.
  8. Priti Dimri, Shashank Lingwal and Ashish Negi "A Relative Superior Julia Set and Relative Superior Tricorn and Multicorns of Fractals" International Journal of Computer Application (0975-8887), Volume 43- No. 6, April 2012, (ISBN : 973-93-80867-44-1).
  9. A Ereneko, "Iteration of entire functions", Dynamical Systems and Ergodic theory, Banach Center Publ. 23, Polish Sc. Pub. , Warsaw 1989, 339-345.
  10. Pierre Fatou, "Sur Iteration des functions transcendantes entires", Acta Math 47(1926), 337-378.
  11. S. Ishikawa, "Fixed points by a new iteration method", Proc. Amer. Math. Soc. 44 (1974), 147-150.
  12. G. Julia, "Sur 1' iteration des functions rationnelles", J Math Pure Appli. 8 (1918), 737-747.
  13. Shashank Lingwal, Ashish Negi and Sumiti Kapoor "A Study of New Fractals Complex Dynamics for Inverse and Logarithmic Functions" International Journal of Computer Application (0975-8887), Volume 43- No. 5, April 2012, (ISBN : 973-93-80867-43-3).
  14. B. B. Mandelbrot, " The Fractal Geometry of Nature", W. H. Freeman, New York,1983.
  15. J. Milnor, "Dynamics in One Complex Variable: Third Edition", Princeton University Press, 2006.
  16. Ashish Negi, Shashank Lingwal and Yashwant S. Chauhan "Complex and Inverse Complex Dynamics of Fractals using Ishikawa Iteration", International Journal of Computer Application (0975-8887), Volume 40- No. 12, February 2012, (ISBN : 978-93-80866-52-1).
  17. Rajeshri Rana and Yashwant Singh Chauhan "Escape Time Fractals of Inverse Tangent Function", International Journal of Computer & Organization Trends, Volume 3, Issue 3 (2013), ISSN : 2249-2593.
  18. Rajeshri Rana, Yashwant Singh Chauhan and Ashish Negi "Generation of New Fractals for Sine Function", Int. J. Comp. Tech. Appl. , Vol 2 (6), 1747-1754, ISSN : 2229-6093.
  19. Rajeshri Rana, Yashwant S Chauhan and Ashish Negi. "Ishikawa Iterates for Logarithmic Function", International Journal of Computer Applications 15(5):47- 56, February 2011. Published By Foundation of Computer Science. ISBN: 978-93-80747-50-1.
  20. Rajeshri Rana, Yashwant S Chauhan and Ashish Negi. "Non Linear Dynamics of Ishikawa Iteration", International Journal of Computer Applications 7(13):43– 49, October 2010. Published By Foundation of Computer Science. ISBN: 978-93-80746-97-5.
  21. Dierk Schleicher and Johannes Zimmer, "Escaping Points of Exponential Maps", Journal of the London Mathematical Society (2) 67(2003), 380–400.
Index Terms

Computer Science
Information Sciences

Keywords

Fractals Relative Superior Mandelbrot Set Relative Superior Julia Set Ishikawa Iteration.