CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Complex Nature of Fractal Geometry

by Deepak Negi, Udaibhuan Trivedi, Ashish Negi
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 57 - Number 17
Year of Publication: 2012
Authors: Deepak Negi, Udaibhuan Trivedi, Ashish Negi
10.5120/9203-3734

Deepak Negi, Udaibhuan Trivedi, Ashish Negi . Complex Nature of Fractal Geometry. International Journal of Computer Applications. 57, 17 ( November 2012), 1-8. DOI=10.5120/9203-3734

@article{ 10.5120/9203-3734,
author = { Deepak Negi, Udaibhuan Trivedi, Ashish Negi },
title = { Complex Nature of Fractal Geometry },
journal = { International Journal of Computer Applications },
issue_date = { November 2012 },
volume = { 57 },
number = { 17 },
month = { November },
year = { 2012 },
issn = { 0975-8887 },
pages = { 1-8 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume57/number17/9203-3734/ },
doi = { 10.5120/9203-3734 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:00:40.976034+05:30
%A Deepak Negi
%A Udaibhuan Trivedi
%A Ashish Negi
%T Complex Nature of Fractal Geometry
%J International Journal of Computer Applications
%@ 0975-8887
%V 57
%N 17
%P 1-8
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The Mann iteration process and Ishikawa Iteration process are generally used to approximate the fixed point. There are a lot of work is done by researchers and still researches are being conducted to study and reveal the new concepts unexplored. Recently, Negi, Rana and Chauhan have explored the study of complex dynamics on various functions using Mann and Ishikawa Iterative processes. In this paper we have reviewed the recent work done work on the Mann iteration. This review contains a wide variety of existing iteration schemes as its special cases.

References
  1. Argyris, J. Andreadis, I. Karakasidis, TE. On perturbation of the Mandelbrot map. Chaos, Solitons & Fractals 2000; 11:1131–6.
  2. Branner B "The Mandelbrot Set", Proceedings of Symposia in Applied Mathematics39 (1989), 75-105.
  3. Cooper GRJ. Julia sets of the complex Carotid–Kundalini function. Comput Graphics 2001; 25:153–8.
  4. Chauhan Y. S. Rana R,and Negi A,, "Mandel-Bar Sets of Inverse Complex Function", International Journal of Computer Applications (0975-8887) Volume 9- No. 2, November 2010
  5. Chauhan, Y. S. , R. Rana and Negi. A, New Tricorns and Multicorns of Ishikawa Iterates, In Press, Int. Journal of Computer Application (Oct. 2010 Edition).
  6. Devaney RL. A first course in chaotic dynamical systems: theory and experiment. CO: Westview Press; 1992.
  7. Devaney RL. The fractal geometry of the Mandelbrot Set: I. Periods of the bulbs. Fractals, graphics, and mathematics education.
  8. Gujar G. U, Bhavsar C. V "Fractals from in the Complex c-Plane", Computers and Graphics 15, 3 (1991), 441-449.
  9. Gujar G. U, Bhavsar V. C and Vangala N, "Fractals from in the Complex z-Plane", Computers and Graphics 16, 1 (1992), 45-49
  10. Ishikawa S, "Fixed points by a new iteration method", Proc. Amer. Math. Soc. 44 (1974), 147-150.
  11. Mann R. , W Mean value methods in iteration, Proc. Amer. Math. Soc. , 4, 1953, 506-510.
  12. Rani. M: Cubic Superior Julia Sets. Proceedings of the European Computing Conference, june 2006
  13. Rani. M. Negi . A, New Julia sets for complex Carotid–Kundalini functionl. Chaos, Solitons and Fractals, june 2006
  14. Negi A, Agarwal S. : Inverse Circular Saw International Journal of Computer Applications (0975 – 8887) Volume 36– No. 8, December 2011 13
  15. Negi . A, Rani. M. : Midgets of superior Mandelbrot set, Chaos, Solitons and Fractals, june 2010
  16. Negi . A, Rani. M. : A new approach to dynamic noise on superior Mandelbrot set. Chaos, Solitons and Fractals, june 2006
  17. Peitgen H, Jürgens H, Saupe D. Chaos and fractals: new frontiers of science. New York: Springer-Verlag; 2004
  18. Philip AGD. Wrapped midgets in the Mandelbrot set. Comput Graphics 1994; 18(2):239–48.
  19. Pickover C, "Computers, Pattern, Chaos, and Beauty", St. Martin's Press, NewYork, 1990.
  20. Rana R, Chauhan Y. S. and Negi A, Non Linear dynamics of Ishikawa Iteration, In Press, Int. Journal of Computer Application (Oct. 2010 Edition).
  21. Rana R, Chauhan Y. S. and Negi A, Complex dynamics of Ishikawa iterates for non Integer values, In Press, Int. Journal of Computer Application (Nov. 2010 Edition).
  22. Rana R, Chauhan . S. Y, Negi A, "Inverse Complex Function Dynamics of Ishikawa Iterates", International Journal of Computer Applications (0975-8887) Volume 9- No. 1, November 2010.
  23. Rani . M, and Kumar. V, Superior Julia set,J. Korea Soc. Math. Educ. Ser. D; Res. Math. Educ. , 8(4), 2004, 261-277.
  24. Rani M. Iterative procedures in fractals and chaos, PhD Thesis, Department of Computer Science, Gurukula Kangri Vishwavidyalaya, Hardwar, India, 2002.
  25. Romera M, Pastor G, Montoya F. On the cusp and the tip of a midget in the Mandelbrot set antenna. Phys Lett A 1996; 221(3–):158–62. MR1409563 (97d: 58073).
  26. Schu. J, Iterative construction of fixed points of asymptotically non expansive mappings, J. Math. Anal. Appl. 158(1991) 407–413.
  27. Shirriff K. W, "An investigation of fractals generated by ", Computers and Graphics 13, 4 (1993), 603-607.
Index Terms

Computer Science
Information Sciences

Keywords

Relative Superior Mandelbrot Set Complex Dynamics Relative Superior Julia Set Ishikawa Iteration

Powered by PhDFocusTM