We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
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 Dynamics of Superior Multibrots

by Sunil Shukla, Ashish Negi, Priti Dimri
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 42 - Number 15
Year of Publication: 2012
Authors: Sunil Shukla, Ashish Negi, Priti Dimri
10.5120/5769-7990

Sunil Shukla, Ashish Negi, Priti Dimri . Complex Dynamics of Superior Multibrots. International Journal of Computer Applications. 42, 15 ( March 2012), 28-33. DOI=10.5120/5769-7990

@article{ 10.5120/5769-7990,
author = { Sunil Shukla, Ashish Negi, Priti Dimri },
title = { Complex Dynamics of Superior Multibrots },
journal = { International Journal of Computer Applications },
issue_date = { March 2012 },
volume = { 42 },
number = { 15 },
month = { March },
year = { 2012 },
issn = { 0975-8887 },
pages = { 28-33 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume42/number15/5769-7990/ },
doi = { 10.5120/5769-7990 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:31:22.324692+05:30
%A Sunil Shukla
%A Ashish Negi
%A Priti Dimri
%T Complex Dynamics of Superior Multibrots
%J International Journal of Computer Applications
%@ 0975-8887
%V 42
%N 15
%P 28-33
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The Multibrot fractal is a modification of the classic Mandelbrot and Julia sets and it is given by the complex function where and is a constant. This Fractal is particularly interesting, with beautiful shapes and lots of spirals. In this paper we have presented different characteristics of Multibrot function using superior iterates. Further, different properties like trajectories, fixed point, its complex dynamics and its behavior towards Julia set are also discussed in the paper.

References
  1. Blanchard, P. : Complex analytic dynamics on the Riemann sphere, Bull Amer Math Soc 1984; 11(1), 85-141.
  2. Copper, G. R. J. : Chaotic behaviour in the Carotid – Kundalini map function, Computer Graphics 2000;24,165-70.
  3. Devaney, R. L. : Chaos, Fractals and dynamics, Computer experiments in mathematics, Menlo Park,Addison – Wessley (1992).
  4. Devaney, R. L. : The fractal Geometry of the Mandelbrot set , 2. How to count and how to add . Symposium in honor of Benoit Mandelbrot (Curaco 1995), Fractal 1995;3(4),629-40[MR1410283(99d:58095)].
  5. Gordon, R. J. Copper. : Chaotic behaviour in the Carotid – kundalini map function, Chaos and Graphics, Computers and Graphics 24(2000)465-470.
  6. Peitgen, H. O. ; Jurgens, H. ; Saupe, D. : Chaos and Fractals, New frontiers of science, New York Springer,1992 984pp.
  7. Peitgen, H. O. ; Ritcher, P . H. : The beauty of Fractals, Berlin, Springer, 1986.
  8. Pickover, C. A. : Keys of Infinity, New York, wiley, 1995.
  9. Speigel, M. R. : Theory and problems of complex variables, New York, McGraw-Hill, 1972, 313pp.
  10. Ushiki, S. : "Phoenix", IEEE Transactions on Circuits and Systems, Vol. 35, No. 7, July 1988, pp. 788-789.
  11. Rani, M. ; Kumar, V. : Superior Julia set, J Korea Soc Math Edu Series D: Res Math Edu 2004; 8(4), 261-277.
  12. Julia, G. : Sur 1' iteration des functions rationnelles, J Math Pure Appl. , 1918; 8, 47-245.
Index Terms

Computer Science
Information Sciences

Keywords

Complex Dynamics Multibrot

Powered by PhDFocusTM