Research Article
A Relative Superior Julia Set and Relative Superior Tricorn and Multicorns of Fractals
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 43 - Issue 6 |
| Published: April 2012 |
| Authors: Priti Dimri, Shashank Lingwal, Ashish Negi |
10.5120/6109-8327
|
Priti Dimri, Shashank Lingwal, Ashish Negi . A Relative Superior Julia Set and Relative Superior Tricorn and Multicorns of Fractals. International Journal of Computer Applications. 43, 6 (April 2012), 29-36. DOI=10.5120/6109-8327
@article{ 10.5120/6109-8327,
author = { Priti Dimri,Shashank Lingwal,Ashish Negi },
title = { A Relative Superior Julia Set and Relative Superior Tricorn and Multicorns of Fractals },
journal = { International Journal of Computer Applications },
year = { 2012 },
volume = { 43 },
number = { 6 },
pages = { 29-36 },
doi = { 10.5120/6109-8327 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2012
%A Priti Dimri
%A Shashank Lingwal
%A Ashish Negi
%T A Relative Superior Julia Set and Relative Superior Tricorn and Multicorns of Fractals%T
%J International Journal of Computer Applications
%V 43
%N 6
%P 29-36
%R 10.5120/6109-8327
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In this paper we investigate the new Julia set and a new Tricorn and Multicorns of fractals. The beautiful and useful fractal images are generated using Ishikawa iteration to study many of their properties. The paper mainly emphasizes on reviewing the detailed study and generation of Relative Superior Tricorn and Multicorns along with Relative Superior Julia Set.
References
- R. Abraham and C. Shaw, Dynamics : "The geometry of Behaviour, Part One: Periodic Behaviour, Part Two : Chaotic Behaviour" Aerial Press, Santa Cruz, Calif,(1982)
- Alan F. Beardon, "Iteration of Rational Functions", Springer Verlag, N. York, Inc. (1991)
- B. Branner and J. Hubbard, "The iteration of Cubic Polynomials". Part I, Acta. Math. 66(1998), 143-206
- Yashwant S Chauhan, Rajeshri Rana and Ashish Negi, "New Julia Sets of Ishikawa Iterates", International Journal of Computer Applications (0975-8887), Volume 7 – No. 13, October 2010
- 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
- R. M. Crownover, "Introduction to Fractals Chaos, Mandelbrot sets", Jones and Barlett Publishers, (1995)
- R. L. Daveney, "An Introduction to Chaotic Dynamical Systems " Springer-Verlag, N. york. Inc. 1994
- R. L. Daveney, "A First Course in Chaotic Dynamical System : Theory and Experiment" , Addison-Wesley, 1992. MR1202237
- S. Ishikawa, "Fixed points by a new iteration method", Proc. Amer. Math. Soc. 44(1974), 147-150
- Manish Kumar, and Mamta Rani, "A New Approach to Superior Julia Sets", J. nature. Phys. Sci, 19(2), (2005), 148-155
- Eike Lau and Dierk Schleicher, "Symmetries of fractals revisited. ", Math. Intelligencer (18)(1)(1996), 45-51. MR1381579 Zbl 0847. 30018.
- B. B. Mandelbrot, "The Fractal aspects of iteration of for complex and z" Ann. N. Y. Acad. Sci. 357(1980), 249-259
- W. R. Mann, "Mean Value Methods in iteration", Proc. Amer. Math. Soc. 4 (1953), 506-510
- J. Milnor, "Dynamics in one complex variable; Introductory Lectures", Vieweg(1999)
- Shizuo Nakane, and Dierk Schleicher, "Non-local connectivity of the Tricorn and multicorns", Dynamical Systems and chaos (1)(Hachioji, 1994), 200-203, World Sci. Publ. , River Edge, NJ, 1995 MR1479931.
- Ashish Negi, "Generation of Fractals and Applications", Thesis, Gurukul Kangari Vishwvidyalaya, (2005)
- 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
- M. Rani and V. kumar, "Superior Mandelbrot Set", J Korea Soc. Math. Edu. Series, DResearch in Maths. Edu. No. 4,8(2004), 279-291
- K. Shirriff, "Fractals from Simple Polynomial Composite Functions", Computer and Graphics, 17(6), Nov. 1993, pp 701-703
- R. Winters, "Bifurcation in families of Antiholomorphic and biquadratic maps", Thesis, Boston Univ. (1990).
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