Generation of Anti-Fractals in SP-Orbit

International Journal of Computer Trends and Technology (IJCTT)          
© 2017 by IJCTT Journal
Volume-43 Number-2
Year of Publication : 2017
Authors : Mandeep Kumari, Sudesh Kumari, Renu Chugh
DOI :  10.14445/22312803/IJCTT-V43P115


Mandeep Kumari, Sudesh Kumari, Renu Chugh  "Generation of Anti-Fractals in SP-Orbit". International Journal of Computer Trends and Technology (IJCTT) V43(2):105-112, January 2017. ISSN:2231-2803. Published by Seventh Sense Research Group.

Abstract -
In this paper we generate a new class of Tricorns and Multicorns using SP iteration (a four-step feedback process) and explore the geometry of superior antifractals. Other researchers have already generated antifractals using Picard, Mann, ishikawa and Noor orbits that are examples of one –step, two-step, three-step and four-step feedback processes.

[1] Ashish, M. Rani, and R. Chugh, Dynamics of antifractals in Noor Orbit, International Journal of Computer Applications, Volume 57, Number 4 (2012) pp 11-15.
[2] B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, New York, NY, USA, 1982.
[3] D. Negi and A. Negi, A behavior of Tricorns and Multicorns in N-Orbit, International Journal of Applied Engineering Research, Volume 11, Number 1 (2016) pp 675-680.
[4] E. Lau, and D. Schleicher, Symmetries of fractals revisited, Math. Intelligencer (18)(1)(1996), 45-51.
[5] G. Julia, “Sur l’iteration des functions rationnelles,” Journal de Math´ematiques Pures et Appliqu´ees, vol. 8, pp. 737–747, 1918.
[6] H. O. Peitgen, H. Jurgens, and D. Saupe, Chaos and Fractals, Springer-Verlag, New York, 1994.
[7] M. Abbas and T. Nazir , A new iteration process applied to constained minimization and feasibility problems, Matemathykm Bechnk (66)(2) (2014), 223-234.
[8] M. Kumari, Ashish and R. Chugh, New Julia And Mandelbrot Sets for a New Faster Iterative Process, International Journal of Pure and Applied Mathematics, Volume-107, No. 1, 2016, 161-177.
[9] M. Rani, and M. Kumar, Circular saw Mandelbrot sets, in: Proc. 14th WSEAS Int. Conf. on Appl. Math.(Math’09), 2009, 131-136.
[10] M. Rani, Superior antifractals, in: IEEE Proc. ICCAE 2010, vol. 1, 798-802.
[11] M. Rani, Superior tricorns and multicorns, in: Proc. 9th WSEAS Int. Conf. on Appl. Comp. Engg. (ACE’10), 2010, 58-61.
[12] R. L. Devaney, A first course in chaotic dynamical systems: theory and experiment, Addison-Wesley, New York, 1992.
[13] R. Winters, Bifurcations in families of antiholomorphic and biquadratic maps, Ph.D Thesis, Boston Univ., London, 1990.
[14] S. Nakane, and D. Schleicher, Non- local connectivity of the tricorn and multicorns: Dynamical system and chaos(1)(Hachioji,1994), 200-203, World Sci. Publ., River Edge, NJ, 1995.
[15] S. Nakane, and D. Schleicher, On multicorns and unicorns: I. Antiholomorphic dynamics hyperbolic components and real cubic polynomials, Int. J. Bifur. Chaos Appl. Sci. Engr., (13)(10)(2003), 2825-2844.
[16] W. D. Crowe, R. Hasson, P. J. Rippon, and P. E. D. Strain-Clark, On the structure of the Mandelbar set, Nonlinearity, (2)(4)(1989), 541-553.
[17] W. Phuengrattana, S. Suantai, On the rate of convergence of Mann Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, Journal of Computational and Applied Mathematics,(235)(2011), 3006-3014.
[18] Y. S. Chauhan, R. Rana, and A. Negi, New tricorn and multicorn of Ishikawa iterates, Int. J. Comput. Appl., (7)(13)(2010), 25-33.

Antipolynomial, antifractal, Tricorn, Multicorn, SP-orbit.