Research Article
New-Fangled Mandelbrot and Julia Sets for Logarithmic Function
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 85 - Issue 13 |
| Published: January 2014 |
| Authors: Suraj Singh Panwar, Pawan Kumar Mishra |
10.5120/14899-3390
|
Suraj Singh Panwar, Pawan Kumar Mishra . New-Fangled Mandelbrot and Julia Sets for Logarithmic Function. International Journal of Computer Applications. 85, 13 (January 2014), 7-14. DOI=10.5120/14899-3390
@article{ 10.5120/14899-3390,
author = { Suraj Singh Panwar,Pawan Kumar Mishra },
title = { New-Fangled Mandelbrot and Julia Sets for Logarithmic Function },
journal = { International Journal of Computer Applications },
year = { 2014 },
volume = { 85 },
number = { 13 },
pages = { 7-14 },
doi = { 10.5120/14899-3390 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2014
%A Suraj Singh Panwar
%A Pawan Kumar Mishra
%T New-Fangled Mandelbrot and Julia Sets for Logarithmic Function%T
%J International Journal of Computer Applications
%V 85
%N 13
%P 7-14
%R 10.5120/14899-3390
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In this paper we explore the dynamics of complex logarithmic function for integer and non-integer values. We have used Ishikawa iteration method for generating fractals and analyzed them.
References
- Mandelbrot, Benoit B. , "The fractal geometry of nature. " Macmillan. ISBN 978-0-7167-1186-5, 1983.
- Barnsley, Michale F. , Devaney, Robert L. , Mandelbrot, Benoit B. , Peitgen, Heinz-Otto, Saupe, Dietmar and Voss, Richard F. , "The Science of Fractal Images", Springer – Verlag 1988.
- Batty, Michael ,"Fractals - Geometry Between Dimensions," New Scientist (Holborn Publishing Group) 105 (1450): 31, 1985-04-04.
- Negi, Ashish, "Generation of Fractals and Applications", Thesis, Gurukul Kangri Vishwavidyalaya, 2005.
- Mandelbrot, Benoit B. , " Fractals and Chaos" Berlin: Springer. pp. 38, ISBN 978-0-387-20158-0. "A fractal set is one for which the fractal (Hausdorff-Besicovitch) dimension strictly exceeds the topological dimension", 2004.
- Edgar, Gerald, "Classics on Fractals", Boulder, CO: Westview Press. ISBN 978-0-8133-4153-8, 2004.
- Agarwal Shafali and Negi, Dr. Ashish, "Midgets of Transcendental Superior Mandelbar Set", International Journal of Computer Science Issues (IJCSI), Vol. 9, Issue 4, No. 3, July 2012.
- Negi, Ashish and Rani, Mamta, "Midgets of Superior Mandelbrot Set", Chaos, Solitons and Fractals, July 2006.
- Chauhan,Y. S. , Rana R. and Negi, Ashish, "New Julia Sets of Ishikawa Iterates", International Journal of Computer Applications (IJCA), Volume 7, No. 13, October 2010.
- Ishikawa, S, "Fixed points by a new iteration method", Proc. Amer. Math. Soc. 44, (1974), pp. 147-150.
- Chauhan,Y. S. Rana R. and Negi, Ashish, "New Tricorn & Multicorns of Ishikawa Iterates", International Journal of Computer Applications (IJCA), Volume 7, No. 13, October 2010.
- Rana, R. , Chauhan Y. S. and Negi, Ashish , "Ishikawa Iterates for Logarithmic function", International Journal of Computer Applications (IJCA), Volume 15, No. 5, February 2011.
- Daveney, R. L. , "An Introduction to Chaotic Dynamical Systems ", Springer-Verlag, New York. Inc. 1994.
- Devaney, Robert L. ,"A First Course in Chaotic Dynamical Systems: Theory and Experiment", Addison-Wesley, MR1202237, 1992.
- Peitgen H. and Richter P. H. , "The Beauty of Fractals", Springer-Verlag, Berlin, 1986.
Index Terms
Keywords