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
Reseach Article

Variants of Koch curve: a Review

Published on April 2012 by Mamta Rani, Riaz Ul Haq, Deepak Kumar Verma
Development of Reliable Information Systems, Techniques and Related Issues (DRISTI 2012)
Foundation of Computer Science USA
DRISTI - Number 1
April 2012
Authors: Mamta Rani, Riaz Ul Haq, Deepak Kumar Verma
b7bc9e38-0164-4bc9-a7d2-6c3378ecf1a2

Mamta Rani, Riaz Ul Haq, Deepak Kumar Verma . Variants of Koch curve: a Review. Development of Reliable Information Systems, Techniques and Related Issues (DRISTI 2012). DRISTI, 1 (April 2012), 20-24.

@article{
author = { Mamta Rani, Riaz Ul Haq, Deepak Kumar Verma },
title = { Variants of Koch curve: a Review },
journal = { Development of Reliable Information Systems, Techniques and Related Issues (DRISTI 2012) },
issue_date = { April 2012 },
volume = { DRISTI },
number = { 1 },
month = { April },
year = { 2012 },
issn = 0975-8887,
pages = { 20-24 },
numpages = 5,
url = { /proceedings/dristi/number1/5925-1006/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 Development of Reliable Information Systems, Techniques and Related Issues (DRISTI 2012)
%A Mamta Rani
%A Riaz Ul Haq
%A Deepak Kumar Verma
%T Variants of Koch curve: a Review
%J Development of Reliable Information Systems, Techniques and Related Issues (DRISTI 2012)
%@ 0975-8887
%V DRISTI
%N 1
%P 20-24
%D 2012
%I International Journal of Computer Applications
Abstract

The von Koch snowflake curve is a mathematical curve, and is being used as antenna in wireless communications. There are various variants of the Koch curve scattered in literature. This paper attempts to present a critical review of the variants of Koch curve.

References
  1. Michael F. Barnsley, and Hawley Rising, Fractals Everywhere (2nd ed.), Academic Press Professional, Boston, 1993.
  2. John Briggs, Fractals: The Patterns of Chaos (2nd ed.), Thames and Hudson, London, 1992.
  3. Anthony Barcellos, The fractal geometry of Mandelbrot, The College Mathematics Journal, 15(2), 1984, 98-114.
  4. M. Chandra, and M. Rani, Categorization of fractal plants. Chaos, Solitons, Fractals, 41(3), 2009 1442-1447.
  5. Robert L. Devaney, A First Course in Chaotic Dynamical Systems: Theory and Experiment, Westview Press, CO, 1992.
  6. Ron Eglash, African Fractals: Modern Computing and Indigenous Design, Rutgers University Press, New Brunswick, 1999.
  7. K. Falconer, Fractal Geometry: Mathematical foundations and applications, Second edition, John Wiley & Sons, NJ, 2003.
  8. Riaz Ul Haq, Design and Simulation of Variants of Koch Models for Fractal Antenna, MS thesis, Faculty of Computer Systems & Software Engineering, University Malaysia Pahang, Kuantan, Malaysia, 2011.
  9. Riaz Ul Haq, Mamta Rani, and Norrozila Sulaiman, Categorization of superior Koch fractal antennas, in: IACSIT Proc. Int. conf. on Intelligence and Information Technology, Lahore, Pakistan (ICIIT 10), Oct 28-30, 2010, vol. 1, 551-554.
  10. Riaz Ul Haq, Norrozila Sulaiman, and Mamta Rani, Superior fractal antennas, in: Proc. Malaysian Technical Univ. Conf. on Engg. and Tech., Melaka, Malaysia, Jun 28-29, 2010, 23-26.
  11. R. Hohlfeld, and N. Cohen, Self-similarity and the geometric requirements for frequency independence in antenna, Fractals, 7(1), 1999, 79-84.
  12. Heinz-Otto Peitgen, Hartmut Jürgens, and Dietmar Saupe, Chaos and Fractals: New frontiers of science (2nd ed.), Springer-Verlag, New York, 2004. MR2031217 Zbl 1036.37001
  13. Gongwen Peng, and Tian Decheng, The fractal nature of a fracture surface, J. Phys. A: Math. Gen., 23(14), 1990, 233-257.
  14. S. Prasad, Superior Koch curves, Int. J. Artif. Life Res., 2(4), 2011, 24-31.
  15. M. Rani, Fractals in Vedic heritage and fractal carpets, in: Proc. National seminar on History, Heritage and Development of Mathematical Sciences, 2005, 110-121.
  16. Mamta Rani, Iterative Procedures in Fractals and Chaos, Ph. D. Thesis, Department of Computer Science, Gurukula Kangri Vishwavidyalaya, Hardwar, India, 2002.
  17. M. Rani, and S. Goel, Categorization of new fractal carpets, Chaos, Solitons, Fractals, 41(2), 2009, 1020-1026.
  18. Mamta Rani, Riaz Ul Haq, Norrozila Sulaiman, Koch Curves: Rewriting System, Geometry and Application, Journal of Computer science, 7(9), 2011, 1358-1362.
  19. Mamta Rani, Riaz Ul Haq, Norrozila Sulaiman, New Koch Curves and Their Classification, Chaos & Complexity Letters, 6(3), 2011.
  20. M. Rani, and V. Kumar, New fractal carpets. Arab. J. Sci. Eng., Sect. C Theme Issues, 29(2), 2004, 125-134. MR2126593
  21. M. Rani, and S. Prasad, Superior Cantor sets and superior Devil's staircases. Int. J. Artif. Life Res., 1(1), 2010, 78-84.
  22. K. M. Roskin, and J. B. Casper, From Chaos to Cryptography, 1998. http://xcrypt.theory.org/
  23. Nicoletta Sala, Architecture and Time, Chaos Complex. Lett., 5(3), 2011, 33-43.
  24. M. Schroeder, Fractals, Chaos, Power Laws: Minutes from an infinite paradise, W. H. Freeman and Company, New York, 1991.
  25. S. L. Singh, S. N. Mishra and W. Sinkala, A new iterative approach to fractal models, Commun. Nonlinear. Sc. Numer. Simul. 17(2), 2012, 521-529.
  26. K. J. Vinoy, K. A. Jose and V. K. Varadan, Multi-band characteristics and fractal dimension of dipole antennas with Koch curve geometry, in: Proc. Antennas and Propagation Society International Symposium, 4, 2002, 106-109.
  27. K. J. Vinoy, K. A. Jose and V. K. Varadan, Impact of fractal dimension in the design of multi-resonant fractal antennas, Fractals, 12, 2004, 55-66.
Index Terms

Computer Science
Information Sciences

Keywords

Koch Curve koch Snowflake