CFP last date
20 December 2024
Reseach Article

New Sierpenski Curves in Complex Plane

by Priti Dimri, Munish Singh Chauhan, Ashish Negi
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 58 - Number 12
Year of Publication: 2012
Authors: Priti Dimri, Munish Singh Chauhan, Ashish Negi
10.5120/9334-3644

Priti Dimri, Munish Singh Chauhan, Ashish Negi . New Sierpenski Curves in Complex Plane. International Journal of Computer Applications. 58, 12 ( November 2012), 19-22. DOI=10.5120/9334-3644

@article{ 10.5120/9334-3644,
author = { Priti Dimri, Munish Singh Chauhan, Ashish Negi },
title = { New Sierpenski Curves in Complex Plane },
journal = { International Journal of Computer Applications },
issue_date = { November 2012 },
volume = { 58 },
number = { 12 },
month = { November },
year = { 2012 },
issn = { 0975-8887 },
pages = { 19-22 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume58/number12/9334-3644/ },
doi = { 10.5120/9334-3644 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:02:19.180803+05:30
%A Priti Dimri
%A Munish Singh Chauhan
%A Ashish Negi
%T New Sierpenski Curves in Complex Plane
%J International Journal of Computer Applications
%@ 0975-8887
%V 58
%N 12
%P 19-22
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The Sierpinski triangle also known as Sierpinski gasket is one of the most interesting and the simplest fractal shapes in existence. There are many different and easy ways to generate a Sierpinski triangle. In this paper we have presented a new algorithm for generating the sierpinski gasket using complex variables.

References
  1. Barnsley, M. , 1988, "Fractals Everywhere (San Diego: Academic Press, Inc).
  2. Barrallo, J. and Jones, D. , 1999, "Coloring algorithms for dynamical systems in the complex plane", ISAMA 99 Proceedings, 31-38.
  3. Barralo, J. and Sanchez, S. , 2001, "Fractals and multi layer colouring algorithms", Bridges Conference Proceedings 2001, 89.
  4. Crownover Richard M. , "Introduction to Fractals and Chaos" (Jones and Bartlett, Boston, 1995).
  5. Devaney, R. and Keen, L. (Eds. ), 1989, "Chaos and Fractals: the Mathematics Behind the Computer Graphics", Proceedings of Symposia in Applied Mathematics vol. 39 (Providence: American Mathematical Society).
  6. Devaney, R. L. : "Chaos, Fractals and dynamics, Computer experiments in mathematics", Menlo Park, Addison – Wessley (1992).
  7. Falconer K. J. , "Techniques in Fractal Geometry", Wiley, 1997.
  8. Falconer, K. , 2003, "Fractal Geometry: Mathematical Foundations and Applications" (West Sussex: John Wiley & Sons, Ltd).
  9. George Cantor "On the Power of Perfect Sets of Points in Classics on Fractals" (Westview Press, 2004) pp. 11­23.
  10. H. Von Koch, "On a continuous curve without tangents constructible from elementary geometry", Classics on fractals (G. Edgar, ed. ), Addison-Wesley, Reading, Massachusetts, 1993, pp. 25-45.
  11. Hutchinson, J. E. , "Fractals and Self-similarity", Indiana Univ. Math. J. ,30(1981), 713-747.
  12. Hyburn G. T. W, "Topological characterization of the Sierpinski curve", Fund. Math. 45 (1958), 320–324.
  13. Louwsma Joel , "Homeomorphism groups of the sierpinski carpet and sierpinski gasket"
  14. Mandelbrot, Benoit B. ,"The Fractal Geometry of Nature". New York: W. H. Freeman and Company, 1982.
  15. Milnor J. and Tan L. A. , "Sierpinski Carpet as Julia set". Appendix F in Geometry and dynamics of quadratic rational maps, Experiment. Math. 2 (1993), 37–83.
  16. Milnor. , "Dynamics in One Complex Variable", Vieweg, 1999.
  17. Peitgen, H. O. ; Jurgens, H. ; Saupe, D. : "Chaos and Fractals", New frontiers of science, New York Springer,1992 984pp.
  18. Peitgen, Heinz-Otto, and Peter H. Richter,"The Beauty of Fractals". New York: Springer Verlag, 1986.
  19. Pickover, C. A. ," Computers, Pattern, Chaos,Beauty". St. Martin's Press. ISBN 0-486-41709-3
  20. Ponomarev S. P. "On some properties of Van Koch curves". Siberian Mathematical Journal, 2007, Vol. 48, No 6, 1046-1059 . ]
  21. Warclaw Sierpinski, "Sur une courbe dont tout point est un point de ramication". Compt. Rendus Acad. Sci. Paris, 160:302{305, 1915.
  22. Wegmann H. , "Die HausdorfF-Dimension von kartesis"
  23. Weierstrass K. , "On Continuous Functions of a Real Argument that do not have a Well­De?ned Differential Quotient" in Classics on Fractals (Westview Press, 2004) pp. 3­9.
Index Terms

Computer Science
Information Sciences

Keywords

Sierpinski Gasket Fractal Coloring Complex variables