The week's pick
Reseach Article
New Escape Time Koch Curve in Complex Plane
by
Priti Dimri,
Dharmendra Kumar,
Ashish Negi
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 58 - Number 8 |
| Year of Publication: 2012 |
| Authors: Priti Dimri, Dharmendra Kumar, Ashish Negi |
10.5120/9302-3521
|
Priti Dimri, Dharmendra Kumar, Ashish Negi . New Escape Time Koch Curve in Complex Plane. International Journal of Computer Applications. 58, 8 ( November 2012), 19-24. DOI=10.5120/9302-3521
@article{
10.5120/9302-3521,
author = {
Priti Dimri,
Dharmendra Kumar,
Ashish Negi
},
title = { New Escape Time Koch Curve in Complex Plane },
journal = {
International Journal of Computer Applications
},
issue_date = { November 2012 },
volume = { 58 },
number = { 8 },
month = { November },
year = { 2012 },
issn = { 0975-8887 },
pages = {
19-24
},
numpages = {9},
url = {
https://ijcaonline.org/archives/volume58/number8/9302-3521/
},
doi = { 10.5120/9302-3521 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:01:56.151138+05:30
%A Priti Dimri
%A Dharmendra Kumar
%A Ashish Negi
%T New Escape Time Koch Curve in Complex Plane
%J International Journal of Computer Applications
%@ 0975-8887
%V 58
%N 8
%P 19-24
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract
Von Koch curves allow numerous variations and have inspired many researchers and fractal artists to produce amazing pieces of art. In this paper we present a new algorithm for plotting the Koch curve using complex variables. Further we have applied various coloring algorithms to generate complex Koch fractals.
References
- Barnsley, M. , 1988, "Fractals Everywhere" (San Diego: Academic Press, Inc).
- Barrallo, J. and Jones, D. , 1999, "Coloring algorithms for dynamical systems in the complex plane", ISAMA 99 Proceedings, 31-38.
- Barralo, J. and Sanchez, S. , 2001, "Fractals and multi layer colouring algorithms", Bridges Conference Proceedings 2001, 89.
- Box Dimension of Koch's Curve (http://classes. yale. edu/fractals/FracAndDim/BoxDim/BoxDim. html)
- 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).
- Devaney, R. L. : "Chaos, Fractals and dynamics", Computer experiments in mathematics, Menlo Park, Addison – Wessley (1992).
- Devaney, R. L. : "The fractal Geometry of the Mandelbrot set , 2. How to count and how to add . Symposium in honor of Benoit Mandelbrot (Curaco 1995), Fractal 1995;3(4),629-40[MR1410283(99d:58095)].
- Falconer, K. , 2003, Fractal Geometry: "Mathematical Foundations and Applications" (West Sussex: John Wiley & Sons, Ltd).
- HYBURN G. T. W, "Topological characterization of the Sierpinski curve", Fund. Math. 45 (1958), 320–324.
- George Cantor "On the Power of Perfect Sets of Points" in Classics on Fractals (Westview Press, 2004) pp. 1123.
- 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.
- http://www. ehow. com/about_5332193_koch-curve. html#ixzz28iB4f5OO
- Falconer K. J. , "Techniques in Fractal Geometry", Wiley, 1997.
- Mandelbrot, Benoit B, "The Fractal Geometry of Nature". New York: W. H. Freeman and Company, 1982.
- MILNOR J. and TAN LEI, A "Sierpinski Carpet" as Julia set. Appendix F in Geometry and dynamics of quadratic rational maps, Experiment. Math. 2 (1993), 37–83.
- MILNOR J. , "Dynamics in One Complex Variable", Vieweg, 1999.
- P. Prusinkiewicz and G. Sandness: "Attractors and repellers of Koch curves". Proceedings of Graphics Interface'88, pp. 217?228"
- Peitgen, H. O. ; Jurgens, H. ; Saupe, D. : "Chaos and Fractals, New frontiers of science", New York Springer,1992 984pp.
- Peitgen, Heinz-Otto, and Peter H. Richter, "The Beauty of Fractals". New York: Springer Verlag, 1986.
- Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe, "Fractals for the Classroom". New York: Springer Verlag, 1992.
- Pickover, C. A. ," Computers, Pattern, Chaos, and Beauty". St. Martin's Press. ISBN 0-486-41709-3
- Ponomarev S. P. On some properties of Van Koch curves. Siberian Mathematical Journal, 2007, Vol. 48, No 6, 1046-1059.
- Richard M. Crownover, "Introduction to Fractals and Chaos" (Jones and Bartlett, Boston, 1995).
- 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