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.