A Study on Mandelbrot Sets to Generate Visual Aesthetic Fractal Patterns

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Abstract:

The fractal pattern is a highly visual aesthetic image. This article describes the generation method of Mandelbrot set to generate fractal art patterns. Based on the escape time algorithm on complex plane, the visual aesthetic fractal patterns are generated from Mandelbrot sets. The generated program development, a pictorial information system, is integrated through the application of Visual Basic programming language and development integration environment. Application of the development program, this article analyzes the shape of the fractal patterns generated by the different power orders of the Mandelbrot sets. Finally, the escape time algorithm has been proposed as the generation tools of highly visual aesthetic fractal patterns.

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111-116

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February 2013

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[1] B.B. Mandelbrot: Fractal: Form, Chance, and Dimension (W.H. Freeman Publications, San Francisco 1977).

Google Scholar

[2] B.B. Mandelbrot: The Fractal Geometry of Nature (W.H. Freeman Publications, San Francisco 1982).

Google Scholar

[3] K.J. Falconer: The Geometry of Fractal Sets (Cambridge University Press, Cambridge 1985).

Google Scholar

[4] H.O. Peitgen and P.H. Richter: The Beauty of Fractals (Springer-Verlag, Heidelberg 1986).

Google Scholar

[5] K.J. Falconer: Fractal Geometry: Mathematical Foundations and Application (John Wiley and Sons Press, New York 1991).

Google Scholar

[6] K.J. Falconer: Techniques in Fractal Geometry (John Wiley and Sons Press, New York 1997).

Google Scholar

[7] B.B. Mandelbrot, D.E. Passoja and A. Paully: Nature Vol. 308 (1984), p.721

Google Scholar

[8] A.L. Goldberger and B.J. WEST: The Yale Journal of Biology and Medicine Vol. 60 (1987), p.421

Google Scholar

[9] R.P. Taylor and J.C. Sprott: Nonlinear Dynamics, Psychology, and Life Sciences Vol. 12(1) (2008), p.117

Google Scholar

[10] K.T. Lam and Y.F. Chang: Journal of Design Education Vol. 1(1) (2010), p.31

Google Scholar

[11] K.T. Lam and K.H. Wen: Journal of Design Education Vol. 1(3) (2010), p.45

Google Scholar

[12] S. Bajaj and A. Kaushik: International Journal of Engineering Research and Applications Vol. 2(1) (2012), p.229

Google Scholar