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ISSN : 1226-0657

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Vol.14 No.3

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A Fast Construction of Generalized Mandelbrot Sets Using Main Componentswith Epicycloidal Boundaries

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2007, v.14 no.3, pp.191-196
Geum, Young-Hee
Lee, Kang-Sup
Kim, Young-Ik
Geum,, Y. , Lee,, K. , & Kim,, Y. (2007). A Fast Construction of Generalized Mandelbrot Sets Using Main Componentswith Epicycloidal Boundaries. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 14(3), 191-196.

Abstract

The main components in the generalized Mandelbrot sets are under a theoretical investigation for their parametric boundary equations. Using the boundary geometries, a fast construction algorithm is introduced for the generalized Mandelbrot set. This fast algorithm definitely reduces the construction CPU time in comparison with the naive algorithm. Its graphic implementation displays the mysterious and beautiful fractal sets.

keywords
Mandelbrot set, fractal set, epicycloid, degree-n bifurcation set

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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