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

한국수학교육학회지시리즈B:순수및응용수학 / 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 (DEPARTMENT OF APPLIED MATHEMATICS, CHEONAN CAMPUS, DANKOOK UNIVERSITY)
Lee, Kang-Sup (DEPARTMENT OF MATHEMATICS EDUCATION, SEOUL CAMPUS, DANKOOK UNIVERSITY)
Kim, Young-Ik (DEPARTMENT OF APPLIED MATHEMATICS, CHEONAN CAMPUS, DANKOOK UNIVERSITY)

Geum, Young-Hee, Lee, Kang-Sup, & Kim, Young-Ik. (2007). A FAST CONSTRUCTION OF GENERALIZED MANDELBROT SETS USING MAIN COMPONENTS WITH EPICYCLOIDAL BOUNDARIES. 한국수학교육학회지시리즈B:순수및응용수학, 14(3), 191-196.

복사

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

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논문 상세

Vol.14 No.3

A FAST CONSTRUCTION OF GENERALIZED MANDELBROT SETS USING MAIN COMPONENTS WITH EPICYCLOIDAL BOUNDARIES

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

Abstract

한국수학교육학회지시리즈B:순수및응용수학