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An efficient construction of period-2 bulbs in the cubic Mandelbrot set with parametric boundaries

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Abstract

A parametric boundary equation is established for the principal period-2 bulb in the cubic Mandelbrot set. Using its geometry, an efficient escape-time algorithm which reduces the construction time for the period-2 bulbs in the cubic Mandelbrot set is introduced and the implementation graphic results display the fascinating fractal beauty

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Authors and Affiliations

  1. Department of General Mathematics, Dankook University, Anseo-dong 29, Cheonan, 330-714, Chungnam, Korea

    Young Hee Geum & Young Ik Kim

  2. Department of Mathematics Education, Dankook University, Hannam-dong, Yongsan-gu, 140-714, Seoul, Korea

    Kang Sup Lee

Authors
  1. Young Hee Geum
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  2. Young Ik Kim
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  3. Kang Sup Lee
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Correspondence to Kang Sup Lee.

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Geum, Y.H., Kim, Y.I. & Lee, K.S. An efficient construction of period-2 bulbs in the cubic Mandelbrot set with parametric boundaries. J. Appl. Math. Comput. 25, 109–118 (2007). https://doi.org/10.1007/BF02832341

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  • DOI: https://doi.org/10.1007/BF02832341

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