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Groebner basis, resultants and the generalized Mandelbrot set

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  • Geum, Young Hee
  • Hare, Kevin G.

Abstract

This paper demonstrates how the Groebner basis algorithm can be used for finding the bifurcation points in the generalized Mandelbrot set. It also shows how resultants can be used to find components of the generalized Mandelbrot set.

Suggested Citation

  • Geum, Young Hee & Hare, Kevin G., 2009. "Groebner basis, resultants and the generalized Mandelbrot set," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1016-1023.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:1016-1023
    DOI: 10.1016/j.chaos.2009.02.039
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    References listed on IDEAS

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    1. Negi, Ashish & Rani, Mamta, 2008. "Midgets of superior Mandelbrot set," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 237-245.
    2. Pastor, G. & Romera, M. & Álvarez, G. & Arroyo, D. & Montoya, F., 2007. "On periodic and chaotic regions in the Mandelbrot set," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 15-25.
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    Cited by:

    1. Lateef Olakunle Jolaoso & Safeer Hussain Khan, 2020. "Some Escape Time Results for General Complex Polynomials and Biomorphs Generation by a New Iteration Process," Mathematics, MDPI, vol. 8(12), pages 1-18, December.

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