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An effective algorithm to compute Mandelbrot sets in parameter planes

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Abstract

In McMullen (2000) it was proven that copies of generalized Mandelbrot set are dense in the bifurcation locus for generic families of rational maps. We develop an algorithm to an effective computation of the location and size of these generalized Mandelbrot sets in parameter space. We illustrate the effectiveness of the algorithm by applying it to concrete families of rational and entire maps.

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Authors and Affiliations

  1. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007, Tarragona, Catalonia, Spain

    Antonio Garijo & Jordi Villadelprat

  2. Departament de Matemàtica i Informàtica and Graduate School of Mathematics, Universitat de Barcelona, 08007, Barcelona, Catalonia, Spain

    Xavier Jarque

Authors
  1. Antonio Garijo
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  2. Xavier Jarque
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  3. Jordi Villadelprat
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Correspondence to Xavier Jarque.

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Garijo, A., Jarque, X. & Villadelprat, J. An effective algorithm to compute Mandelbrot sets in parameter planes. Numer Algor 76, 555–571 (2017). https://doi.org/10.1007/s11075-017-0270-8

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  • DOI: https://doi.org/10.1007/s11075-017-0270-8

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