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1992•International Journal of Bifurcation and ChaosRequires access

NONANALYTIC DYNAMICS FOR GENERATING THE MANDELBROT SET: A TUTORIAL

Wolfgang Metzler, A. BRELLE, Klaus Dieter Schmidt

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Abstract

From experimental work, nonanalytic quadratic maps are known which generate the Mandelbrot set as well as Julia sets not different from those obtained by the complex analytic quadratic family z↦z2+c, c∈C. This paper presents a tutorial on how to generate analytically the complete class of real parameter-dependent quadratic maps of the plane, all having, for instance, the Mandelbrot set in common with the quadratic family. In the analytical case, the transformations involved are rotations or reflections.

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What this paper is about

From experimental work, nonanalytic quadratic maps are known which generate the Mandelbrot set as well as Julia sets not different from those obtained by the complex analytic quadratic family z↦z2+c, c∈C. This paper presents a tutorial on how to generate analytically the complete class of real parameter-dependent quadratic maps of the plane, all having, for instance, the Mandelbrot set in common with the quadratic family. In the analytical case, the transformations involved are rotations or reflections.

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Available abstract

From experimental work, nonanalytic quadratic maps are known which generate the Mandelbrot set as well as Julia sets not different from those obtained by the complex analytic quadratic family z↦z2+c, c∈C. This paper presents a tutorial on how to generate analytically the complete class of real parameter-dependent quadratic maps of the plane, all having, for instance, the Mandelbrot set in common with the quadratic family. In the analytical case, the transformations involved are rotations or reflections.

Key concepts: Mandelbrot set, Julia set, Quadratic equation, Complex quadratic polynomial, Complex plane, Mathematics, Set (abstract data type), Class (philosophy)

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