The Mandelbrot Set

Heinz-Otto Peitgen and Peter H. Richter
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Heinz-Otto Peitgen: Universität Bremen, Fachbereich Mathematik
Peter H. Richter: Universität Bremen, Fachbereich Physik

Chapter 4 in The Beauty of Fractals, 1986, pp 56-62 from Springer

Abstract: Abstract For polynomials of second order, p(x) = a2x2 + a1x + ao, an almost complete classification of the corresponding Julia sets can be given in terms of the Mandelbrot set. First note that p(x is conjugate to p c (z)=z2 + c by means of the coordinate transformation $$ x \mapsto z = a_2 x + a_1 /2,with{\text{ }}c = a_0 a_2 + \frac{{a_1 }} {2}\left( {1 - \frac{{a_1 }} {2}} \right). $$

Date: 1986
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DOI: 10.1007/978-3-642-61717-1_4

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