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The Mandelbrot set

Figure 3: A plot of the whole Mandelbrot set. The resolution in x and y direction is 350 points and the iteration depth is 200 iterations. The color function is potted in Figure 8
\includegraphics {Pics/bigmandel.ps}

Definition 2 (The Mandelbrot set)   The Mandelbrot-set $ M$ is the set of all complex numbers $ c$, for which the iteration of the function $ Q_c:=z^{2}+c$ with the start value $ z_0$ is bounded.
\begin{subequations}\begin{align}z_0=c \\ z_{n+1}=Q(z_n) \qquad n\geq 1\\ M:=\... ..._{n\to\infty}\vert Q_c(z_n)\vert <\infty \right \} \end{align}\end{subequations}


Subsections
Tino Kluge
2000-12-05