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I've post this question just because I'm curious,

Mandelbrot set is defined as: $ z_{n+1} = z^2_n + c $, if $n \rightarrow \infty $ and it doesn't diverge we get the border. This border is unlimited and it's direction isn't definite, so I think it's a problematic.

My question is if we can write the border in a parametric way like this: $ \left \lbrace \begin{array}{l} x = x(t) \\ y = y(t) \end{array} \right. $ , if we need some extra variabile to approximate the system or it's impossible to write it in this form. ($z \in \mathbb{C}$ so we can decompose it in: $z = x + yi$)

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    @GEdgar: Thank you very much, the note has been very useful. Even if I don't understand how can I use Fourier series, I've seen how to get coefficients (the most important thing), I report the [link](http://www.mrob.com/pub/muency/laurentseries.html) taken from a comment.2012-10-05

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