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: $z = x + yi$)