Parametric equation of Mandelbrot curve on k-th iteration?

Question

Is there a way to write the parametric equation of the Mandelbrot-set's boundary curve at every $k^{th}$ iteration?

Answer 1

You could try the Laurent Series for the conformal map from the complement of the unit disc to the complement of the Mandelbrot set, put in $w = r \exp(2 \pi i t)$ where $r > 1$ depends on $k$ (something like $r = 1 + 2^{-k}$, not sure of the exact formula). But it is very slow to converge.