This question may not have a definitive answer. However, if someone is able to illuminate the topic for me, I would be very grateful.
The Mandelbrot set is the set obtained from the quadratic recurrence equation{1}:
$ \begin{equation} z_{n+1}=z_n^2 + c \end{equation} $
I'm sure most of you know what the graphical representation of the Mandelbrot set looks like, so I won't post a picture of it here.
Question
Have there been any attempts to derive the Mandelbrot set equation purely from it's graphical representation?
I would imagine that this would involve some sort of machine learning process which searches through program space trying to find a correct program with the smallest Kolmogorov complexity{2}.
What branch of mathematics works on solving this type of problem?
Thank you.