Hypercomputing the Mandelbrot Set?

The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the (non-)computability of the set. It considers two models of decidability over the reals (which have been treated much more thoroughly and technically by Hertling (2005), Blum, Shub and Smale, Brattka (2003) and Weihrauch (1999 and 2003) among others), two over the computable reals (the Russian school and hypercomputation) and a model over the rationals.