  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.
