  The Mullineux map is a combinatorial function on partitions which describes
the effect of tensoring a simple module for the symmetric group in
characteristic $p$ with the one-dimensional sign representation. It can also be
interpreted as an isomorphism between crystal graphs for
$\widehat{\mathfrak{sl}}_p$. We give a new combinatorial description of the
Mullineux map by expressing this crystal isomorphism as a composition of
isomorphisms between different crystals. These isomorphisms are defined in
terms of new generalised regularisation maps introduced by Millan Berdasco.
  We then given two applications of our new realisation of the Mullineux map,
by providing purely combinatorial proofs of a conjecture of Lyle relating the
Mullineux map with regularisation, and a theorem of Paget describing the
Mullineux map in RoCK blocks of symmetric groups.
