  We give a conjectural characterisation of the stable reduction of plane
quartics over local fields in terms of their Cayley octads. This results in
p-adic criteria that efficiently give the stable reduction type amongst the 42
possible types, and whether the reduction is hyperelliptic or not. These
criteria are in the vein of the machinery of "cluster pictures" for
hyperelliptic curves. We also construct explicit families of quartic curves
that realise all possible stable types, against which we test these criteria.
We give numerical examples that illustrate how to use these criteria in
practice.
