  We present the results of an experimental study of patterned segregation in a
horizontally shaken shallow layer of a binary mixture of dry particles. An
order parameter for the segregated structures is defined and the effect of the
variation of the combined filling fraction, $C$, of the mixture on the observed
pattern formation is systematically studied. The surprising result is that
there is a critical event associated with the onset of the pattern, at
$C=0.647\pm0.049$, which has the characteristics of a second order phase
transition, including critical slowing down.
