  The NC versus P-hard classification of the prediction problem for sandpiles
on the two dimensional grid with von Neumann neighborhood is a famous open
problem. In this paper we make two kinds of progresses, by studying its
freezing variant. First, it enables to establish strong connections with other
well known prediction problems on networks of threshold Boolean functions such
as majority. Second, we can highlight some necessary and sufficient elements to
the dynamical complexity of sandpiles, with a surprisingly crucial role of
cells with two grains.
