  The "SOS" in the title does not refer to the international distress signal,
but to "solid-on-solid" (SOS) surface growth. The catastrophic cascades are
those observed by Buldyrev {\it et al.} in interdependent networks, which we
re-interpret as multiplex networks with agents that can only survive if they
mutually support each other, and whose survival struggle we map onto an SOS
type growth model. This mapping not only reveals non-trivial structures in the
phase space of the model, but also leads to a new and extremely efficient
simulation algorithm. We use this algorithm to study interdependent agents on
duplex Erd\"os-R\'enyi (ER) networks and on lattices with dimensions 2, 3, 4,
and 5. We obtain new and surprising results in all these cases, and we correct
statements in the literature for ER networks and for 2-d lattices. In
particular, we find that $d=4$ is the upper critical dimension, that the
percolation transition is continuous for $d\leq 4$ but -- at least for $d\neq
3$ -- not in the universality class of ordinary percolation. For ER networks we
verify that the cluster statistics is exactly described by mean field theory,
but find evidence that the cascade process is not. For $d=5$ we find a first
order transition as for ER networks, but we find also that small clusters have
a nontrivial mass distribution that scales at the transition point. Finally,
for $d=2$ with intermediate range dependency links we propose a scenario
different from that proposed in W. Li {\it et al.}, PRL {\bf 108}, 228702
(2012).
