  We describe a new phenomenon in models of coalescence and fragmentation, that
of gel-shatter cycles. These are dynamical, unforced, stochastic cycles in
which slow, approximately deterministic coalescence up to and beyond gelation
is followed by abrupt random shattering. We describe their appearance in
simulations of stochastic models with multiplicative kernels for coalescence
and spontaneous fragmentation into monomers (`shattering'). The regime in which
such cycles occur is characterized by a cyclicity order parameter, and we
provide a simple scaling argument which describes both this regime and those
which border it.
