  We investigate stationary, spatially localized patterns in lattice dynamical
systems that exhibit bistability. The profiles associated with these patterns
have a long plateau where the pattern resembles one of the bistable states,
while the profile is close to the second bistable state outside this plateau.
We show that the existence branches of such patterns generically form either an
infinite stack of closed loops (isolas) or intertwined s-shaped curves
(snaking). We then use bifurcation theory near the anti-continuum limit, where
the coupling between edges in the lattice vanishes, to prove existence of
isolas and snaking in a bistable discrete real Ginzburg--Landau equation. We
also provide numerical evidence for the existence of snaking diagrams for
planar localized patches on square and hexagonal lattices and outline a
strategy to analyse them rigorously.
