  The anti-continuum limit of a monotone variational recurrence relation
consists of a lattice of uncoupled particles in a periodic background. This
limit supports many trivial equilibrium states that persist as solutions of the
model with small coupling. We investigate when a persisting solution generates
a so-called lamination and prove that near the anti-continuum limit the
collection of laminations of solutions is homeomorphic to the (N-1)-dimensional
simplex, with N the number of distinct local minima of the background
potential. This generalizes a result by Baesens and MacKay on twist maps near
an anti-integrable limit.
