  Groves are spanning forests of a finite region of the triangular lattice that
are in bijection with Laurent monomials that arise in solutions of the cube
recurrence. We introduce a large class of probability measures on groves for
which we can compute exact generating functions for edge probabilities. Using
the machinery of asymptotics of multivariate generating functions, this lets us
explicitly compute arctic curves, generalizing the arctic circle theorem of
Petersen and Speyer. Our class of probability measures is sufficiently general
that the limit shapes exhibit all solid and gaseous phases expected from the
classification of EGMs in the resistor network model.
