  For a class of $\zz^2$ Markov Random Fields (MRFs) $\mu$, we show that the
sequence of successive differences of entropies of induced MRFs on strips of
height $n$ converges exponentially fast (in $n$) to the entropy of $\mu$. These
strip entropies can be computed explicitly when $\mu$ is a Gibbs state given by
a nearest-neighbor interaction on a strongly irreducible nearest-neighbor
$\zz^2$ shift of finite type $X$. We state this result in terms of
approximations to the (topological) pressures of certain functions on such an
$X$, and we show that these pressures are computable if the values taken on by
the functions are computable. Finally, we show that our results apply to the
hard core model and Ising model for certain parameter values of the
corresponding interactions, as well as to the topological entropy of certain
nearest-neighbor $\zz^2$ shifts of finite type, generalizing a result in
\cite{Pa}.
