  For any two-dimensional nearest neighbor shift of finite type X and any
integer n > 0, one can define the horizontal strip shift H_n(X) to be the set
of configurations on Z x {1,...,n} which do not contain any forbidden
transitions for X. It is always the case that the sequence h(H_n(X))/n of
normalized topological entropies of the strip shifts approaches h(X), the
topological entropy of X. In this paper, we use probabilistic methods from
interacting particle systems to show that for the two-dimensional hard square
shift H, in fact h(H_{n+1}(H)) - h(H_n(H)) also approaches h(H), and the rate
of convergence is at least exponential. A consequence of this is that h(H) is
computable to any tolerance 1/n in time polynomial in n. We also give an
example of a two-dimensional block gluing nearest neighbor shift of finite type
Y for which h(H_{n+1}(Y)) - h(H_n(Y)) does not even approach a limit.
