We study subshifts of nite type on f0;1g Z 2 of the form where in a nite window there is always either one on no 1's present. The problem is converted to a tiling/covering problem on the (nZ) 2 lattice and its shifts. In this setup we consider the uniqueness of the equilibrium measure, density of 1's at equilibrium and the topological entropy. Further insight is achieved by realizing that the equilibrium measure is the ground state of an extremely simple probabilistic cellular automaton. Our study indicates critical behavior in this one parameter class of rules.