Stationary distribution for a majority voter model

Let Z(d) represent a set of voters who can hold either of two opinions, zero or one. At each moment of time a voter is chosen at random and changes her opinion according to the opinion of her neighborhood. If the transition probability to one for a site with no one in its current neighborhood is zero, the Markov chain has two attractors at all zeros and all ones. Otherwise and this is the case we tackle-the chain is ergodic. Previous work on the 1-D model with neighborhood two/three led to a closed form expression for the stationary distribution, function of the number of 0-1 borders within the configuration. We now extrapolate the results to the five-neighborhood case and to the 2-D voter model.