The spatial entropy of two-dimensional subshifts of finite type

In this paper, two recursive formulas for computing the spatial entropy of two-dimensional subshifts of finite type are given. The exact entropy of a nontrivial example arising in cellular neural networks is obtained by using such formulas. We also establish some general theory concerning the spatia l entropy of two-dimensional subshifts of finite type. In particular, we sh ow that if either of the transition matrices is rank-one, then the associat ed exact entropy can be explicitly obtained. The generalization of our resu lts to higher dimension can be similarly obtained. Furthermore, these formu las can be used numerically for estimating the spatial entropy.