  The complete framework for the $\epsilon$-machine construction of the one
dimensional Ising model is presented correcting previous mistakes on the
subject. The approach follows the known treatment of the Ising model as a
Markov random field, where usually the local characteristic are obtained from
the stochastic matrix, the problem at hand needs the inverse relation, or how
to obtain the stochastic matrix from the local characteristics, which are given
via the transfer matrix treatment. The obtained expressions allow to perform
complexity-entropy analysis of particular instance of the Ising model. Three
examples are discussed: the 1/2-spin nearest neighbor and next nearest neighbor
Ising model, and the persistent biased random walk.
