  Markov Random Field models are powerful tools for the study of complex
systems. However, little is known about how the interactions between the
elements of such systems are encoded, especially from an information-theoretic
perspective. In this paper, our goal is to enlight the connection between
Fisher information, Shannon entropy, information geometry and the behavior of
complex systems modeled by isotropic pairwise Gaussian Markov random fields. We
propose analytical expressions to compute local and global versions of these
measures using Besag's pseudo-likelihood function, characterizing the system's
behavior through its \emph{Fisher curve}, a parametric trajectory accross the
information space that provides a geometric representation for the study of
complex systems. Computational experiments show how the proposed tools can be
useful in extrating relevant information from complex patterns. The obtained
results quantify and support our main conclusion, which is: in terms of
information, moving towards higher entropy states (A --> B) is different from
moving towards lower entropy states (B --> A), since the \emph{Fisher curves}
are not the same given a natural orientation (the direction of time).
