  Despite being invented in 1951 by R. Kikuchi, the 2-D Cluster Variation
Method (CVM), has not yet received attention. Nevertheless, this method can
usefully characterize 2-D topographies using just two parameters; the
activation enthalpy and the interaction enthalpy. This Technical Report
presents 2-D CVM details, including the dependence of the various configuration
variables on the enthalpy parameters, as well as illustrations of various
topographies (ranging from scale-free-like to rich club-like) that result from
different parameter selection. The complete derivation for the analytic
solution, originally presented simply as a result in Kikuchi and Brush (1967)
is given here, along with careful comparison of the analytically-predicted
configuration variables versus those obtained when performing computational
free energy minimization on a 2-D grid. The 2-D CVM can potentially function as
a secondary free energy minimization within the hidden layer of a neural
network, providing a basis for extending node activations over time and
allowing temporal correlation of patterns.
