  In this report the authors examine the possibility of using the Fractal
Attrition Equation as a metamodel to describe outcomes of cellular automaton
combat models. This Fractal Attrition Equation has been proposed as a
replacement for the Lanchester equation. Unlike Lanchester's equation, it is
based on a measurement of the spatial distribution of forces involved in a
battle, and incorporates this by use of the concept of the fractal dimension.
In this report, the form of the expected Loss-Exchange-Ratio function based on
this equation is determined. It is shown how this function can be used as a
Metamodel to describe the outcome of some cellular automaton models. While this
is not an exhaustive proof of the validity of the equation, the case discussed
does display interesting features which should be further investigated. This is
particularly so given the earlier work of the authors in demonstrating that the
Fractal Attrition Equation explains certain features of historical combat data.
