A Metamodel for Describing the Outcomes of the Mana Cellular Automaton   Combat Model Based on Lauren's Attrition Equation
  In 1999 the author suggested an equation to describe the rate and temporal distribution of battle casualties. This equation was proposed as a replacement for the Lanchester equation. Unlike Lanchester's equation, the author's equation 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 match for the case studied is convincing, pointing to the potential of the equation to be adopted more generally for combat models. This is particularly so in the context of earlier work studying historical battle data that also supports an equation of the form of the author's proposal. 
M. K. Lauren