FRACTALS AND COMBAT MODELING: USING MANA TO EXPLORE THE ROLE OF ENTROPY IN COMPLEXITY SCIENCE

Combat data collected from World War II and a cellular automaton combat model called MANA are shown to display fractal properties. This strongly supports our earlier hypotheses as to the nature of combat attrition data. It also provides a method by which we can judge a combat model's ability to produce realistic synthetic combat data. The data appear to display properties extremely similar to those of the fractal cascade models used to describe turbulent dynamics. Interestingly, the fractal parameters appear to depend on how the model is set up, implying that they are determined by the boundary and initial conditions. Examination of the dynamical rules used in the MANA model simulation suggests that the model entities need to respond to changes in the level of order on the battlefield grid for fractal behavior to occur. Such data imply that the entropy of the battlefield is dependent on the scale at which it is examined. We speculate that such formations in a military case effectively act to isolate the highest level of command from disorder in the lowest. If disorder within a force grows to the point where that force can no longer maintain a fractal-like distribution, the force distribution may tend to become uniformly random, effectively destroying its viability as a combat unit.