Characterising the Difference between Complex Adaptive and Conventional   Combat Models
  An attempt is made to quantitatively demonstrate the difference between a complex adaptive combat model and conventional combat models. The work shows that complex adaptive models may give rise to "turbulent" dynamics, which emerge once the battlefield is no longer "linear", i.e. once military formations no longer form ordered lines or columns. This is done using a cellular automaton model. This model exhibits a high degree of complexity, leading to a rich variety of behaviour. Conventional statistical methods fail to adequately capture this richness. Particular attention is paid to the properties of the attrition function. It is found that this function is discontinuous and possesses non-linear properties such as clustering of casualties, scaling of the statistical moments of the data and fat-tailed probability distributions. Fractal methods are found to be capable of quantifying these properties. A particularly significant result is the non-linearity of the pay-off of improved weapons performance. This contrasts with conventional models, where the attrition rate usually depends in a linear way on kill probability. Additionally, the model is found to possess at least two attractive states. A transition exists between the two cases in some situations. This transition appears to behave in an analogous way to the transition between laminar and turbulent states in fluid dynamics. 
M. K. Lauren