Irrelevance of the fractal dimension term in the fractal attrition equation

Abstract

The modified Fractal Attrition Equation (mFAE) models the casualties produced by Map Aware Non-uniform Automata (MANA), an agent based combat modelling distillation, at each MANA time step. The mFAE has three important differences from the simple early twentieth century models of casualties that used only the numbers on each side to make predictions. Firstly, only those agents within range of the enemy may inflict casualties. Secondly, the detection range is assumed to be greater than the range of weapons and a fitting factor assumed to represent the gap between these two ranges, is introduced. This builds in one of the assumptions of Network Centric Warfare, that you will be able to see your enemies before they can shoot at you. Thirdly, and novelly, a fractal dimension is introduced. We postulate that the important part of the information used in calculating the fractal dimension has already been incorporated into the model through the consideration of range. We test this hypothesis by comparing the outcomes of the mFAE with and without the fractal term on three scenarios: that used by the developers of the mFAE; best practice MANA tactics from the literature; and a rout scenario. When the two models are scaled to fit the MANA casualties there is no significant difference in fit. We conclude that the fractal term in the mFAE is redundant. References

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