Diffuse Gaussian multiple-shot patterns

When multiple weapons are aimed against a single target, it is sometimes effective to aim the shots in a pattern around the target, rather than all directly at it. Determining the optimal shot pattern has been an object of analysis since World War II, when John von Neumann first employed the ‘Diffuse Gaussian’ damage function in the process of simplifying a one dimensional bombing problem. This paper generalizes the method, and explains how it can be used in a spreadsheet to find optimal patterns.