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Meta-Morphological Technique for a Multi-Parameter Design Index

Complex design and morphologic problems, consisting of multiple parameters, can be described, modelled and indexed using a meta-morphological technique presented here. All design and morphologic variables can be mapped in Euclidean n-dimensional space, where n is the number of variables. This meta-space contains all the possible solutions to the problem and each point in this solution n-space is a candidate solution. The desired solution, represented by a specific point in this space and coded (addressed) by its n-dimension Cartesian co-ordinates, is ranked by the hyper-distance of this point from the origin. The hyper-distance itself provides a design index (or hyper-index) of the solution and can be determined by the known hyper-Pythagorean theorem. The procedure is recursive and applies to complex design problems which are hierarchical and composed of problem-within-problem-within-problems. Here the parameters are composed of subparameters, and the solutions are correspondingly mapped in a recursive, fractal n-cube composed of sub-cubes composed of sub-sub-cubes. The total composite index is determined by the recursive application of the hyper-Pythagorean theorem and represents a quantification of the morphological complexity of the design. The model is independent of the design problem, and has attractive possibilities for application in computer-aided design environments. The application is shown with the hypothetical selection of a space frame from a number of alternatives.