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It is shown that the partial elimination of the incompleteness of formal axiomatic statements about the incompleteness of the metal structure, according to Gödel's theorem, possibly by fitting this structure using the language of fractal geometry. In this regard, the book gives the step-by-step algorithm aimed at determination of the fractal dimension of the identifiable structure as well as examples of the application of topological and fractal evaluations to forecast characteristics of the material quality.