Fractal Dimension Measurement Uncertainty

When designing complex systems, the problem of optimization is particularly relevant, that boils down to the solution of many inverse difficulties in developing a model of an object and its research. The using of complex objects in automatic design systems, which contain elements that jointly solve some general task of standard inverse calculation from specified system parameters to design characteristics or production technology, is also complicated. During such calculations, the use of such a characteristic parameter as the fractal dimension of the system elements allows one to significantly simplify the models used.. The principle of hierarchical organization of fractal-type models, in which it is possible to ascertain the absence of influence of scale on the properties of the object, i.e. extrapolation of the results of studying the properties of one of the scale levels to others is often found in nature and certainly manifests itself in material structures and functions that characterize the distribution of physical quantities in the space-time continuum. Despite its promise, its use in modeling the fractal dimension is complicated by issues of the accuracy of determining this parameter by various methods. The article is devoted to the development of a method for calculating the uncertainty of fractal dimension measurement, which is fully discribe the measuring results.