Pattern analysis of fractal-like systems

Abstract

The features of the Fourier spectra of fractal-like systems are studied. On the basis of theoretical studies, the features of the scaling invariants of the objects under consideration in light fields are determined, which manifest themselves in the form of stable local formations — patterns. Particular attention is paid to the problem of stability of the ratios of the scaling characteristics of the analyzed systems and their Fourier transforms. The possibility of identifying and systematizing various fractal systems based on the estimation of their scaling parameters is considered. An analysis of the stability of the scaling parameters of the probing radiation to changes in the parameters of the systems under study indicates that the pattern approach to improving the methods of optical diagnostics is promising.