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The effect structural changes in fractal-like multilayered structures with metamaterial inserts have on the stability of the shape of fractal patterns in their optical spectra is investigated. Calculations using the model of approximants allows scaling parameters to be obtained that establish the relationship between structural features and their optical spectra.

Algorithms for constructing dendrites and analyzing their fractal characteristics are considered. Multi-parameter identification that includes the determination of scaling parameters is proposed. Patterns that determine the relationship between the structure features of dendrites and their diffraction patterns are obtained.

A simple method for constructing a 2D fractal cluster of nanodendrities formed in the self-organization process of nanoparticles is presented. The relationship between the structural features of dendrite-type lattices and the fractal characteristics of both studied objects and their diffraction patterns is revealed.

Fractal pattern analysis is performed for aperiodicmultilayer systems with metamaterials. Morphological features of pattern formation in optical characteristics of structures with different geometry are revealed having regard to the manifestation of the phase-compensation effect and presence of metamaterial layers.

On the basis of the use of fractal concepts the conditions for the stability of patterning structures in the optical spectra of approximants aperiodic structures are defined. The conditions of the optical characteristics of different types of equivalence approximants are described.

This work is aimed at solving one of the fundamental problems of modern fractal optics. The goal is to establish general laws that relate structural features of fractal-like systems and their associated spectral characteristics. Establishing such laws allows finding new diagnostic approaches for exploration of fractal-like systems and their formation processes. Nanocluster systems and multilayer structures, also with inclusion of metamaterial inserts, were chosen as the objects of research. A wide variety of applications of varying physical nature is enabled as fractal optics successfully penetrate into interdisciplinary technologies and theoretical concepts. In this work, particular interest is paid to scaling properties of structures of the studied systems and their optical characteristics. Based on theoretically obtained amplitude and phase distributions of light waves that diffract or interfere in the analyzed systems, the features of scaling in light fields are determined. When analyzing the obtained modeling results, a comparison is made between the structural features of the studied systems revealed by the scaling parameters in diffraction patterns and transmission spectra.