The paper proposes a number of methods for neural network-assisted sedimentography based on discrete angular rotation algorithms and real-time correlation-spectral analysis, including those using synthetic data to identify the layered structures. Their applicability to various layered materials is shown, from geomineral textures formed by cyclic sedimentation to the layered graphene oxide-based membranes fabricated either by deposition onto a substrate or by other methods. It is pointed out that the main physical properties, in particular, permeability of such layered structured materials strongly depend on the layered structure, while the latter depends on the preparation method, which makes it possible to predict the main functional properties of membranes based on the results of the neural network-assisted sedimentography and real-time correlation-spectral analysis of the self-assembled multilayers and/or multilayer nanomaterials (both synthetic and natural, formed under geological conditions or during biomineralization). To prove the universal nature of the approach proposed, a description of the methodological aspects of the study and presentation of the experimental data are preceded by an analytical literature review in five parts (containing more than 200 references), in which, from the standpoint of physical reductionism, various forms of sedimentation are analyzed based on the unified physical background—from soft matter physics (colloids, polymers, mesophases), biochemistry, cell biology, and biomedicine, to nanomineralogy, hydrogeology and geology of sedimentary rocks, including pyroclastic ones and rhythmic sedimentation products. The proposed methodological approaches allow, regardless of the scale of the structured materials, to analyze the uniformity of the layers and angular distributions (angular anisotropy) for different stages of their formation, as well as the chemical substitution of such textures or rhythmic sedimentation products on the arbitrary time scales (from minutes of the laboratory experiments to the geological eons in the case of analysis of the natural sedimentary multilayers). In the experimental part, we showed that the order parameters of the synthetic and natural layered textures can be quite close, and also illustrated the scale dependence of the order parameters calculated using Legendre and Chebyshev polynomials. Both methods developed on the basis of discrete angular rotation algorithms and correlation-spectral techniques based on 2D FFT are suitable for identifying the orientational disorganization of the structural elements in multilayer structured materials and their anisotropy. In the future, such techniques can be used in a wide range of scientific and applied problems from the analysis of nanomaterials (such as carbon multilayer nanostructures and MXenes) to experimental mineralogy and interpretation of geophysical sounding results.