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Formulation of the problem. At the present stage of the development of science education and information technology, their integration, complementarity, and implementation are essential. Therefore, the search for methods of teaching natural sciences, based on the principles of self-organization and computer modeling, corresponds to the immediate tasks of the present. Materials and methods. Methods of comparative analysis, computer modeling, and generalization strategy are used. The study is based on the physics course content and the use of the programming language. Results. An innovative fractal approach to the teaching of physical and mathematical disciplines is proposed as a method of improving independent and creative computer modeling of natural phenomena. The fundamental principles of object-oriented programming (encapsulation, inheritance, polymorphism) have proven to be influential in shaping the physical and mathematical aspects of the information architecture of the perception of educational disciplines. The possibility of using this approach in other sections of physics is demonstrated. The developed iterations of the fractal structure are presented in the example of the study of the "Geometric Optics" and "Wave Optics" sections of physics. It is shown that each iteration is characterized by synergy: the addition of a new iteration provides a high-quality and in-depth perception of new information. Conclusions. The formation of the specified integrated fractal structure conditions the integrity of information perception and its formation happens intuitively. The analysis of the conducted studies confirmed the innovativeness and effectiveness of the fractal approach. This approach can be used to develop systems for the processing and transmission of information, intelligent information materials, and artificial intelligence.

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A synergetic model of the transition to a non-crystalline state is proposed, which enables us to investigate the temperature dependence of the microscopic parameters (meansquare displacements, the proportion of atoms in soft atomic configurations, power constants) under the influence of the external control parameter -the cooling velocity. Their analysis has been performed on the basis of experimental researches for noncrystalline semiconductors of the system As-S(Se). It has been shown that formation of self-organized structures in the non-crystalline solids is carried out in accordance with the technological conditions of obtaining as a method of the system self-organization. The dependence of the period and lifetime of self-organized structures on the cooling velocity has been studied. The established value of the period of spatial inhomogeneity L c ≈ 10…10 2 Å correlates with the nanosized midlle order in non-crystalline materials of the system As-S(Se) and decreases with increasing the cooling velocity.

Discussed in this paper are the singularity and self-organizing effect of instability and randomness under the influence of external white noise on formation of non-crystalline materials. The random nature of the receiving medium together with the disorganizing effect was found to be capable to initiate formation of qualitatively new self-organized structures in non-crystalline solids. Also analyzed in the paper is the effect of a random temperature field applied to the melt during the cooling process in non-crystalline As-S(Se) semiconductor systems. The conditions for a non-crystalline system in a fluctuating external environment to adjust its properties to the average properties of the environment and to correspond to the deterministic case were identified. Furthermore, the conditions for non-additive reaction of the system to a random environment and formation of a new mode of energy conversion in the self-organized structure at the nanoscale level are determined. The spectrum of the structures created in this way is more diverse as compared to the spectrum corresponding to respective deterministic conditions.