Fractal self-organization of educational systems into hyperbolic rank distributions

Introduction. Cenology is a new scientific field that arose more than forty years ago, studying cenoses of different nature (techno-, bio-, eco-, cosmo-, sociocenoses). At the same time, it was found out that the objects of cenoses self-organize into hyperbolic rank distributions (GRR) at all scale levels. Technogenic self-organization is described by B.I. Kudrin. Earlier it was reported about the self-organization of space objects (satellites of planets, planets, stars, star clusters, galaxies, clusters of galaxies) in exploration at all cosmic levels and the fractal nature of this process (R.V. Gurina). It was concluded that the deterministic nature of these processes: God does not play dice. Are similar processes taking place in the field of education? The purpose of this study was to find the answer to this question. Purpose setting. Generalization and analysis of the results of the study of hyperbolic rank distributions (GRR) of educational systems for the period 2002 – 2024; classification of GRR by scale levels. Methodology and methods of the study. Induction, deduction, analogy; graphical construction and approximation of GRP using computer programs; comparison of GRP by the Pearson method. Results. Examples from the graphical evidence base for this period are given: ratings of students, educational institutions of cities, countries. As it turned out, they are all classic hyperboles of varying steepness. In the process of analyzing the results, the synergetic fractal nature of educational objects organized into cenoses, like bio- and technocenoses, was revealed, which is the novelty and scientific value of the study. At the same time, fractality is an integral property of educational values, as well as of technocenoses. Unlike Mandelbrot fractals, the self – organization of objects in education, as well as in technology, is carried out at different hierarchical levels not according to a geometric, but according to a cenological type – in GRR. The considered set of educational facilities is distributed over five scale levels and forms a fractal megasystem, the model of which is presented in the form of a level scheme. Conclusion. The results obtained are a contribution to the theory and practice of cenology, a new scientific field, expanding its scope to the field of education; the Pareto 80/20 principle is a logical consequence of the law of GRR.