Integration of interdisciplinary directions in the study of fractal geometry elements

This paper deals with the problem of integrating interdisciplinary areas in research activities that underlie developmental learning. In the conditions of new educational standards introduction deep system transformations of the whole educational process are supposed. The search for solutions to the problems of individualizing the educational route, polar motivation, increasing interest in physics and mathematics lead to the need to design individual methods of pedagogical activity, to implement new approaches and technologies in the natural science cycle of consistent development of holistic research activities, mastering the stages and methods of scientific knowledge. One of the opportunities for the formation of educational and cognitive activity and creative potential in the study of Physics and Mathematics is to study the elements of fractal geometry for analyzing the complex structure of processes of various physical nature, in view of the fact that today there is a large number of problems in Physics, Chemistry, Biology, Geology and Economics, where the fractal structure is the main characteristic of the system. Practical tasks on the construction of fractal sets with the identification of the main signs of self-similarity and the possibility of their computer modeling are considered. Students of grades 9–11 and students of the university are given the task of creating their own images of fractals, investigating the fractality of coastal river lines, constructing self-similar figures according to the algorithm «Games in chaos» and studying the contracting affine transformations with obtaining various modifications (attractors) of the Serpinsky triangle. The results obtained enable them to conclude that simple mathematical rules can generate self-similar formations with respect to nonlinear transformations, and argue that simple rules can be at the heart of complex structures and processes.