Fractal geometry. Teaching, tasks, algorithms, synergetics, aesthetics, applications

In this training manual, works devoted to research in the field of fractal geometry, which currently located numerous applications - in physics, economics, pedagogy, nanotechnologies and other areas are placed. The author pays particular attention to the methodology of studying fractal geometry and the development of multi-stage mathematical and information tasks, the implementation of which is aimed at developing the creativity and competence of students. The book is given a special place is given to the construction of the sets of Julia on a complex plane and building a Feigenbaum tree on the material plane of a fractal structure. Algorithms for constructing fractal sets using affin transformations and L-systems are described in sufficient detail, and computer technologies for creating artistic compositions are also described and examples of compositions created by the author and its students are given. This manual is addressed to students studying in the areas of training and specialties included in the UGS: “mathematics and mechanics”, “physics and astronomy”, “applied mathematics and computer science”, “physical and technical sciences and technologies”, “technologies of materials”, and “technologies”, and other physical, mathematical and engineering areas of training. The book will be useful to graduate students and teachers of mathematics and computer science, specialists in the field of fractal geometry, synergetics, nonlinear dynamics, as well as teachers of mathematics and computer science, secondary school students with in -depth study of mathematics