Scientific Bulletin. Physical and Mathematical Research


This article is devoted to the study of the future position of fractal measurements. Different methods of computer modeling of a wide range of classes of fractal geometric objects are described in detail, as well as the main methods of mathematical analysis of fractal size of virtual and real fractals are described. The article explains the differences between the concept of fractals, their properties, B. Mandelbrot's tariff, Hausdorf-Bezikovich scale, Minkowski-Buligan scale, topological measurement, the concept of fractal measurement and measurement in Euclidean geometry. This article provides basic information about fractals. A detailed description of the various methods of computer modeling of a wide range of classes of geometric and temporal fractal objects is given. It also describes the main well-known methods of mathematical analysis of the fractal size of virtual and real fractals. The basics of fractal theory, the concept of fractal size are described. Examples of numerous project fractals (Cox, Minkowski, Serpin, Lev, Kontor, etc.) are considered. Issues of chaos theory, the scheme of modeling fractals with the determination of the size of unusual attractors, as well as the calculation procedures for the determination of fractal dimensions are considered. Fractal measurements of several geometric objects have also been identified. These include the Cox curve, the Given curve, the Office set, the four-sided star-shaped fractal, the fractal dimension divided by the middle of the side of the triangle, and the fractal dimension divided by the middle of the height of the triangle. Hausdorf-Bezikovich and Minkowski-Buligan measurements were used to determine the fractal scale. Differences in approaches to fractal analysis of real existing and abstract mathematical fractals indicate that a special numerical algorithm must be used to calculate the capacitive size of the fractals. The results are obtained at each step of the iteration, which are presented in the form of formulas and graphs.

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