Determination of Dimensions of Complex Geometric Objects with Fractal Structure

Abstract

This article is given to the assurance of the dimensions of complex geometric objects with fractal structures. A detailed depiction of the different mathematical methods for deciding the dimensions of complex geometric objects with a fractal structure and the investigation of errors in determining the fractional measure of complex geometric objects are displayed. The article presents the concept of fractal estimation, properties, topological estimation, estimations of designs and scenes in nature, differences between Hausdorf-Bezikovich measurement and Mandelbrot-Richardson measurement, fractal measurements. Dimensions of complex geometric objects with several fractal structures have too been identified. In particular, the Mandelbrot-Richardson scale was used to calculate the fractal dimensions of four-sided star fractals, eight-sided star fractals, the Cox curve, and the Given (cap) curves. Hausdorf-Bezikovich and Mandelbrot-Richardson measurements were used to determine the fractal scale. Most articles describe the study of the properties of complex objects in graphical form. In this article, the measurement properties of complex objects are studied on the premise of mathematical equations and special methods are used to compare and calculate the fractional measurements of fractal structures, as well as the results of a number of experiments at each iteration, which are presented in formulas and charts. In addition, different methods of measuring fractal structure images are presented, as well as information on their practical application.