Methods and algorithms of geometric modeling of fractal structured objects

Abstract

This article presents methods and algorithms for geometric modeling of objects with fractal structures. Analytical equations of fractal structures were constructed using geometric shapes and their basic concepts. Algorithms have been developed using methods of R-function, binomial theorem, and two-dimensional geometric transformation in the 2D plane of computer graphics. The fractal dimension of the fractal based on the Pascal triangle was determined. The expressions obtained on the basis of the developed algorithm are presented in the form of a formula. A software tool was developed based on the algorithms developed using the presented methods. This software tool allows you to automate the interior and exterior decoration, equipment and design of the room in home construction, decorating construction products with patterns, creating patterns of carpets, designing them and choosing the colors and patterns of their products. The results obtained using the software tool are presented graphically.