Development of Fractal Equations of National Design Patterns based on the Method of R-Function

Abstract

The paper is dedicated to the development of fractal equations of national design patterns based on the method of R-function (RFM). Using the equation of the line, the equation of the circle, and the structural means of the method of R-functions R0: R-conjunctions, R-disjunctions and R-reflections constructed various tree-like fractals, equations of fractals, consisting of intersections, tangents of circles. By setting the number of iterations n and the angle of inclination  various pre-fractals are generated based on these equations. These fractals are very beautiful, which can be used in creating computer landscapes, in various illustrations, telecommunications, the textile industry, when drawing patterns in ceramic and porcelain products, as well as developing patterns of modern design of Uzbek national carpets and costumes, etc.