Constructive-synthesizing modelling of three-dimensional fractal surfaces

Abstract

The study considers the fractal properties of architectural structures, in particular, mul-ti-tiered structures such as a pagoda. The pagoda is an example of a building where each lev-el repeats the geometric motif of the previous one, decreasing in scale but maintaining the overall structure and proportions. Representation of the pagoda model using fractal geometry and Bézier surfaces to re-produce curved elements is the main element of the work. An algorithm for the formation of an architectural structure, where each level is modelled on the basis of the previous one through a sequential reduction of its geometric elements, is proposed. The formation is car-ried out with the help of constructors based on constructive-synthesizing modelling. This ap-proach allows for the automatic creation of new levels of the structure while maintaining their self-similarity. One of the key tools used in the work is parametric constructors, which allow generat-ing three-dimensional images of multi-level structures. Particular attention is paid to Bezier surfaces, which are used to build curved elements at each level of the pagoda, ensuring smooth transitions between surfaces. The algorithmic constructors allows you to interactively adjust the parameters of the structure by changing the number of levels, their proportions and geometric features. As a result, a set of algorithms and tools for building fractal structures has been pre-sented that can be used both in architectural design and in modelling complex geometric shapes. The process of creating such models is described in detail through an iterative ap-proach, where each level of the structure is the result of modifying the previous one according to clearly defined rules.