Determination of the Experimental Computational Complexity of Formation of Spatial Graph Fractals Using Constructive-Synthesizing Modelling

Abstract

Purpose. The study is aimed at obtaining indicators of computational complexity for the formation of spatial graph fractals, which in turn requires developing a software application for the formation of spatial graph fractals, which allows them to be visually viewed, as well as creating tools for calculating indicators of computational complexity. Methodology. The approach of constructive-synthesizing modeling is used to form spatial graph fractals, which is based on the rules of production inherent in formal grammars. Constructive- synthesizing modeling involves a number of transformations, such as: specialization, interpretation and concretization. Structural transformations describe how a spatial graph fractal can be formed, which includes the definition of the subject area, attributes, operations on attributes, substitution rules, conditions and restrictions on operations, description of algorithms, and implementation in the form of software. The indicators of basic operations performed at the assembler level are determined, such as: arithmetic, assignment, comparison and transition. To calculate the indicators of the iteration of the formation of a graph fractal at the code level, special counters are added. The operation counters are located only in those sections of the code that are directly executed during the iteration. Findings. A program was developed in C# with a graphical interface. The indicators of the experimental computational complexity for the formation of spatial graph fractals by means of constructive-synthesizing modeling based on the use of different types of crystal lattices have been determined. The found dependencies have a correlation ratio close to unity. Originality. The experimental computational complexity of the formation of spatial graph fractals by means of constructive-synthesizing modeling has been determined. As the basis for the formation of spatial graph fractals, various types of crystal lattices are used, which describe the arrangement of atoms of crystalline substances. Practical value. Determining the indicators of basic operations makes it possible to predict the execution time of an iteration of forming spatial graph fractals, as well as to optimize the algorithms for performing this iteration. Analysis of the indicators of basic operations makes it possible to find bottlenecks in the algorithms for forming spatial graph fractals.