EFFICIENCY OF A RANDOMIZED SYSTEM OF ITERATIVE FUNCTIONS OVER A DETERMINIST SYSTEM OF ITERATIVE FUNCTIONS IN THE CONSTRUCTION OF FRACTAL IMAGES WITH LIMITED RESOLUTION CAPACITY

Abstract

This article raises the issue of analysis and selection of a system of iterative functions for constructing a fractal image with limited image resolution. The efficiency of using the randomized system of iterative functions (RSIF) over the deterministic system of iterative functions (DSIF) in constructing fractal images is considered. The formulas for calculating the number of operations depending on the image resolution for a randomized and deterministic system of iterative functions are derived. On the basis of the derived dependencies, graphs were constructed that clearly demonstrate the superiority of one method over another. The formula for the efficiency of using RSIF over DSIF is derived, which is directly proportional to the area of the image and does not depend on the number of self-similar figures of the first iteration. The results of this article show that the use of a randomized system of iterative functions will significantly reduce the number of operations for constructing a fractal image, compared to the use of a deterministic system of iterative functions. Also, the analysis of systems of iterative functions showed that the calculation of operations using a randomized system of iterative functions can be performed in real time, which is very important when forming an image database for training neural networks, which in turn must perform the task of recognizing fractal structures and objects Fractal analysis is very important in modern scientific research, where it is necessary to describe natural and physical phenomena whose geometry is very complex, so the choice of tools to determine the parameters of the fractal structure is a very important and complex process with complex mathematical calculations that can be simplified with the help of trained neural networks. networks The results of the work will form the basis of an automated system for determining the fractal dimension using trained neural networks.