DESIGN AND DEVELOPMENT OF A WEB SYSTEM FOR CREATING FRACTAL IMAGES

Abstract

The article describes in detail the process of developing a web system for modeling and visualization of fractal images, based on modern mathematical models of fractal sets. The main goal of the research is to create a tool for interactive construction of fractals, which allows users to adjust model parameters, explore their properties and visualize the results in real time. As part of the work, several key tasks were solved. An analysis of theoretical models of fractal sets was performed, including the Mandelbrot set, the Barnsley fern, and the Koch curve. The main properties of these models, such as self-similarity, infinite detail and fractal dimension, which are defining for fractal objects, were studied. Special attention is paid to the study of algorithms that describe the process of constructing fractals. Several fractal structure modeling algorithms have been developed and implemented. Methods of iterative function of systems (IFS), as well as other approaches to the generation of fractal images, were used. The algorithms were tested for efficiency and stability, and their ability to generate fractals of varying degrees of complexity was investigated. Their computational efficiency and scalability for the construction of large structures were evaluated. A web system was created that integrates the developed modeling algorithms and provides users with a convenient interface for managing fractal parameters. The system allows you to change the types of fractals, adjust the number of iterations, scale, color schemes and other parameters that affect the construction and visualization of fractal structures. The web system has been tested on examples of various fractal structures such as the Mandelbrot set, the Barnsley fern and the Koch curve. A visual analysis of the obtained images was carried out, the accuracy and stability of the algorithms when changing the input data was checked. As a result of testing, the possibility of generating a wide range of fractal images was revealed, which confirms the efficiency and reliability of the developed system.