: 71-80
Received: December 01, 2021
Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University

This paper has been considered the results of the development of the randomized system of iterated functions (RSIF) formation algorithm from the existing fractal image of the “Fractal Dust” type (the Cantor set). The mathematical formulas and patterns for calculating the RSIF coefficients have been derived. This algorithm is to find the formulas of functions relative to the center of the first iteration of the fractal structure. This makes it possible to determine a randomized system of iterative functions from an existing fractal image. The construction algorithm does not use recursive functions and the entry of the loop into the loop, which allows without spending a lot of computing power, and is quite optimized. The algorithm will allow you to make direct and inverse transformations without involving additional software and hardware resources. The use of forward and inverse transformations will allow in the future to form a source data set for neural networks which will form the basis of object recognition systems.

[1] Richard M. (2000), Cronover. Fractals and chaos in dynamical systems. Fundamentals of theory. Moscow: Postmarket. 352 p.
[2] Feder E. (1991), Fractals: Per. with English. Moscow: Mir. 254 p.
[3] Demenok S. L. (2012), Just a fractal. СПб.: ООО “Страта”. 168 р.
[4] Tsvetkov A. S. (2016), PASCAL programming language, ABC Pascal programming system. St. Petersburg Pavlovsk, 2015–2016. 46 p.
[5] Mandelbrot, B. (2002), Fractal geometry of nature. Moscow: Institute of Computer Research. 656 p.
[6] Yunak O. M., Peleshchak B. M., Ohremchuk N. L., Metlevich Y. R. (2016), Transformation of an image of a fractal structure of the type “Fractal dust” (Cantor set) into a randomized system of iterative functions, XII International Scientific and Practical Conference “Latest Achievements in European Science-2016”, Vol. 13, Sofia “White CITY-BG” Ltd., 90 p.
[7] Mandelbrot B. B. (2009), Fractals and Chaos. Many Mandelbrot and other wonders. Moscow – Izhevsk: SIC “Regular and chaotic dynamics”. 392 p.
[8] Kronover, R. M. (2000), Fractals and chaos in dynamical systems. Fundamentals of theory. Moscow: Postmarket. 352 p.
[9] Paitgen, H.-O., Richter P. H. (1993), The beauty of fractals. Images of complex dynamic systems: trans. with English. Moscow: Mir. 176 p.