Construction of the fractal image of the “cantor dust” type using a randomized system of iterating functions

Abstract

The article examines the results of the development of an algorithm for determining the number of pixels of a fractal image of the "Fractal dust" type (Cantor's set) created using resolution-limited RSIF. Mathematical formulas and schemes for calculating the number of pixels of the fractal image and the number of iterations of the RSIF fractal have been derived. This algorithm consists in finding formulas depending on the number of figures of the first iteration, similarity coefficients, and resolution. This makes it possible to determine the number of pixels for an existing fractal image with different resolutions. The calculation algorithm does not use the entry of a loop into a loop and recursive functions, and is quite optimized, which allows without spending a lot of computing power. The use of formulas in the future will make it possible to determine the number of random events (stochastic movement of a point), to ensure the quality of the reproduced image using RSIF, will make it possible to form an initial data set for neural networks, which will form the basis of object recognition.