Graph fractals with the variability of the formation process
DOI:
https://doi.org/10.34185/1991-7848.itmm.2025.01.050Keywords:
indicators; computational complexity, fractals, graph, software, information technology, formal grammars.Abstract
The determination of the experimental computational complexity of the formation of graph fractals allows us to evaluate and compare fractals that use different types of crystal lattices. A program in the C# language with a separate module for calculating the corresponding indicators was developed for the modeling of graph fractals. The approach of constructive-synthesizing modeling based on formal grammars is used for the generation of fractals, which consists of a number of transformations and provides flexible options for configuring the generation of graph fractals. The computational complexity was calculated based on the calculation of arithmetic operations, comparisons, assignments, and jumps during the formation of fractals. Dependencies on the type of crystal lattice used and the number of iterations used were determined. It was established that the asymptotic complexity of the algorithm for forming fractal lattices is O(ax).
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