MODELING A THREE-DIMENSIONAL PYRAMID WITH A CYLINDRICAL PASS-THROUGH FRAGMENT BASED ON R-FUNCTIONS AND ITERATED FUNCTION SYSTEMS (IFS)
Keywords:
Sierpinski triangle, fractal geometry, R-functions (RFM), Iterative function systems (IFS), 3D fractal, cylinderAbstract
This research is devoted to developing a novel type of composite three-dimensional geometric model constructed on the basis of one of the fundamental objects of fractal geometry - the Sierpinski tetrahedron (Sierpinski pyramid). By inserting a vertical cylindrical volume passing through the fractal pyramid, a complex spatial structure is obtained, featuring a system of voids organized according to fractal principles. The methodological framework relies on two fundamental approaches: (1) constructing a primary analytical–geometrical model using R-functions (RFM); and (2) reconstructing the full iterative three-dimensional fractal structure through Iterated Function Systems (IFS).
References
НУРАЛИЕВ, Ф., НАРЗУЛЛАЕВ, О., НАБИЕВ, И., & НУРИМБЕТОВ, Б. О некоторых методах геометрического моделирования 2D/3D объектов сложной фрактальной структуры. Научно-технологический центр уникального приборостроения РАН КОНФЕРЕНЦИЯ: АКУСТООПТИЧЕСКИЕ И РАДИОЛОКАЦИОННЫЕ МЕТОДЫ ИЗМЕРЕНИЙ И ОБРАБОТКИ ИНФОРМАЦИИ Суздаль, 09–12 октября 2023 года.
Falconer, K. 2014 Fractal geometry: Mathematical foundations and applications (3rd ed.). Wiley.
Peitgen, H.-O., Jürgens, H., & Saupe, D. Chaos and fractals: New frontiers of science. Springer.
Sierpinski, W. Sur une courbe cantorienne qui contient une image biunivoque de toute courbe simple. Comptes Rendus de l’Académie des Sciences, 162, 104–106.
Rvachev, V. L. 1982. Theory of R-functions and some applications. Naukova Dumka.
Levin, V. L., & Rvachev, V. 2007. Geometry of R-functions and computational methods. Springer.
Barnsley, M. 1988. Fractals everywhere. Academic Press.
Hutchinson, J. 1981. Fractals and self-similarity. Indiana University Mathematics Journal, 30(5), 713–747.
Nayak, A., & Ren, X. 2015. Boolean operations on fractal surfaces: Analytical modeling and geometric transformations. Journal of Computational Geometry, 9(2), 113–129.
Werner, D. H., & Ganguly, S. 2003. An introduction to fractal antenna engineering. Wiley-IEEE Press.
Nuraliev F. et al. Geometric modeling of three-dimensional fractal structures. Case studies on the Sierpinski triangle and the Menger sponge //AIP Conference Proceedings. – AIP Publishing LLC, 2025. – Т. 3377. – №. 1. – С. 020007.
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Copyright (c) 2025 Бахберген Нурымбетов, Rashidjon Xoliqnazarov
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