View in EDS

Geometric modeling of three-dimensional fractal structures. Case studies on the Sierpinski triangle and the Menger sponge.

Saved in:
Bibliographic Details
Title: Geometric modeling of three-dimensional fractal structures. Case studies on the Sierpinski triangle and the Menger sponge.
Authors: Nuraliev, Fakhriddin1 (AUTHOR), Nurimbetov, Bakhbergen1 (AUTHOR) baxbergen.n@gmail.com, Ismailov, Kamolitdin1 (AUTHOR), Karimbaeva, Aziza1 (AUTHOR)
Source: AIP Conference Proceedings. 2025, Vol. 3377 Issue 1, p1-8. 8p.
Subject Terms: *GEOMETRIC modeling, *FRACTALS, *ANALYTIC geometry, *AFFINE transformations, *GEOMETRIC shapes
Abstract: This article explores three-dimensional fractal structures, their extensive applications in contemporary fields, and the geometric modeling techniques employed in their construction. The study examines the use of analytic geometry equations, iterative function systems (IFS), and the R-function method in generating three-dimensional Menger sponges and Sierpinski triangles. The geometric construction of these fractals utilizes affine transformations in three-dimensional space, providing a robust framework for their precise modeling and analysis. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:This article explores three-dimensional fractal structures, their extensive applications in contemporary fields, and the geometric modeling techniques employed in their construction. The study examines the use of analytic geometry equations, iterative function systems (IFS), and the R-function method in generating three-dimensional Menger sponges and Sierpinski triangles. The geometric construction of these fractals utilizes affine transformations in three-dimensional space, providing a robust framework for their precise modeling and analysis. [ABSTRACT FROM AUTHOR]
ISSN:0094243X
DOI:10.1063/5.0300184