MATHEMATICAL PROPERTIES OF FRACTAL GEOMETRY AND ITERATIVE FUNCTION SYSTEM

Authors

  • Golib Rashidovich Berdiev TUIT named after Muhammad al-Khwarizmi
  • Adxamjon Ilhomjon o'g'li To‘xtasinov TUIT named after Muhammad al-Khwarizmi
  • Farxod Nurali o'g'li Parmonqulov TUIT named after Muhammad al-Khwarizmi

Keywords:

Fractal, fractal geometry, design, construction, architectural form, geometry, model, truss, modeling, IFS, generative systems

Abstract

This article discusses the concepts of fractal and fractal geometry, as well as the design of rule-based properties in the constructional construction of structural trusses used on top of buildings, based on the principles of fractal geometry and the analysis of the mechanical properties of these novel structures. Fractal based truss. This article presents a mathematical method for constructing geometric fractal shapes. The use of an iterative function system (IFS) has been proposed in the construction of fractal forms. We determined the fractal dimension of the constructed fractal form and showed its correlation with the mass value of the farm.

References

Mandelbrot, B. B., The Fractal Geometry of Nature, W. H. Freeman and Co., New York, 1983

Devany, R. L., A First Course in Chaotic Dynamical Systems. Reading, Massachusetts: Addison-Wesley Publishing Company, Inc., 1992

Barnsley M. F., Fractals Everywhere, Academic Press, Inc., 1988.

Hutchinson, J. E., Fractals and Self-Similarity. Indiana University Mathematical Journal, 1981; 30 (5), 713–747

Asayama, S. and Mae, T., Fractal Truss Structure and Automatic Form Generation Using Iterated Function System, Proceeding of ICCCBE-X, 2004; Weimar, Germany

Radin, C. and Conway, J., Quaquaversal Tiling and Rotations, preprint, Princeton University Press, Princeton, 1995.

S.Anarova, S.Sadullaeva, G. Berdiev. “Calculation of building dimensions in the method of composition fractal analysis”, 2021 International Conference on Information Science and Communications Technologies (ICISCT). 3-5 Nov. 2021. DOI:10.1109/ICISCT52966.2021.9670390

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Published

2022-04-28

How to Cite

Berdiev, G., To'xtasinov, I., & Parmonqulov, F. (2022). MATHEMATICAL PROPERTIES OF FRACTAL GEOMETRY AND ITERATIVE FUNCTION SYSTEM. CENTRAL ASIAN JOURNAL OF EDUCATION AND COMPUTER SCIENCES (CAJECS), 1(2), 35–48. Retrieved from https://cajecs.com/index.php/cajecs/article/view/25

Issue

Vol. 1 No. 2 (2022): CAJECS

Section

Technical sciences

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