Methods of Creating Fractals from Geometric Shapes
Keywords:
Girih, element, composition, pattern, star-shaped, shape, geometric shape.
Abstract
This article links modern fractal art, which has entered the visual arts, with the science of applied decorative arts, and highlights the presence of fractals in geometric shapes and the methods of constructing them. This paper explores various methods of generating fractals using geometric shapes, including iterative processes, affine transformations, and substitution rules. By examining these techniques, we aim to provide a comprehensive understanding of fractal construction and its applications in mathematics, computer graphics, and natural modeling.
References
1. Barnsley, M. F. (1988). Fractals Everywhere. Academic Press.
2. Prusinkiewicz, P., & Lindenmayer, A. (1990). The Algorithmic Beauty of Plants. Springer-Verlag.
3. Grünbaum, B., & Shephard, G. C. (1987). Tilings and Patterns. W. H. Freeman.
4. Sierpiński, W. (1916). Sur une courbe dont tout point est un point de ramification. Comptes Rendus de l'Académie des Sciences de Paris, 162, 629–632.
5. Falconer, K. (2003). Fractal Geometry: Mathematical Foundations and Applications (2nd ed.). John Wiley & Sons.
6. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. W. H. Freeman.
7. Peitgen, H.-O., Jürgens, H., & Saupe, D. (1992). Chaos and Fractals: New Frontiers of Science. Springer-Verlag.
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9. Edgar, G. A. (1990). Measure, Topology, and Fractal Geometry. Springer-Verlag.
10. Vicsek, T. (1992). Fractal Growth Phenomena (2nd ed.). World Scientific.
11. Mandelbrot, B. B. (1977). Fractals: Form, Chance, and Dimension. W. H. Freeman.
12. Barnsley, M. F., & Demko, S. (1985). Iterated function systems and the global construction of fractals. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 399(1817), 243–275.
13. Hutchinson, J. E. (1981). Fractals and self-similarity. Indiana University Mathematics Journal, 30(5), 713–747.
14. Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. W. H. Freeman.
15. Peitgen, H.-O., & Richter, P. H. (1986). The Beauty of Fractals: Images of Complex Dynamical Systems. Springer-Verlag.
16. Tricot, C. (1995). Curves and Fractal Dimension. Springer-Verlag.
2. Prusinkiewicz, P., & Lindenmayer, A. (1990). The Algorithmic Beauty of Plants. Springer-Verlag.
3. Grünbaum, B., & Shephard, G. C. (1987). Tilings and Patterns. W. H. Freeman.
4. Sierpiński, W. (1916). Sur une courbe dont tout point est un point de ramification. Comptes Rendus de l'Académie des Sciences de Paris, 162, 629–632.
5. Falconer, K. (2003). Fractal Geometry: Mathematical Foundations and Applications (2nd ed.). John Wiley & Sons.
6. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. W. H. Freeman.
7. Peitgen, H.-O., Jürgens, H., & Saupe, D. (1992). Chaos and Fractals: New Frontiers of Science. Springer-Verlag.
8. Devaney, R. L. (1990). Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics. Addison-Wesley.
9. Edgar, G. A. (1990). Measure, Topology, and Fractal Geometry. Springer-Verlag.
10. Vicsek, T. (1992). Fractal Growth Phenomena (2nd ed.). World Scientific.
11. Mandelbrot, B. B. (1977). Fractals: Form, Chance, and Dimension. W. H. Freeman.
12. Barnsley, M. F., & Demko, S. (1985). Iterated function systems and the global construction of fractals. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 399(1817), 243–275.
13. Hutchinson, J. E. (1981). Fractals and self-similarity. Indiana University Mathematics Journal, 30(5), 713–747.
14. Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. W. H. Freeman.
15. Peitgen, H.-O., & Richter, P. H. (1986). The Beauty of Fractals: Images of Complex Dynamical Systems. Springer-Verlag.
16. Tricot, C. (1995). Curves and Fractal Dimension. Springer-Verlag.
Published
2025-05-22
How to Cite
Khasanova, M. A. (2025). Methods of Creating Fractals from Geometric Shapes. CENTRAL ASIAN JOURNAL OF ARTS AND DESIGN, 6(2), 93-97. Retrieved from https://cajad.centralasianstudies.org/index.php/CAJAD/article/view/523
Section
Articles
