Fractals and the structure of the universe

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Abstract

This article examines the phenomenon of fractals and their role in understanding the structure of the universe. Fractals are complex geometric structures characterized by self-similarity, finding applications in various fields of science, from mathematics to biology. Examples of fractals in nature are provided, including galaxies, clouds, the nervous system, and natural landscapes. The discussion highlights how fractals assist in modeling complex systems, analyzing data, and understanding the evolution of different structures. The article emphasizes the importance of fractals as a tool for studying natural processes and their significance for further research in quantum physics and chaos theory.

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About the authors

Rustam Kh. Rakhimov

Institute of Materials Science of the Academy of Science of Uzbekistan

Author for correspondence.
Email: rustam-shsul@yandex.com
ORCID iD: 0000-0001-6964-9260
SPIN-code: 3026-2619

Dr. Sci. (Eng.); Head, Laboratory No. 1, Institute of Renewable Energy Sources

Uzbekistan, Tashkent

References

  1. Rakhimov R.Kh. Fractals in quantum mechanics: from theory to practical applications. Computational Nanotechnology. 2024. Vol. 11. No. 3. Pp. 125–160. doi: 10.33693/2313-223X-2024-11-3-125-160. EDN: QFISKE.
  2. Feynman R. QED – a strange theory of light and matter. Moscow: AST, 2018. 192 p.
  3. Logunov A.A. Henri Poincaré and the theory of relativity. Moscow: Nauka, 2004. 256 p.
  4. Arsenov O.O. Grigory Perelman and the Poincaré conjecture. Moscow: Eksmo, 2010. 256 p.
  5. Poincare A. Latest works. Izhevsk: Scientific Publishing Center “Regular and Chaotic Dynamics”, 2001. 208 p.
  6. Uchiyama R. What physics has come to. Transl. from Japanese. Preface by Academician V.L. Ginzburg. Moscow: Znanie, 1986. 224 p.
  7. Mandelbrot B. Fractal Geometry of nature. Moscow: Institute of Computer Research, 2002, 656 p.
  8. Yakimova N.N. Fractal universe and the golden ratio. Moscow: LIBROKOM, 2008. 44 p.
  9. Rakhimov R.Kh. Relationship and interpretation of effects in quantum mechanics and classical physics // Computational Nanotechnology. 2024. Vol. 11. No. 3. Pp. 98–124. doi: 10.33693/2313-223X-2024-11-3-98-124. EDN: QEHXLV.
  10. Rakhimov R.Kh. Possible mechanism of pulsed quantum tunneling effect in photocatalysts based on nanostructured functional ceramics. Computational Nanotechnology. 2023. Vol. 10. No. 3. Pp. 26–34. doi: 10.33693/2313-223X-2023-10-3-26-34. EDN: QZQMCA.
  11. Lopes R., Betrouni N. Fractal and multifractal analysis: A review. Medical Image Analysis. 2009. Vol. 13 (4). Pp. 634–649. doi: 10.1016/j.media.2009.05.003.
  12. Lopes R., Dubois P., Makni N. et al. Classification of brain SPECT imaging using 3D local multifractal spectrum for epilepsy detection. International Journal of Computer Assisted Radiology and Surgery (IJCARS). 2008. Vol. 3. Pp. 341–346. doi: 10.1007/s11548-008-0227-4.
  13. Prigarin S.M., Hahn K., Winkler G. Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion. Numerical Analysis and Applications. 2008. Vol. 1 (2). Pp. 163–178. doi: 10.1134/S1995423908020079.
  14. Pruess S.A. Fractals in the Earth Sciences. Some remarks on the numerical estimation of fractal dimension. NY: Plenum Press, 1995. Pp. 65–75.
  15. Barton C.C., La Pointe P.R. Fractals in the Earth Sciences. NY: Plenum Press, 1995. 265 p.
  16. Gang Wang, Hai Huang, Hongbo Xie et al. Multifractal analysis of ventricular fibrillation and ventricular tachycardia. Medical Engineering & Physics. 2007. Vol. 29. Issue 3. Pp. 375–379.
  17. Grassberger P., Badii R., Politi A. Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors. Journal of Statistical Physics. 1988. Vol. 51. Pp. 135–178. doi: 10.1007/BF01015324.
  18. Kushnarev P.I. Scientific and methodological foundations of quantitative assessment of gold ore deposit exploration. Dis. ... of Dr. Sci. (Eng.). Moscow: All-Russian Research Institute of Mineral Resources named after N.M. Fedorovsky, 2021.
  19. Trunev A.P. Electron structure, hydrino and cold nuclear fusion. Chaos and Correlation. International Journal. 25.11.2011. URL: https://chaosandcorrelation.org/Chaos/CR7_1_2010.pdf
  20. Maisi, V.F., Saira O.-P., Pashkin Yu.A. et al. Real-time observation of discrete Andreev tunneling events. Physical Review Letters. 2011. Vol. 106. Issue 21. 217003/1-4. doi: 10.1103/physrevlett.106.217003.
  21. Maitra N.T., Heller E.J. Barrier tunneling and reflection in the time and energy domains: The battle of the exponentials. Physical Review Letters. 1997. Vol. 78 (16). Pp. 3035–3038. doi: 10.1103/PhysRevLett.78.3035.
  22. Makhlin Y., Schön G., Shnirman A. Quantum-state engineering with Josephson-junction devices. Reviews of Modern Physics (RMP). 2001. Vol. 73, P. 357–400. doi: 10.1103/RevModPhys.73.357.
  23. Morello A., De Jongh L.J. Dynamics and thermalization of the nuclear spin bath in the single-molecule magnet Mn12-ac: Test for the theory of spin tunneling. Physical Review B. 2007. Vol. 76 (18). 4425. doi: 10.1103/PhysRevB.76.184425.
  24. Golʹdanskii V.I., Trakhtenberg L.I, Fleurov V.N. Tunneling phenomena in Chemical Physics. London: Routledge, 1988. 334 p. doi: 10.1201/9780203734957.
  25. Falconer K. Fractal Geometry: Mathematical foundations and applications. Wiley, 2003. doi: 10.1002/0470013850.
  26. Falconer K. Fractal Geometry: Mathematical foundations and applications. John Wiley & Sons, 1990.

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