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The Two-Scale Fractal Dimension: A Unifying Perspective To Metabolic Law

Author

Listed:
  • QURA TUL AIN

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P. R. China)

  • JI-HUAN HE

    (��National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, Suzhou, P. R. China‡School of Science, Xi’an University of Architecture and Technology, Xi’an, P. R. China)

  • XIAO-LI QIANG

    (�School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, P. R. China)

  • ZHENG KOU

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, P. R. China)

Abstract

The laws governing life should be as simple as possible; however, theoretical investigations into allometric laws have become increasingly complex, with the long-standing debate over the scaling exponent in allometric laws persisting. This paper re-examines the same biological phenomenon using two different scales. On a macroscopic scale, a cell surface appears smooth, but on a smaller scale, it exhibits a fractal-like porous structure. To elaborate, a few examples are given. Employing the two-scale fractal theory, we theoretically predict and experimentally verify the scaling exponent values for basal, active, and maximal metabolic rates. This paper concludes that Rubner’s 2/3 law and Kleiber’s 3/4 law are two facets of the same truth, manifested across different scale approximations.

Suggested Citation

  • Qura Tul Ain & Ji-Huan He & Xiao-Li Qiang & Zheng Kou, 2024. "The Two-Scale Fractal Dimension: A Unifying Perspective To Metabolic Law," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(01), pages 1-11.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:01:n:s0218348x24500166
    DOI: 10.1142/S0218348X24500166
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