THE TWO-SCALE FRACTAL DIMENSION: A UNIFYING PERSPECTIVE TO METABOLIC LAW

Qura Tul Ain, Ji-Huan He, Xiao-Li Qiang and Zheng Kou
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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

FRACTALS (fractals), 2024, vol. 32, issue 01, 1-11

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.

Keywords: Scaling Law; Fractal Geometry; Cell Morphology; Two-Scale Fractal Theory (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500166

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