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

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

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

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XIAO-LI QIANG

https://orcid.org/0000-0001-9328-0774

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

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, and

ZHENG KOU

https://orcid.org/0000-0003-4758-2872

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

E-mail Address: kouzheng@gzhu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218348X24500166Cited by:4 (Source: Crossref)

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:

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Vol. 32, No. 01

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Received 25 September 2023

Accepted 24 November 2023

Published: December 14, 2023

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This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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

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