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The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms


  • Geoffrey B. West
  • James H. Brown
  • Brian J. Enquist


The existence of fractal-like networks effectively endows life with an additional fourth spatial dimension. This is the origin of quarter-power scaling which is so pervasive in biology. Organisms have evolved hierarchical networks which terminate in invariant units, such as capillaries, leaves, mitochondria, and oxidase molecules, which are independent of organism size. Natural selection has tended to maximize both metabolic capacity by maximizing the scaling of exchange surface areas, and internal efficiency by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and explicit models and should apply to virtually all organisms.

Suggested Citation

  • Geoffrey B. West & James H. Brown & Brian J. Enquist, 1999. "The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms," Working Papers 99-07-047, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:99-07-047

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    Cited by:

    1. Elliott, Robert J.R. & Sun, Puyang & Xu, Qiqin, 2015. "Energy distribution and economic growth: An empirical test for China," Energy Economics, Elsevier, vol. 48(C), pages 24-31.
    2. Sachdeva, Vedant & Phillips, James C., 2016. "Oxygen channels and fractal wave–particle duality in the evolution of myoglobin and neuroglobin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 1-11.
    3. Dalgaard, Carl-Johan & Strulik, Holger, 2011. "Energy distribution and economic growth," Resource and Energy Economics, Elsevier, vol. 33(4), pages 782-797.
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    5. repec:eee:ecomod:v:220:y:2009:i:16:p:1880-1885 is not listed on IDEAS
    6. repec:eee:thpobi:v:117:y:2017:i:c:p:23-42 is not listed on IDEAS
    7. repec:spr:scient:v:112:y:2017:i:1:d:10.1007_s11192-017-2333-y is not listed on IDEAS
    8. Husmann, Kai & Möhring, Bernhard, 2017. "Modelling the economically viable wood in the crown of European beech trees," Forest Policy and Economics, Elsevier, vol. 78(C), pages 67-77.
    9. Chen, Yanguang, 2017. "Multi-scaling allometric analysis for urban and regional development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 673-689.
    10. Chen, Yanguang, 2012. "The mathematical relationship between Zipf’s law and the hierarchical scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3285-3299.
    11. Song, Dong-Ming & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2009. "Statistical properties of world investment networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2450-2460.
    12. De Martino, S. & De Siena, S., 2012. "Allometry and growth: A unified view," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4302-4307.
    13. Christopher Watts & Nigel Gilbert, 2014. "Simulating Innovation," Books, Edward Elgar Publishing, number 13981.
    14. Liu, Chuang & Zhou, Wei-Xing & Yuan, Wei-Kang, 2010. "Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2675-2681.
    15. Dalgaard, Carl-Johan & Strulik, Holger, 2008. "Energy Distribution, Power Laws, and Economic Growth," Hannover Economic Papers (HEP) dp-385, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.

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    Allometry; fractal geometry; scaling in biology;

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