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

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

    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.

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    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 99-07-047.

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    Date of creation: Jul 1999
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    Handle: RePEc:wop:safiwp:99-07-047

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    Related research

    Keywords: Allometry; fractal geometry; scaling in biology;

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    Cited by:
    1. Dalgaard, Carl-Johan & Strulik, Holger, 2011. "Energy distribution and economic growth," Resource and Energy Economics, Elsevier, vol. 33(4), pages 782-797.
    2. Dalgaard, Carl-Johan & Strulik, Holger, 2008. "Energy Distribution, Power Laws, and Economic Growth," Hannover Economic Papers (HEP) dp-385, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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