Geoffrey B. West and James H. Brown discovered that allometric scaling laws, including the 3/4 power law for metabolic rates, are characteristic of all organisms. One factor which increases biological diversity is body size, which varies over 21 orders of magnitude in biological organisms. Yet some universal rates and regular relationships stay constant. The metabolic rate of biological life-forms scales approximately as the 3/4-power of mass from complex molecules up to the largest multicellular organisms.
Similarly, time-scales (such as lifespans and growth-rates) and sizes (such as genome lengths, RNA densities, and tree heights) scale as power laws with exponents which are typically simple multiples of 1/4. West and Brown have shown that these 1/4 power scaling laws follow from underlying principles embedded in the dynamical and geometrical structure of space-filling, fractal-like, hierarchical branching networks.
These scaling laws can be applied to artificial structures as well. Like biological systems, counties and cities have evolved branching networks that transport a variety of resources.
- Wikipedia Entry for Power Law
- Geoffrey B. West, James H. Brown, and Brian J. Enquist A General Model for the Origin of Allometric Scaling Laws in Biology, Science Vol 276 April (1997) 122-126
- Geoffrey B. West and James H. Brown, Life's Universal Scaling Laws, Physics Today, September (2004) 36-42