It seems pretty well established that organisms grow according to a 3/4-power law. For example, Niklas and Enquist, in their paper "Invariant scaling relationships for interspecific plant biomass production rates and body size," PNAS 2001, 98(5):2922 -2927, say:
Annualized rates of growth $G$ scale as the 3/4-power of body mass $M$ over 20 orders of magnitude of $M$ (i.e., $G \propto M^{\frac{3}{4}}$).
Does anyone know if there is some geometric reason to expect such a growth-rate law?
$\frac{d M}{d t} \sim M^{\frac{3}{4}}$
Apparently attempts to derive this growth-rate law from Kleiber's Law, which claims that metabolic rate scales as $M^{\frac{3}{4}}$, are controversial. So I was wondering if there might be some geometric viewpoint that makes growth proportional to $M^{\frac{3}{4}}$ not unexpected.