Allometric morphogenesis of complex systems: Derivation of the basic equations from first principles

Abstract

Allometric morphogenesis is the generation of form or pattern as a result of differential growth according to power-law relationships among the elements of a complex system. This phenomenon has been noted in a variety of fields for many years, in some cases for centuries, and yet it has never been related to the underlying determinants of the systems. By starting with fundamental properties of the component mechanisms in such systems, one can derive a basic growth equation from which the well-known law of allometric morphogenesis follows naturally.