Nature's Patterns and the Fractional Calculus - 2

Complexity increases with increasing system size in everything from organisms to organisations.

The nonlinear dependence of a system's functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information).

In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system's information gradient.

Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations.