A Principle of Fractal-Stochastic Dualism, Couplings,Complementarity and Growth

Abstract

Gompertzian dynamics appears in the Markovian model of the simpliest coupling of conditional probabilities. The solution of the corresponding Langevin equation relates probabilty distribution and the Gompertz function. Simplistic macroscopic Gompertzian dynamics emerges according to the principle of fractal-stochastic dualism. This occurs owing to both the complex coupling of probabilities of microscopic processes and the existence of fractal structure of time and space; the essence of life. That coupling leads not only to the emergence of the simplistic macroscopic dynamics, but also to the emergence of the complementary supramolecular system and its corresponding optimal morphology. Complementarity seems to be an intrinsic feature od complexity.