Gompertzian growth as a self-similar and allometric process

The Gompertz law of growth has puzzled scientists for decades: while it suc cessfully described growth kinetics of various biological systems (e.g., tu mor growth), its foundation has remained unclear. In this paper I recognize the Gompertzian growth as founded on self-similarity, which is so abundant in natural phenomena that it justifiably represents a fundamental natural paradigm. The self-similarity leads to an allometric principle: the sizes o f a given biological system at different times are related by a simple powe r law. The stated relation can be also viewed as basic functional growth eq uation with unique nonconstant solutions being the Gompertz and the exponen tial functions. This equation also provides the description of growth and r egression dynamics in terms of a difference equation which already has foun d practical application in characterizing tumor growth kinetics.