On the Gompertzian growth in the fractal space-time

An analytical approach to determination of time-dependent temporal fractal dimension bt(t) and scaling factor at(t) for the Gompertzian growth in the fractal space-time is presented. The derived formulae take into account the proper boundary conditions and permit a calculation of the mean values 〈bt(t)〉 and 〈at(t)〉 at any period of time. The formulae derived have been tested on experimental data obtained by Schrek for the Brown-Pearce rabbit's tumor growth. The results obtained confirm a possibility of successful mapping of the experimental Gompertz curve onto the fractal power-law scaling function y(t)=attbt and support a thesis that Gompertzian growth is a self-similar and allometric process of a holistic nature.