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 rabbitʹs 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.