Abstract
An analytical approach to determination of time-dependent temporal fractal dimension b t ( t) and scaling factor a t ( 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 〈 b t ( t)〉 and 〈 a t ( 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 ) = a t t b t and support a thesis that Gompertzian growth is a self-similar and allometric process of a holistic nature.
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