Summary
The Gompertz function describes global dynamics of many natural processes including growth of normal and malignant tissues. On one hand, the Gompertz function defines a fractal. The fractal structure of time-space is a prerequisite condition for the coupling and Gompertzian growth. On the other hand, the Gompertz function is a probability function. Its derivative is a probability density function. Gompertzian dynamics emerges as a result of the co-existence of at least two antagonistic processes with the complex coupling of their probabilities. This dynamics implicates a coupling between time and space through a linear function of their logarithms. The spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium between regular states with predictable dynamics and chaotic states with unpredictable dynamics; a fact important for cancer chemoprevention. We conclude that the fractal-stochastic dualism is a universal natural law of biological complexity.
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© 2005 Birkhäuser Verlag Basel
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Waliszewski, P., Konarski, J. (2005). A Mystery of the Gompertz Function. In: Losa, G.A., Merlini, D., Nonnenmacher, T.F., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7412-8_27
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DOI: https://doi.org/10.1007/3-7643-7412-8_27
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