This paper studies the morphology and evolutionary growth of the Nautilus pompilius based on the fractional -trigonometry. Morphological models based on the fractional trigonometry are shown to be superior to those of the commonly assumed logarithmic spiral. The -trigonometric functions further infer fractional differential equations, which, based on power law parametric functions, are used to develop a fractional growth equation modeling evolution from conception to maturity. An important aspect of this work is that it demonstrates a method of determination of the dynamic description of a fractional trigonometrically defined process from its morphological description.
The Fractional Morphology and Growth Rate of the Nautilus pompilius: Preliminary Results Based on the -Fractional Trigonometry
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Lorenzo, C. F. (October 21, 2010). "The Fractional Morphology and Growth Rate of the Nautilus pompilius: Preliminary Results Based on the -Fractional Trigonometry." ASME. J. Comput. Nonlinear Dynam. April 2011; 6(2): 021004. https://doi.org/10.1115/1.4002343
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