The Fractional Morphology and Growth Rate of the Nautilus pompilius: Preliminary Results Based on the R1-Fractional Trigonometry

Abstract

This paper studies the morphology and evolutionary growth of the Nautilus pompilius based on the fractional R1-trigonometry. Morphological models based on the fractional trigonometry are shown to be superior to those of the commonly assumed logarithmic spiral. The R1-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.