Fitting an Origin-Displaced Logarithmic Spiral to Empirical Data By Differential Evolution Method of Global Optimization

Patterns of Rib Growth in the Human Child

“…This is a geometric principle seen throughout nature in animals with shells (Mollusca phylum) and is a common mechanism for rigid organisms to increase in volume without changing their basic shape. A logarithmic spiral pattern is also seen in nature in spider webs, low-pressure weather patterns, and some interstellar structures such as the Whirlpool Galaxy [16]. Although sometimes described as a golden spiral, these spirals in nature are more accurately logarithmic spirals.…”

“…Their shape is sometimes approximated by the Fibonacci sequence of numbers, the golden rectangle, or the golden ratio [17]. Without a center of the spiral being present in actual structures such as shells or ribs, their description as a logarithmic spiral is only a close approximation [16]. Most of the 1 cm/year of growth of the middle ribs seemed to be creating volume by growth of the anterior aspect of the chest, similar to how a nautilus shell grows.…”