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

Introduction: Nature produces amazingly varied geometrical patterns. In particular, logarithmic spirals are abundantly observed in nature. Gastropods/cephalopods (such as nautilus, cowie, grove snail, thatcher, etc.) in the mollusca phylum have spiral shells, mostly exhibiting logarithmic spirals vividly. Spider webs show a similar pattern. The low-pressure area over Iceland and the Whirlpool Galaxy resemble logarithmic spirals. Many materials develop spiral cracks either due to imposed torsion (twist), as in the spiral fracture of the tibia, or due to geometric constraints, as in the fracture of pipes. Spiral cracks may, however, arise in situations where no obvious twisting is applied; the symmetry is broken spontaneously (Néda et al., 2002). Fonseca (1989) found that rank size pattern of the cities of USA approximately follows a logarithmic spiral.