The deep connections between circles, conic sections, the shape of hanging chains and supershapes, also extend to logarithmic spirals. These wonderful curves (discovered by Rene Descartes in 1638) are ubiquitous in nature.The most notorious example is the Nautilus shell, but almost all snails have spiral shells.
The logarithmic spiral is connected with gnomonic growth and with the famous Golden Section. Spirals are observed everywhere in nature, from hurricanes to spiral galaxies.
The shapes of most molluscs however, are not simple spirals, they have varices and combs, reminiscent of discontinuous growth, or growth in phases. If a logarithmic spiral is tranformed into a Gielis’ curve or supershape, the discontinuous growth (or rather the anisotropic development) results immediately.Examples of the “action” of Gielis’ curves on so-called Rose curves or Grandi-curves are observed in various flowers.