Logarithmic Spiral - Logarithmic Spirals in Nature

Logarithmic Spirals in Nature

In several natural phenomena one may find curves that are close to being logarithmic spirals. Here follows some examples and reasons:

• The approach of a hawk to its prey. Their sharpest view is at an angle to their direction of flight; this angle is the same as the spiral's pitch.

• The approach of an insect to a light source. They are used to having the light source at a constant angle to their flight path. Usually the sun (or moon for nocturnal species) is the only light source and flying that way will result in a practically straight line.

• The arms of spiral galaxies. Our own galaxy, the Milky Way, has several spiral arms, each of which is roughly a logarithmic spiral with pitch of about 12 degrees.

• The nerves of the cornea (this is, corneal nerves of the subepithelial layer terminate near superficial epithelial layer of the cornea in a logarithmic spiral pattern).

• The bands of tropical cyclones, such as hurricanes.

• Many biological structures including the shells of mollusks. In these cases, the reason may be construction from expanding similar shapes, as shown for polygonal figures in the accompanying graphic.

• Logarithmic spiral beaches can form as the result of wave refraction and diffraction by the coast. Half Moon Bay, California is an example of such a type of beach.