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A logarithmic spiral.

The size of the spiral increases but its shape is unaltered with each successive curve. Logarithmic spirals are self-similar, in that scaling them gives the same result as rotating them. Starting at any point and moving inwards along the spiral, one has to circle the center infinitely often before reaching it; yet the total distance covered on this path is finite.

There are many logarithmic spirals in nature:

• 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 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, is believed to have four major spiral arms, each of which is roughly a logarithmic spiral with pitch of about 12 degrees, an unusually small pitch angle for a galaxy such as the Milky Way.
• The arms of tropical cyclones, including hurricanes.
• Many biological structures including spider webs and the shells of mollusks.