Behold: Messier 51, aka ‘The Whirlpool’ – a grand design spiral galaxy 60,000 light-years across – with its arms digitally unwound (bottom) in a transformation of a magnificent Hubble Space Telescope portrait from 2005 (top). To wit:
In fact, M51 is one of the original spiral nebulae, its winding arms described by a mathematical curve known as a logarithmic spiral, a spiral whose separation grows in a geometric way with increasing distance from the center. Applying logarithms to shift the pixel coordinates in the Hubble image relative to the center of M51 maps the galaxy’s spiral arms into diagonal straight lines. The transformed image dramatically shows the arms themselves are traced by star formation, lined with pinkish star-forming regions and young blue star clusters. Companion galaxy NGC 5195 (top) seems to alter the track of the arm in front of it though, and itself remains relatively unaffected by this unwinding of M51. Also known as the spira mirabilis, logarthimic spirals can be found in nature on all scales. For example, logarithmic spirals can also describe hurricanes, the tracks of subatomic particles in a bubble chamber and, of course, cauliflower.
(Image: Data – Hubble Heritage Project, Unwinding – Paul Howell)