SEPTEMBER 25, 2003
Logarithmic Spirals Isabel and M51
EXPLANATION
Uncomfortably close hurricane Isabel (left) and 30 million light-year distant galaxy M51 actually don’t have much in common. For starters, Isabel was hundreds of miles across, while M51 (the Whirlpool Galaxy) spans about 50,000 light-years making them vastly dissimilar in scale, not to mention the extremely different physical interactions which control their formation and evolution. But they do look amazingly alike, both exhibiting the shape of a simple and beautiful mathematical curve known as a logarithmic spiral, a spiral whose separation grows in a geometric way with increasing distance from the center. Also known as the equiangular spiral, growth spiral, and Bernoulli’s spiral or spira mirabilis, this curve’s rich properties have fascinated mathematicians since its discovery by 17th century philosopher Descartes. Intriguingly, this abstract shape is much more abundant in nature than suggested by the striking visual comparison above. Logarithmic spirals also describe, for example, the arrangement of sunflower seeds, the shapes of nautilus shells, and ... cauliflower.
Credit
Comparison and M51 image copyright Brian Lula; Hurricane Isabel, courtesy GHCC, NASA
