Golden spiral or Fibonacci spiral: Which is more beautiful and why?

Abstract

Spirals, with their widespread presence in both nature and culture, are universally admired. Although there are different types, such as the Archimedean, logarithmic, and golden spirals, they are indiscriminately considered as beautiful. This universal view might explain the lack of studies investigating aesthetic differences among spirals. To show that there are indeed differences, the beauty of the golden spiral was compared with that of the Fibonacci spiral in this empirical study. Since the curvature of the golden spiral changes continuously, whereas that of the Fibonacci spiral does so in steps, the golden spiral was predicted to be aesthetically preferred. The results clearly confirmed this prediction. That the difference in preference was really based on the continuity versus discontinuity of the curvature is supported by the further result that an Archimedean spiral was preferred over a Dürer spiral, which similarly differed in their continuity.