The Great Wave off Kanagawa

Mathematical art isn’t only privy to western art. Surely we’ve all heard of names like Leonardo da Vinci. Some art students might have heard of Brunelleschi, or Pero della Francesca. The latter was quite a mathematician as well. But not many people realize in the Orient, there too exist art with mathematics featured in it.

Hence today’s math-art is dedicated to arts of the East. And today, the featured artist is Katsushika Hokusai from Japan. And the math art featured today is The Great Wave off Kanagawa (or also known as In the Hollow of a Wave off the Coast at Kanagawa). It is perhaps Hokusai’s most famous work in the West.

Upon first look, one can almost immediately discern the amount of self-similarity there is in the picture. The wave is most obviously self-similar, and repeats itself. Interestingly, the tips of the waves also features like claws, as if attempting to grab the poor sailors off their boats.

This is the first of Hokusai’s wood-block paintings in a series called 36 Views of Fuji. You might not notice this on the first glance, Mt. Fuji is actually dwarved by the waves. In later pictures in the set, Hokusai shows even more intricate fractal sets, including Julia-sets. If anything, this is testament to his attention to detail.

Also, if you notice carefully, the curves of the waves are actual curvatures of proper circles. Not elipses, but circles.

This image, though turbulent (and I don’t usually post such images on Math-Art), nevertheless does qualify completely as a proper piece of work of art, featuring multiple mathematical concept, which I like. Then again, looking at the helpless sailors also gives me a squirmishly good feeling about things. Or maybe I’m just a sadist.

Trivia: Mount Fuji is featured twice in this picture. Have fun looking for a second Mt. Fuji.