Piano Waves and Fractals

by Mary Martialay on October 27, 2011

The Great Wave

Usually when I write about fractals, it’s in relation to the work of Ron Eglash – Rensselaer professor of science and technology studies – on African fractals as part of efforts to engage minority students in the “STEM” fields of science, technology, engineering, and mathematics.

But this time around, it’s about music. Piano music. And a concert to be performed at the Curtis R. Priem Experimental Media and Performing Arts Center (EMPAC) on November 9.

The concert will include performances by Rensselaer and College of Saint Rose students and faculty, and the program – a mix of contemporary and classical pieces – begins with Claude Debussy’s famous composition La Mer, depicting oceanscapes from the French seacoast and the English Channel.

The concert is titled Piano Waves (for more information , check out this news release). Some pieces will enlist four grand pianos playing simultaneously. And by way of illustration, Michael Century – Rensselaer professor, performer and concert organizer – proposed the image at the top of this post.

The image adorned the cover of an early album recording of La Mer, and is taken from a Japanese print. This much I knew when I sent the image to our web designers to accompany the news release.

Within hours of publishing the release on our website, I received this message from  Robert W. Messler, Jr., a Rensselaer professor in the Department of Materials Science and Engineering:

I noted with interest the painting chosen to help promote the forthcoming piano concert at the EMPAC. It is “The Great Wave” by Japanese artist Katsushika Hokusia (1760-1819).

Many at RPI would probably by intrigued to know that the great French mathematician Benoit Madelbrot, father of fractal geometry and the mathematics of chaos, spotted fractals in this painting, made more than 150 years before the phenomenon was recognized.

Note that at the crest of the great curling wave are smaller curling waves, with still smaller curling waves at their crests. The similarity to what has become the most recognized symbol of fractals (as attachment) is astounding. Mandelbrot refers to what Hokusia captured in his “Great Wave” as self similarity.

Personally, I think this is worth being to the community’s attention. We are, after all, mostly nerds.


Robert W. Messler, Jr., ’65/’71
Professor, MS&E

Agreed. And let this stand as a “Rensselaer moment” in the connection between science and art. Thank you Prof. Messler!