In 2004, I created a new poster for the SouthEast Geometry Conference. I had just written some code to find shortest paths or geodesics on a polyhedral surface, and was anxious to try it out as an art project. So I started with a model of the Stanford Bunny and added a spray of geodesics from a point on the back of the bunny’s head. The resulting paths crisscross and make an interesting pattern on the surface. Sadly, I had to do the graphic design myself, so I don’t think it’s as good as a poster as it was as a rendering. You decide:
In the summer of 2004, I ran a summer program on Mathematics and Visualization which enrolled four art students and four science students for a series of joint projects in science and art. We started with the project of building our own image filters in MATLAB. Here’s an example of a filter created by Seth Dowling based on reshaping the pixel data in an image using a space-filling curve:
Most of the student projects focused on the idea of tensegrity, in which different elements in tension and compression are balanced against one another to create intricate and sturdy shapes. The summer ended with a group art show at the main gallery in the Lamar Dodd School of Art at UGA.
I have installed various versions of a piece based on the knot tightening movies available elsewhere on this webpage called Everything in its Right Place in the Contemporary Mathematical Photography and New Media Exhibition at the New Image Gallery of James Madison University, in the final show of the Math and Art summer program in 2004, and at the Joint Meetings of the AMS, MAA, and SIAM in 2005. I don’t have a good photograph of any of these installations, but the photo at left is ok. I’m not showing this piece anymore, but you can see the color version and the very high-resolution color version.
A main focus of my research work has been the study of the shapes of knotted tubes when they are pulled tight. With my coauthors Joseph Fu, Rob Kusner, John Sullivan, and Nancy Wrinkle, I found a tight configuration of a link known as the Borromean rings. These Electric Image pictures show the configuration:
These Borromean rings were built from a simpler configuration– a simple clasp formed by two ropes pulled across each other. That configuration turns out to have the surprising feature that there is a small space between the tubes. These pictures show the tubes and the space between them.
All of these pictures ended up in the paper Criticality for the Gehring Link Problem.
Every eight years, the University of Georgia math department holds a massive international conference on the subject of topology. In 2001, I got the chance to design the poster for the conference. I created the image below, and my brother Luke Cantarella did the layout. I originally had the idea of drawing a knot for the conference, but settled on the idea of drawing a knot inside out. The picture below is the space left when a knotted tube is removed from a 3-dimensional sphere. I created the surface as the tube around a knotted curve using my software tube, and then relaxed it using Brakke’s Evolver. The final render used the free raytracer POV-Ray.