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Radiosity in Math 4510 applied math course
When ambient light is reflected and reradiated in an image, finding the final distribution of light in the image requires the solution of a very large linear algebra problem. The total light R_i radiating from a face i is given by R_i = E_i + Σ F_ij R_j, where i is the light emitted by face i and the Fij are “view factors” describing the…
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The Flocktree
The Flocktree is a sculptural installation of a flock of pigeons cast in an expanding urethane foam supported and grouped by a collection of nesting aluminum frames. The interplay between the rigorous order imposed by the frames and the fluid organic shape of the flock raises questions about the way the viewer makes sense of collections of…
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SouthEast Geometry Conference Poster 2004
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…
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Mathematics and Visualization Summer Program 2004
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…
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A Practical Introduction to Mathematical Visualization
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Everything in Its Right Place
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…
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Images of Borromean Rings and Tight Clasp
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: …
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2001 Georgia Topology Conference Poster
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,…