This summer, I will be assisting Professor George Francis with his Philever project for illiMath2002. The Philever project is an ongoing investigation into the sphere eversions proposed by Tony Phillips and Bryce DeWitt. We will be reconstructing their hand-drawn diagrams using a computer program designed in previous REUs, which will allow us to explore these eversions by "flying" through the sphere as the eversion is taking place. Our goal is to eventually get the eversions into the CAVE, where we will be able to "walk" through the sphere, as well.
The computer program we will use has two parts, an editor and a viewer. The editor allows us to reconstruct the sphere, level by level, which is then manipulated in the viewer. To view the source code and a description of the programs (and how to download them and use them), click here. Once you have the software properly installed, you may download and view some of our work.
Our files have been archived here according to date. The files in the earlier dates are less interesting than the later files. In general, the bigger the file, the more interesting the construction. The program could not handle all the levels of the sphere at once, so we constructed it in sections, which we hope to eventually put together in the CAVE to make the entire sphere.
For more information on sphere eversions, in general, click here.