To aid my study I developed some tools in Mathematica to enable my computations and to assist my visualization, using geomview.

There is a release version of a package to implement the eyeball diffeomorphism between the real Grassmannian of oriented two-planes in four-space (which is the same as the set of oriented great circle links) and the product of two two-spheres. Examples are given, visualizing some optimal packings in this Grassmannian, due to Conway, Hardin, and Sloane.

There is also a beta version of an expository notebook and package on classical projective configurations, covering Pascal's and Briachon's Theorems, Reye's configuration of desmic tetrahedra, Schläffli's double six, and culminating in the 27 lines on a cubic surface. Note These depend on the Eyeball.m package above.

I am the author of the ever popular Mathematica package braids.m for visualizing and computing braids. Note This was last updated for Mathematica 2.2; it does work, with many ignorable warnings, under Mathematica 3.x.

I started in mathematics studying hyperbolic dynamics in dimension three. In particular, I proved that two-dimensional hyperbolic attractors for flows are determined up to topological equivalence on an isolating neighborhood by a simple combinatorial object. That insight lead to the realization that the initial segment of the census of cusped hyperbolic three-manifolds consists entirely of such isolating neighborhoods. Consequently, my earliest mathematical software was the 1990 NeXT port of snappea. I had a lot of fun writing a WISYWIG knot editor and developing the graphics hacks for horoball packings. Since then I have continued to contribute ideas to the snappea project.