We have produced preliminary visualizations of tightening knots and links using our Ridgerunner software. We have completed a composite movie, tightening of many knots and links, and a tangle demonstration. A preprint with the full description of our method will be available soon (although the paper linked above gives you a Cliffs Notes version). Also see the contact set data for tight knots page. This arxiv article describes some of our results as well as how to interpret these images. This work is in collaboration with Ted Ashton, Jason Cantarella, and Michael Piatek.

We produced candidates for the minimum equilateral stick number in a chapter of Physical knots: knotting, linking, and folding geometric objects in R^3 (volume 304 of the AMS Contemporary Mathematics series), pages 55-75. The calculations were performed using KnotPlot. This work is in collaboration with Rob Scharein.

Our original ropelength data is associated with a publication in Experimental Mathematics, 12(3):287-302, 2003. Simulated annealing for ropelength minimization was performed on a catalogue of knots. We make the final data available, as well as a variety of spatial and topological measurements. Michael Piatek did much of the work on the computations.

This work explores ropelength optimization with a hard bound on curvature. Our hope is to capture the shape of ropelength minimizers in physical materials with curvature constraints. Visualizations with associated spatial characters are available as is the paper published in Physical Review E, 70:011803, 2004. This work was in collaboration with Greg Buck and Michael Piatek did much of the work on the computations.