Eric Rawdon's Data Page

We make available a variety of visualizations and data associated with tight knots and links as a service to the community. Many of these works are in collaborations with other researchers. Visit my preprints and published papers page to find the papers and my collaborators.

Visualizing the tightening of knots and links

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.

Upper bounds for equilateral stick numbers

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.

Can computers discover ideal knots

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.

Role of flexibility in entanglement

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.

Knot type: 3.1 4.1 5.1 8.18 8.19 8.21 9.39 9.49
Convergence: [pdf] [pdf] [pdf] [pdf] [pdf] [pdf] [pdf] [pdf]

Energy, ropelength, and other physical aspects of equilateral knots

Energy optimized and ropelength optimized knots are available with spatial characteristics. The associated paper appears in Journal of Computational Physics, 186(2):426-456, 2003.
16 edge / 32 edge optimized for ropelength
16 edge / 32 edge optimized for energy
This work was done in collaboration with Ken Millett.

This work has been supported by NFS DMS 0311010, 0296098, 0074315. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.