History

Knotilus was conceived by Ortho Flint and Stuart Rankin in the summer of 2003 as a tool for the broken curve drawing of a knot or link from a given gauss code in aid of their knot theory research. The initial implementation was carried out by Ralph Furmaniak (who also receives the credit for the name of the web site). This implementation drew a diagram for a link in three stages. The first stage drew a plane graph whose vertices represented the crossings of the diagram and whose edges, which represented the knot itself, were piecewise linear curves with two segments each (degenerate when forming a nugatory crossing). The second stage then annealed this graph, using forces that were developed and scaled by trial and error, while the final stage used MetaPost to draw the final knot/link diagram, writing the output as a Postscript file.

There was a problem with the first stage which was never fully resolved. We knew that there were circumstances under which the procedure would not be able to complete the construction of the diagram. This problem was ameliorated by adding a probabilistic aspect to the procedure, which very significantly increased the success rate.

There were also problems with the second stage, the annealing of the graph. It was important not only not to lose planarity in the annealing steps, but it was also important not to change the embedding isotopy class. Unfortunately, this initial implementation did occasionally fail in this regard.

Overall, the program turned out quite usable drawings, and it was decided to provide access to its capabilities as well as the database of alternating knots that we had compiled by that time. So it was that in July of 2003, the first knotilus went online.

In the summer of 2004, one small change was made to knotilus by Bruce Fontaine (Bruce had joined the research team of Rankin and Flint as a successor to Peter de Vries in the project to enumerate the prime alternating links). By processing the logs of the MetaPost run, it was possible to extract the Bezier spline data for the curves that MetaPost was producing, and so the knot/link drawing was also made available in xypic format. Also a request was made that we provide access to the underlying piecewise linear graph from which the diagram was constructed and so this too was provided as an option at about the same time.

Late in the summer of 2005, most of the coding work for the prime alternating links was completed, and attention was turned to the overhaul of the knotilus web site, only to be interrupted by the demands of the school year. In the spring of 2006, we again turned our attention to the knotilus web site and its problems, and by July of 2006, three years after the initial knotilus went online, the new implementation went live, replacing the old version. The new implementation not only fixed the problems and limitations of the original version, but offered many improvements as well.