KnotPlot is a wonderful program for generating, viewing, playing with knots. The program itself has been around for a while, but I first saw it yesterday at a talk on knots. A description of the features of KnotPlot:
Knots can be loaded from a database of almost 1000 knots and links or sketched by hand in three dimensions. Also, knots may be constructed via the Conway notation or using a tangle calculator. A number of special knot types (torus knots, knot chains, Lissajous knots) may be created on the fly. Finally, new knots can be created from old knots using a number of transformations.
There are lots of extras beyond knots, such as creating knots from braids, Celtic knots, and other fascinating demos. In addition to a nice learning tool for knot theory, this is the kind of thing I could spend hours just playing with.
