KnotPlot is two things: a comprehensive application for exploring knots, and a comprehensive web site for exploring knots. We're talking knots here as in mathematical knot theory, which (I think) is the study of the abstract properties of knots and knot-like things.

The software is not easy to use (it's classic ivory-tower-ware, full of sophisticated baffling controls), but is amazing to play with. I have no idea what knot theory is really about, but I like the pictures.