Below are some sample screenshots of a tool I am developing for knot analysis. The tool can represent any mathematical knot, link, or braid on an M X N grid of cells, using a method common to Celtic knot artists. Presently, the tool can evaluate the Kauffman and Jones polynomial of a knot.

If you have a Java enabled web browser, you can run a demo of the tool by clicking here.

A simple trefoil knot

The 6_3 knot

A link