I have been fascinated by Celtic Knots for quite a while. While most of my work with Celtic Knots has been with felt tip on graph paper, I have also generated *many* knots using MSPaint. The following are just a few of the knots I have created.
knot01 | knot02 | knot03 | knot04 | knot05 | knot06 | knot07 | knot08 | knot09 | knot10 | knot11 | knot12 | knot13 | A Christmas Nancy | post-modern
The knots above are all jpg versions of bitmaps. If a gridwork is imposed on these knots, it can be seen that every one of the knots can be formed using tiles in one of 26 shapes. This means that I can use tables to store these knots. I have created two table implemented knots, one without cell borders, and one with cell borders, which shows us our gridwork.
I am also including some notes on the analysis I did while designing an (as yet unwritten) java applet to facilitate the dynamic creation of Celtic Knots.
Not really on topic, but I am fascinated by the summation of polynomials .