Unit and Other Knots

Further fun with Celtic Knots. Still no code. Is this the dreaded BUFD??¹

I’ve been drawing more knots and examining them for common elements. I had mentioned finding a reference that suggested a dozen possible configurations, and posted my findings so far, where I had found ten:

You can see that I count reflections as different, but not rotations. Made sense to me at the time. But I couldn’t find two more, so I posted something on Mastodon.

Bill Wake found the relevant article, which I glanced at last night at about 0100 hours, before realizing that I was too tired to think.

I’ve still not entirely decoded Liu’s article, but noticed that he included the trivial one-cell knots. At the time, I didn’t see why one would ever do that, but overnight I realized what they might be good for, and sketched this example without and with the unit knots:

I think the second version looks much more symmetric and complete, so I can somewhat see what the units might be good for.

The article linked above mentions something I had already worked out as well: using these individual patterns, you can’t just fling them into the matrix any old way. There must be rules about their use, and it seems clear that they’re going to be somewhat arbitrary-seeming. When you build up the knot using the diamonds, as described in the previous article, it’s all very rote and what to do when the diamonds are complete always seems very obvious.

So, at this writing, I suspect that when I get to coding, I’ll work from the diamond patterns, not the cell ones shown above.

I thought you “Agile” people didn’t do up front design.

Well, you thought wrong, bunkie. We do design all the time, including before we start. Whether this is design or not, I’m not sure. I think I’m just trying to understand the problem, though I am certainly doing some kind of algorithmic conceptualization here. Or, to give it a less fancy name, I’m trying to figure out how one does these knots by hand, prior to automating any part of the process. Makes sense to me, whatever you call it. Surely wouldn’t make sense to start solving the problem before I know what it is and have a sense of how to solve it, would it now?

No, it would not. See you next time!