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Ben Laurie blathering


What Kind Of Knots?

Alice in Wonderland wonders (I guess that’s her job?) what kind of knots we’re tying in Second Life.

She’s not alone. So let me explain. They are “ideal” or “tight” knots. If you imagine a perfect piece of string – one you can bend until it touches itself and that always has a perfectly circular cross section, always the same diameter – and you try to tie a knot with this string, then the shortest possible version, given a fixed diameter piece of string, of that knot is the ideal version.

Ideal knots are interesting not only because they are pretty

but because they predict some of the properties of knotted DNA. Why, no-one knows.

BTW, when I do pictures of ideal knots, I usually show them at half their real diameter. This is because when they’re full sized you can’t see the interesting details in the middle. Pictures like

solve that problem to some extent – and I could do better ones now. The one above doesn’t quite touch itself because when it was drawn we were using points and straight lines to approximate the knot, and those don’t really work, whereas now we use arcs of circles.

Anyway, I’ve been working on these things on and off for around ten years with various collaborators, and I still am, as you can see from the Second Life foolishness. By the way, watching these things render is so much fun its almost worth creating a Second Life character for. I did!

1 Comment

  1. Well that clears it up a bit!

    TYVM, monsieur.

    Comment by Alice — 1 Dec 2006 @ 23:55

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