Final last final honest final true lover's knot - 18 Feb 2024

Again!!?

Yes, I couldn’t leave it alone. However, I finally got it right. This notebook image should gave a hint to how detailed it got:

Notebook image of 8_18 and 8_19

This shows the two knots (8_18 and 8_19) - or the ‘false’ and ‘true’ lover’s knots in my terminology from this previous post - with segments coloured such that each crossing has 3 colours meeting (a proper colouring, in other words).

The crossings are also labelled with a class (like A = b(rg)) showing that 8_19 is more symmetric I think? Also that it only needs 3 colours and not 4 - I dunno, I’m not great at knot topology honestly. Anyway the point is that the version that is non-alternating is 8_19 with the two red B-B segments.

Ok so the actual painting

As it happened, I bought some canvas sheets from a cheap art materials store, and I used ink pencils on it to see what it would look like:

Ink painting on canvas of true lovers knot

I made it a bit spikier than before, and I think it came out reasonably well.

(I’m done. No more versions of this knot!)