Regarding Rope Mats and Rosettes:
https://www.ntnu.no/documents/2004699/12108297/Booklet+3.3.pdf

Here is a 7 bight Turk's Head knot template:

_FxGraph3D a*cos(-3*v)+b*cos(4*v)+c*cos(11*v);a*sin(-3*v)+b*sin(4*v)+c*sin(11*v);0;0;6.283185307179586;0;6.283185307179586;0;500;1.6;5.4;1.2;UV

The 2D curve was swept with a line segment to get 2 more curves from edges.
The over/under crossing remains to be done, perhaps with blend. A script or process to do the crossing would be helpful.

I did write a preliminary .js .htm script, but the formula is presented here in _FxGraph format.
To cover the lissajous rope mats, Turk's Head mats, twisted rosettes, rattan rosettes, and higher orders,
would involve several scripts, or a bunch of submenus. Doing several _FxGraph formulas could also be done.

- Brian