1) Draw the 'skeleton' as a connected (simple?) graph in the plane

2) Place crosses at the midpoint of each edge

3) Connect the crosses with shortest (non-crossing!) connections (bit vague this, but is more obvious by hand)

4) Erase the crosses, and run over the line, assigning under/over as appropriate - you can also thicken at this step

This gives good free-standing knots, although may be more work for the dense knotwork in the OP's examples.

https://en.wikipedia.org/wiki/Algorithmic_art

> From one point of view, for a work of art to be considered algorithmic art, its creation must include a process based on an algorithm devised by the artist. An artist may also select parameters and interact as the composition is generated. Here, an algorithm is simply a detailed recipe for the design and possibly execution of an artwork […]

Creating art by AI certainly also uses an algorithm to some extent but it cannot be said to have devised that algorithm and arguably also not to clearly define all parameters to the algorithm.

If you try to define systematically what that difference is, though, it's not obvious. At the end of day, I think it's something like "degree of difficulty" or "amount of thought", which are vague concepts. Yet most would agree what the author here did requires more skill and thinking than typing "image of celtic knot" into Gemini.

  Uncaught PythonError: Traceback (most recent call last):
  File "<exec>", line 22, in resetKnot
  File "<exec>", line 473, in generateKnot
  File "/lib/python3.12/site-packages/PIL/Image.py", line 2941, in new
    return im._new(core.fill(mode, size, color))
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^