A curve viewed end-on, in the Right view in this case, appears to be exactly a lissajous curve.
The view can be matched to one of the lissajous curves generated by the lissajous01 script.
The x axis does not have a sin or cos, so the lissajous curve is stretched out, rather than being closed.
The second and third curve are "shifted over" 4/3 and 2/3 of half a wavelength respectively.
So other stretched out lissajous curves can be braids with slightly different shapes and different strand numbers.

See page 10:
http://pages.cpsc.ucalgary.ca/~jungle/555/notes/gencyl.pdf

- Brian