Here are some more free-flowing doodle-knots:
If a knot has more than one string in it, the ends of each string have to lie on the same part of the knot (inside or outside) — otherwise it throws off the alternating overlapping pattern of the knot. (Perhaps you can see my mistakes?)
Also see: Knot Theory
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Your drawings are beautiful and complicated. I have no need to look for any mistakes.