I have so many feelings about this, I didn't even get into decision trees or permutations! Books I am reminded of: Ashley's Book of Knots, Godel/Escher/Bach: The Eternal Golden Braid, and Dorothy Sayers' The Nine Tailors. I got way too involved in trying to categorize the designs on this page! Here are my conclusions. Figure 1 is a knot according to calligraphers, but only by traditional naming (King Solomon's knot) - it's technically a plait by its construction. Figure 1 is not a knot but a link according to mathematicians, and according to sailors (that's me), it's at first glance a bend (involves two pieces of material tied to each other), but on further consideration and experimentation it's a "fuck you and your shitty-ass plait-knot". Figure 2 is a knot according to all three groups, and at Figure 3 I decided to move on with my life.