Bowline draws tighter as tension is placed on the standing part of the rope. The "Birmingham bowline" has two loops; the working part is passed twice around the standing part (the "rabbit" makes two trips out of the hole and around the tree). Other two-loop bowline knots include the Spanish bowline and the bowline on the bight; these can be tied in the middle of a rope without access to the ends. A triple bowline is used to make three loops. A Cossack knot is a bowline where the running end goes around the loop-start rather than the main part and
Mutation (knot theory) endpoints of the tangle. There is also a rotation that results from composition of the reflections. A mutation replaces the original tangle by a tangle given by any of these operations. The result will always be a knot and is called a mutant of "K". Mutants can be difficult to distinguish as they have a number of the same invariants. They have the same hyperbolic volume (by a result of Ruberman), and have the same HOMFLY polynomials. Mutation (knot theory) In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots.