At the same time, however, the perfect rope is perfectly flexible - you may bent it without any effort. First results of the extensive numerical search carried out by the Lausanne group for the ideal knots were presented in Ref. The present state of art in this field is presented in Ref. A. Stasiak, V. Katritch and L. H. Kauffman, World Scientific 1998. During the process the knot is forced to change its conformation until no further shrinking is possible.
Figure below shows how the process runs in the case of the trefoil knot.
The phenomenon is of vital importance in the case of composite knots. To test the SONO algorithm I performed a series of tests. Below I briefly describe them. A. Stasiak, V. Katritch and L. H. Kauffman, World Scientific 1998. SONO will disentangle it in a reasonable time finishing with a circle - the unquestionable ideal conformation of the unknot.