Researchers were able to identify general "counting rules," or characteristics that determine a knot's stability. Basically, a knot is stronger if it has more strand crossings, as well as more "twist fluctuations," changes in the direction of rotation from one strand segment to another.
For instance, if a fiber segment is rotated to the left at one crossing and rotated to the right at a neighboring crossing as a knot is pulled tight, this creates a twist fluctuation and thus opposing friction, which adds stability to a knot. If, however, the segment is rotated in the same direction at two neighboring crossing, there is no twist fluctuation, and the strand is more likely to rotate and slip, producing a weaker knot.
A knot can be made stronger if it has more "circulations," which they define as a region in a knot where two parallel strands loop against each other in opposite directions, like a circular flow.
By taking into account these simple counting rules, the team was able to explain why a reef knot, for instance, is stronger than a granny knot. While the two are almost identical, the reef knot has a higher number of twist fluctuations, making it a more stable configuration. Likewise, the zeppelin knot, because of its slightly higher circulations and twist fluctuations, is stronger, though possibly harder to untie, than the Alpine butterfly, a knot that is commonly used in climbing.
Topological mechanics of knots and tangles, Science 03 Jan 2020: Vol. 367, Issue 6473, pp. 71-75
In 2018 the Rockwell International Career Development Associate Professor at MIT, Mathias Kolle’s group engineered stretchable fibers that change color in response to strain or pressure. The researchers showed that when they pulled on a fiber, its hue changed from one color of the rainbow to another, particularly in areas that experienced the greatest stress or pressure.