I've been developing an algorithm in Java for simulating the behaviour of knots as they are tightened. It's based on Piotr Pieranski's "SONO" (Shrink On No Overlaps) algorithm, but rather than shrinking the rope as the iterations progress, my version "tugs" on specified parts of the rope. *(Hopefully this is a more realistic simulation of what happens as a real, physical knot is tied and tightened. I'm interested specifically in real physical knots, and not in the properties of the ideal closed knots of mathematical "knot theory", which is why I have adopted a slightly different process than Pieranski.)* The algorithm is therefore called Tug On No Overlaps, or "TONO"....

Would you like to see the algorithm in action?

I've created a simple applet which will run the TONO process on a choice of two knots: a reef knot or a granny knot. You can watch each knot tighten as your computer carries out the simulation itself....

This applet isn't intended to be particularly instructive - it doesn't necessarily lead you to marvellous new insights about the two knots being shown, and it doesn't make use of all the available features of TONO. But it's a nice toy! The "Statistics" button will show you some statistics about the knot you're processing, which might tell you something interesting... but who knows....