The general properties of knot categories are already known. Real world factors such as the diameter of the line, its mechanical properties and environmental considerations (eg. presence of powder/dust, oil, rain, etc.) will significantly affect the actual deployment properties of a given knot. In addition, there are infinite places within a given knot that forces can be applied. Lines will also degrade over time, and factors such as complexity, time and fingers/hands/tools required-to-reliably tie/untie will also often be practical concerns in selection for deployment. Therefore, while your interest in the algorithmic exploration is interesting, if the goal is to generate novel practical results then there is a lot more complexity to add to the modeling before a useful result might be obtained, and any such result would have to be clearly based in assumptions around deployment scenario.
Sure. you're not telling me (a person who used to model knots in proteins using molecular dynamics, and works with FEA and other mechanical engineering tools) anything really novel.
Humans discovered hundreds of knots just playing around, and developed excellent knots in the past 400 years; new knots, never before tied, were invented some ~100 years ago. One imagines that a bit of searching with a computer might find a few cases that were overlooked.
> new knots, never before tied, were invented some ~100 years ago.
No. I don't believe that. The archeological record has evidence of humans making rope for tens of thousands of years. I can believe that nobody alive had seen and named those particular interlocked pairs of overhand knots; that no written record of them existed until recently. But your claim that those knots had never been tied is quite presumptuous.
