We recently confronted a problem in Great Theoretical Ideas in Computer Science that had to do with wrapping rope around pegs in such a way that removing any one of them would cause the entire mass to fall. The proper answers were, I thought, rather aesthetically pleasing, and as a result I have decided to see if I can create the ultimate knot. There’s actually a lot of mathematical theory behind knots – here’s a diagram i found with only a few minutes of searchging:

I’d like these knots to be generated in a genetic fashion. Perhaps i give the knot maker a specific task to fill, and see what knot best fulfills the task. Perhaps instead I go for visual complexity, or ease of replication by a human being. Imagine chaining together multiple knots…

I would like this program to be able to “play back” how a knot is tied. This generated animation could itself be a point of focus of the project.