Does anyone know of a program or algorithm that generates all possible knots (presumably, from simple to complex)?
That’s an infinity you’re asking for
(if no sort of upper bounds of complexity/crossings
are stipulated.)
For practical knots, I can’t imagine anyone coming
close to figuring this out; OTOH, someone I suppose
could arrange to spit out everything to be found in
[u]Ashley’s Book of Knots.
–dl*
Much like an infinite number set, you can always add another 1 to the biggest number you have, so with any knot set, you can always add another turn or tuck to the biggest (most complex) knot you have.
Strangely, many of our fellow knotters seem intent on getting ever closer to that illusive ∞ …
Derek