D Moews sent me a program that calculates recursive curves. It extends the program included with thing:2363723 - Torus Knots. Many of the curves are knots. Here are four knots generated by the program. Knot 1 is a trefoil.

The fortran souce code and the input parameters for the construction of the four knots are included.

MakerBot

MakerBot Replicator (5th Generation)

Yes

Yes

0.3 mm

Here is D Moews' explanation of how the program works - it's a comment prefixed to the program.

Starting with a circle traversed a number of times, this program repeatedly changes a curve into a generalized helix wrapped around itself by calculating the TNB frame based on the curve and then offsetting the curve by a vector in the NB plane which, as one's point of view moves along the curve, rotates around the origin in the NB plane a specified number of times with a given phase offset.

After generation and translation, the final curve is enclosed in a circular cylinder with specified radius, and a triangular mesh is created, sampling the surface with NCVPTS points along the curve and NCYPTS points around the cylinder. The mesh is then written to a specified output file in STL format.