Here is a different script from the previous post.

The BraidedBands script creates knots that are commonly known as "Turk's-Head knots"
References with more information:
http://www.mi.sanu.ac.rs/vismath/pennock1/index.html
http://www.mi.sanu.ac.rs/vismath/pennock/index.html

Cylindrical equations are used to model two types, Disk, and Cylindrical (Tubular), which may be physically manipulated into each other.
Definitions:
A Bight is a scallop or curve of the rope or cord, at the rim of the knot,
where the cord changes direction. The count of the Bights can be made at
the top rim, or the bottom rim of a cylinder, or the outer or inner rim of a disk.
Bights is a column count, or a radial column count, and is >= 2.

A Lead is the number of revolutions the cord makes around the center of the disk or cylinder, for one Ply only.
The Lead is a ""row count."" Leads is >= 2, for a knot, or no knot will occur, or an unknot.
Per the reference, if a line is drawn from the origin, the number of times the curve crosses the line, is the Lead,
provided Bight and Lead have no Common Divisors.

The Ply count is the number of "parallel" strands of the single cord in the knot.

The GCD (Greatest Common Divisor) of (Bights, Leads) must be equal to 1, or multiple cords will be needed for the knot.

The mathematical knot is a closed curve, and can be a pattern for a physically braided knot.
The physically braided knot is one rope or cord, woven in "parallel" Ply's, with two ends.

Cylindrical coordinates are converted to Cartesian coordinates.

Pipe is handy.
I would like to reconcile these knot formulas with the previous rope mat formulas.

- Brian