After reading the post MoI -> Physical, by libelle, a great deal of searching finally found some parametric equations for a simple braid at renderosity.
http://www.renderosity.com/mod/forumpro/?thread_id=2751275

After getting re-familiarized with FxGraph3D script, a simple 3 filament braid may be created with FxGraph3D.
Centerlines of the filament are parameterized by placing each of the following 3 commands in the command window, sequentially.

_FxGraph3D 25*u;5*sin(u*PI);2*sin(u*2*PI);0;6;0;1;200;0;;;;UV

_FxGraph3D 25*u;5*sin((u+4/3)*PI);2*sin((u+4/3)*2*PI);0;6;0;1;200;0;;;;UV

_FxGraph3D 25*u;5*sin((u+2/3)*PI);2*sin((u+2/3)*2*PI);0;6;0;1;200;0;;;;UV

A simple sweep was made with a circle. The values are not optimized to fill the space, without overlap.

- Brian

The three equations could be turned into a script, with some sliders.

There are also "lissajous braids," and lots of paracord bracelet weaving.
Reeper is a German C4D Plugin which does some braids, but the source code is not provided.