I had a couple of days away from this topic. I wanted to understand a little more about how the loop works…and in fact why the loop is necessary? What is being modified in each iteration of the loop?
I understand that we are looping until the moment at each point is zero. Is the Grasshopper script verifying that this is the case? I couldn’t spot where this was happening.
Thanks 
… not exactly, but yes.
The final momentum action+reaction must be zero.
So we use that as initial data, we are balancing 2 equations.
[Bridge stay cable force]x[R]+[Pier node weight]x[R] = [Beach stay cable force]x[R]
(and R is always the offset distance of evaluated force vector from central point, the base of the Pier)
Bridge force vectors never move, never change… same with beach stay cable force.
The solution wouldn’t need iteration at all if there were no additional variables.
But, we have the pier having a weight, and its weight distribution change with its shape. Its shape is a pseudo-catenary defined by bridge cables AND its own weight. Here why the iteration.
At each iteration what changes are the pier node locations and weights.
If you see, the only element changing during the anemone iterations is the pier polyline, which can define both, node locations and node weights.