While driving home yesterday I was thinking about what you said in the sense of time being circular. Let me throw this out there to you as an alternative. Say you consider time as purely linear and represent it by a piece of yarn. Then take a ball and wrap the ball with the yarn. What you will find is that very different time points will be very close together because of the wrapping. This could account for the non-exact repetition that you mentioned, especially if you allowed the effects of one time to be felt by another provided they were spatially close (on the surface of the ball) although they are distant in time. I think I could work out an equation or two for something like this if I get the time, but in any case I think this might help explain the sort of thing you were looking for...
The diameter of the sphere is not necessarily specified, but would have everything to do with how frequently, or easily history-future-present effected each other. Actually the length of the string, i.e. the length of time would also impact this in the sense that one could wrap layers upon layers of string if the string were long enough with respect to the ball diameter.
I think the string could be connected, although for me it seems more likely not to be.
The exact way the string is wrapped could impact how the process of time-travel/ history-future-present confluence occurs. This is part of why i suggested this model, it makes a very concrete mechanism for remodeling or distorting time -- probably something your villain is in the process of trying to discover.
Mathematically, the shape of a curve is a very meaningful thing and can be described by a few parameters: curvature, arclength and torsion. Manipulation of these (or associated vectors) allows one to transform a curve from a flat loop into helix, spiral or other more complicated curve.
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