The implementation of the iliac tracking algorithm is actually fairly straight forward.  The aortic tracking algorithm passes a pair of starting points to the iliac algorithm.  At that point, the algorithm tracks in a N x M grid in spherical coordinates and finds the longest continuous path which is contained in the vessel.  The immediate problem that comes up is that you end up tracking forward as well as backwards in this method.  That is not as much of a problem as one might think because we have already tracked the aorta up to that point and we know the general direction of the iliac course (down and to the side).  Using those two bits of information allows the algorithm to cast the wide net of potential paths and exclude paths that are illogical.

Once the longest path is determined, the algorithm takes a step in that direction by a fraction of the actual length.  The reason for the fractional step is basically to minimize the number of time that the internal iliac artery is accidentally tracked.

In order to determine the direction of the fractional step, the simplest solution would be to just continue in the direction that is the longest continuous vessel path, but that will often lead the algorithm down undesireable paths. The one alternative is to average the longest path vector with some other set of vectors which represent a directional bias (i.e. the left iliac artery should tend out, down, and anterior).  There are an infinite number of other vectors which you could use and get a result.  The problem is that you don't know beforehand which combination of vectors will result in proper lumen tracking for an arbitrary scan.  

This is where the search for the chaotic attractor comes into play.  If you think of the iliac tracking as an abstract algorithm which depends on a set of variable X1,X2, X3..., then you can conceptualize the iliac tracking as a means of probing the variable space.  The purpose of this exercise is of course to identify the attractor which is assumed to be attainable.  Whether or not that is possible is something we shall have to wait and see