An iterative procedure can also be used for other aspects of the fragmentation. This is possible because, in the string picture, the various points where the string breaks are causally disconnected. Whereas the space-time picture in the c.m. frame is such that slow particles (in the middle of the system) are formed first, this ordering is Lorentz-frame-dependent and hence irrelevant. One may therefore make the convenient choice of starting an iteration process at the ends of the string and proceeding towards the middle.
The string fragmentation scheme is rather complicated for a generic multiparton state. In order to simplify the discussion, we will therefore start with the simple process, and only later survey the complications that appear when additional gluons are present. (This distinction is made for pedagogical reasons, in the program there is only one general-purpose algorithm).