It boils down to an if statement. Once you've reached a certain number of iterations, or the initial branching meets certain conditions, another rule set applies. But those rules are still not all that different - follow the leaf veins, and all their branching throughout.
The article denies that, at least for the species and structures it discusses. It specifically says it's a non iterative process. That's the point the paper is trying to make. I'm not sure if that's the structures you are talking about, but a few comments up declared 'All plants are actually fractals'. The paper says no, at least in the aspects they are talking about, which are structures that appear fractal-like but are not. They also say it's misleading to think of them as fractals, as the processes are importantly different.
The same applies to the roots.