Can I ask why the addition to the length of the river is a function of the length of the river?
Then we extend the river several times, each extension being a random per cent figure of the length of the river in question.
i.e why are we using
Xn+1 = Xn + f(Xn)
Xn+1 = Xn + f(R)
Where R is a random length factor added to the river independent to the length of the river
If I added a rock to the path of my river and it extended the river length by 5 meters it shouldn't matter if my river is 5 or 5000KM long