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To iterate means to repeat, so an iterative process involves repeating something many times.
Imagine some dough, Plasticine or Blu-Tack, something that can be made into a strip then stretched.
We are going to take a length of this material, which we'll regard as the unit length, and put a mark at some fraction distance along it.
Now we are going to follow a procedure and see where our mark ends up.
The material is folded in the middle so that the bottom reaches back to the top.
The material is now only half a unit in length and twice as fat, so it is rolled out or stretched uniformly to become one unit in length again.
Finally we'll note the new position of our mark.
What happens for other start fractions?
Does everything go to a loop?
What size loops appear and for what fractions?