Briefly, we write , and we call the function obtained by composing F with itself n times the n -th iterate of F . The sequence is called the orbit of under F . For the Fibonacci L -system, we have seen that the Fibonacci sequence of a 's and b 's. It can be shown that this limit is true no matter what the initial generation is chosen to be in code-space. In fact, is the only fixed point of F .
Attractors arise as the limiting behavior of orbits.
Sequences can have tremendously variable behavior. The sequence might have a limit. Part of the sequence may tend to one limit point, and others to other limit points. This leads to the following notions. A subsequence of a sequence is a selection where .