In order to work with iterating functions, we'll need to develop some vocabulary and some terminology.
So, again, let's consider the tripling function, 3x, and here is the result of iterating the number 2.
So I start with 2, I triple it to get 6, then I triple 6 to get 18, triple 18 to get 54, and so on.
The starting number, the number we start with, is called the seed or initial condition.
So in this example, the number 2 we would say is the seed or the initial condition.
The seed is just the starting value. The number we put in to get this loop going.
The sequence of numbers we get, as a result of iterating our seed, is known as an itinerary or an orbit.
So, I would say that this sequence of numbers, continuing on, is the itinerary, or orbit, for the seed 2.
An itinerary for a trip is just a list of all the places you visit, in order.
So it makes sense that this would be called an itinerary. It's a list of all the places a number visits as it's iterated, in the order in which it visits them.