1
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In order to work with iterating functions, we'll need to develop some vocabulary and some terminology.
2
00:00:08,142 --> 00:00:18,778
So, again, let's consider the tripling function, 3x, and here is the result of iterating the number 2.
3
00:00:18,778 --> 00:00:27,256
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.
4
00:00:27,256 --> 00:00:39,894
The starting number, the number we start with, is called the seed or initial condition.
5
00:00:39,894 --> 00:00:44,642
So in this example, the number 2 we would say is the seed or the initial condition.
6
00:00:44,642 --> 00:00:50,577
The seed is just the starting value. The number we put in to get this loop going.
7
00:00:50,577 --> 00:01:03,476
The sequence of numbers we get, as a result of iterating our seed, is known as an itinerary or an orbit.
8
00:01:03,476 --> 00:01:14,335
So, I would say that this sequence of numbers, continuing on, is the itinerary, or orbit, for the seed 2.
9
00:01:14,335 --> 00:01:19,975
An itinerary for a trip is just a list of all the places you visit, in order.
10
00:01:19,975 --> 00:01:23,975
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.