RE: Creating List of Sequence Iterates
- To: mathgroup at smc.vnet.net
- Subject: [mg33400] RE: [mg33385] Creating List of Sequence Iterates
- From: "David Park" <djmp at earthlink.net>
- Date: Wed, 20 Mar 2002 01:53:04 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Bob,
Check out Nest and NestList in Help.
f[x_] := 3x + 2
NestList[f, x, 5]
{x, 2 + 3 x, 2 + 3 (2 + 3 x), 2 + 3 (2 + 3 (2 + 3 x)),
2 + 3 (2 + 3 (2 + 3 (2 + 3 x))), 2 + 3 (2 + 3 (2 + 3 (2 + 3 (2 + 3 x))))}
NestList[f, 1, 20]
{1,5,17,53,161,485,1457,4373,13121,39365,118097,354293,1062881,3188645,
9565937,28697813,86093441,258280325,774840977,2324522933,6973568801}
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
> From: Bob Harris [mailto:nitlion at mindspring.com]
To: mathgroup at smc.vnet.net
>
>
> Howdy,
>
> I'm trying to figure out how, with a single expression, I can
> create a list
> of iterates of some sequence.
>
> For example, suppose I have defined F[x_] := 3x+2 and I want to get a list
> that contains F[1], F[F[1]], F[F[F[1]]], etc. It seems like I could do
> something like
>
> iterates = Table [F[ iterates[[n-1]] ] , {n,1,20}]
>
> to get a list of the first 20 iterations of this function (assuming I had
> some way to define interates[[1]]).
>
> Anyone know how I can do that, short of writing the following function?
>
> Iterate[func_ , first_ , iterations_] := Module[ {v, ix},
> v = Table[0, {n, 1, iterations}];
> v[[1]] = first;
>
> For[ix=2, ix<=iterations, ix++, v[[ix]] = func[v[[ix-1]]] ];
>
> v
> ]
>
> Any help would be appreciated. I'm mostly interested in being pointed in
> the right direction.
>
> Thanks,
> Bob H
>
>