       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

> 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, F[F], F[F[F]], 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[]).
>
> 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[] = 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
>
>

```

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