Re: Creating List of Sequence Iterates
- To: mathgroup at smc.vnet.net
- Subject: [mg33394] Re: Creating List of Sequence Iterates
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 20 Mar 2002 01:52:55 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <a76g2a$gm0$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
"Nest[f, expr, n] gives an expression with f applied n times to expr"
and
Nest[f, x, 4]
gives
f[f[f[f[x]]]]
Regards
Jens
Bob Harris wrote:
>
> 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