       RE: Creating List of Sequence Iterates

• To: mathgroup at smc.vnet.net
• Subject: [mg33390] RE: [mg33385] Creating List of Sequence Iterates
• From: David.Annetts at csiro.au
• Date: Wed, 20 Mar 2002 01:52:50 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Bob,

> 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
> 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.

Possibly, what you want is NestList ....

In:=
f[x_] := 3 x + 2

In:=
NestList[f, x, 3]

Out=
{x,2+3 x,2+3 (2+3 x),2+3 (2+3 (2+3 x))}

In:=
% /. x->1

Out=
{1,5,17,53}

In:=
NestList[f, x, 20];

In:=
% /. x->1

Out=
{1,5,17,53,161,485,1457,4373,13121,39365,118097,354293,1062881,3188645,\
9565937,28697813,86093441,258280325,774840977,2324522933,6973568801}

Regards,

Dave.
--------------------------------------------------------
Dr. David Annetts             EM Modelling Analyst
Tel: (+612) 9490 5416         CSIRO DEM, North Ryde
Fax: (+612) 9490 5467         David.Annetts at csiro.au
Include "usual_disclaimers"
--------------------------------------------------------

```

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