Creating List of Sequence Iterates

• To: mathgroup at smc.vnet.net
• Subject: [mg33385] Creating List of Sequence Iterates
• From: Bob Harris <nitlion at mindspring.com>
• Date: Mon, 18 Mar 2002 23:38:59 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```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

```

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