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Re: Creating List of Sequence Iterates

• To: mathgroup at smc.vnet.net
• Subject: [mg33406] Re: [mg33385] Creating List of Sequence Iterates
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Wed, 20 Mar 2002 01:53:14 -0500 (EST)
• References: <200203190438.XAA16778@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Have you heard at all of NestList?

In[1]:=
f[x_] := 3*x + 2
In[3]:=
NestList[f, x, 10]
Out[3]=
{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)))),
  2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*x))))),
  2 +
   3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*x)))))),
  2 +
   3*(2 +
     3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 +
                 3*x))))))),
  2 +
   3*(2 +
     3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 +
                 3*(2 + 3*x)))))))),
  2 +
   3*(2 +
     3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 + 3*(2 +
                 3*(2 + 3*(2 + 3*x)))))))))}

In[4]:=
NestList[f,1,10]
Out[4]=
{1,5,17,53,161,485,1457,4373,13121,39365,118097}

Tomas Garza
Mexico City
----- Original Message -----
From: "Bob Harris" <nitlion at mindspring.com>
To: mathgroup at smc.vnet.net
Subject: [mg33406] [mg33385] Creating List of Sequence Iterates


> 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
>
>

• References:
  • Creating List of Sequence Iterates
    • From: Bob Harris <nitlion@mindspring.com>