Re: newbie: can't Manipulate ListPlot of recurrence

• To: mathgroup at smc.vnet.net
• Subject: [mg96797] Re: newbie: can't Manipulate ListPlot of recurrence
• From: Pillsy <pillsbury at gmail.com>
• Date: Wed, 25 Feb 2009 04:03:23 -0500 (EST)
• References: <go0j40\$n0f\$1@smc.vnet.net>

```On Feb 24, 5:45 am, Tom Roche <tlro... at gmail.com> wrote:
[...]
> Clear[a, y];
> a=3.5;
> y=0.4;
> ListPlot[Table[y=a y (1-y),{50}],Joined->True]
[...]
Clear[a, y];
Manipulate[
ListPlot[Table[y=a y (1-y),{50}],Joined->True], {{a, 3.5}, 0,  4},
{{y, 0.4}, 0, 1}]
> What am I doing wrong? and how can I Manipulate this map?

What you're doing wrong is changing the values of the variable y while you
compute the successive values of your logistic map. Manipulate wants to reflect
the current value of y in its position along the control slider, and y
bounces back and forth. Now, there are quite a few ways to get around this, but
instead of a workaround, I think you're better off using the kernel function that's intended to be used with iterated maps like this one: NestList.

Rest@NestList[a*#*(1-#)&, y, 50]

will produce the same list of values as your Table expression, but y will not have its value modified. NestList will put the initial value (with 0 function applications) as the first element in the returned list, and Rest will get rid of it.

If you stick that in your Mainpulate, it should just work.

Cheers,
Pillsy

```

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