Re: newbie: can't Manipulate ListPlot of recurrence

• To: mathgroup at smc.vnet.net
• Subject: [mg96810] Re: newbie: can't Manipulate ListPlot of recurrence
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Wed, 25 Feb 2009 04:05:46 -0500 (EST)
• References: <go0j40\$n0f\$1@smc.vnet.net>

```The problem is that each change in y (being one of the tracked
variables) is a trigger for another round of calculations, which again
changes y and triggers again, ad infinitum.

One solution would be the use of RecurrenceTable instead of Table
which enables you to use y as the initial condition only and to
specify the map using a different variable. Now y itself is not
changed due to the calculation and no additional trigger occurs:

Clear[a, y];
Manipulate[
ListPlot[RecurrenceTable[{yy[n + 1] == a yy[n] (1 - yy[n]),
yy[0] == y}, yy, {n, 50}], Joined -> True], {{a, 3.5}, 0,
4}, {{y, 0.4}, 0, 1}]

Cheers -- Sjoerd

On Feb 24, 12:45 pm, Tom Roche <tlro... at gmail.com> wrote:
> summary: I'm trying to Manipulate the logistic map. I can ListPlot it,
> but when I try to Manipulate, the UI behaves weirdly.
>
> details:
>
> As advertised by the Subject:, I'm new to Mathematica (specifically
> 7.0.0 for Students for 32-bit Windows on XP Pro) so please excuse any
> lapses in terminology. I'd also appreciate pointers to specific docs
> rather than just an RTFM.
>
> I'm trying to model the logistic map y=a y (1-y):
>
> http://en.wikipedia.org/wiki/Logistic_maphttp://mathworld.wolfram.com/Log=
isticMap.htmlhttp://www.phy.duke.edu/~palmer/notebooks/LogisticMap.nb
>
> To start with I just tried to plot it, which works:
>
> Clear[a, y];
> a=3.5;
> y=0.4;
> ListPlot[Table[y=a y (1-y),{50}],Joined->True]
>
> I'd like to Manipulate a and y, but when I try to
>
> Clear[a, y];
> Manipulate[
>   ListPlot[Table[y=a y (1-y),{50}],Joined->True], {{a, 3.5}, 0,  4}=
,
> {{y, 0.4}, 0, 1}]
>
> I get weird behavior:
>
> 1 initially the y slider oscillates
>
> 2 initially the plot displays but flashes (apparently between two
>   phases) until I click one of the sliders
>
> 3 the y slider will not move
>
> 4 the a slider can be dragged, but to no effect (i.e. the plot does
>   not change)
>
> 5 there are no error messages
>
> What am I doing wrong? and how can I Manipulate this map?
>
> TIA, Tom Roche <Tom_Ro... at pobox.com>

```

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