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Re: Manipulate and ParametricPlot Control?

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  • Subject: [mg114385] Re: Manipulate and ParametricPlot Control?
  • From: Albert Retey <awnl at>
  • Date: Thu, 2 Dec 2010 05:43:29 -0500 (EST)
  • References: <id4sf3$cbg$>


> As a simple test file, I created a notebook (which I don't have any 
> more) containing the one cell
>    Manipulate[ Plot[x^a, {x,0,1}], {a,0,5}]
> (May have had a PlotRange option also; don't recall for sure.)
> Executed it; worked as expected.  
> Decided to set an initial value for a; as best I recall (details are 
> fuzzy), I edited the cell to change {a,0,5} to {{a,1},0,5}  (that's what 
> I intended to do, anyway).
> When I re-executed the cell, I got a live Manipulate that displayed a 
> ***two-dimensional*** (2D) Control -- something I had never seen before, 
> but which looked exactly like the one I more recently found in the 
> ParametricPlot example in the Manipulate Help.  
> Exercising this Manipulate displayed **two** x^a curves, with values 
> corresponding to the H and V axes of the 2D Control.  Functioned fine; 
> no error msgs at any time.
> I made a (presumably erroneous) guess that the edited cell must have 
> somehow been influenced by the earlier execution of the initial, 
> un-edited version of the same cell (I had two implementations of the "a" 
> variable floating around, maybe??).  So, I tried adding Removes before 
> the cell; tried Saving it, Quiting Mathematica, and re-opening it.  The 2D 
> Control obstinately remained (and worked).  This then led to the 
> re-virginating query.

from the documentation:
"Manipulate is a scoping construct that implements lexical scoping."
So the two a will (should) not interact. I have never seen a case that
would suggest that the scoping would break.

> I may have made a typo in the editing I noted above, but I sure as hell 
> did NOT change Plot to ParametricPlot.  And when I try some tests now 
> using Plot[ {f1, f2}, ...] inside a Manipulate, I get two curves -- but 
> never a 2D Control.
> Any ideas what went wrong here?

My guess is that you erroneously entered this:

Manipulate[Plot[x^a, {x, 0, 1}], {a, {0, 1}, 5}]

the x^a will then evaluate to {x^a[[1]],x^a[[2]} and thus two lines are
plotted. From the fact that the lines have the same color you can also
guess that Plot recognizes x^a as two lines only after evaluating the
first argument.



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