dynamic interactivity problem

Question

I am trying to have two panels, the left showing a graphic and two locators, the right one a zoomed-in version in the area defined by the locators.

I've tried

ClearAll[mndpt];
mndpt = Compile[{{c, _Complex}, {maxiter, _Integer}},
   Module[{z, iters},
        iters = 0.;
        z = c;
            While[(iters < maxiter) && (Abs@z < 2),
                iters++;
                z = z^2 + c];
        Sqrt[iters/maxiter]],
   {{z, _Complex}},
   CompilationTarget \[Rule] "C",
   RuntimeOptions \[Rule] "Speed"];

and do

Manipulate[
 Grid[
  {{DensityPlot[mndpt[x + y*I, 200],
        {x, -2, 1}, {y, -1.5, 1.5},
        PlotRange \[Rule] {0, 1}, PlotPoints \[Rule] 80, 
     ColorFunction \[Rule] "Rainbow"],
    DensityPlot[mndpt[x + y*I, 200],
        Dynamic@{x, p1[[1]], p2[[1]]}, Dynamic@{y, p1[[2]], p2[[2]]},
        PlotRange \[Rule] {0, 1}, PlotPoints \[Rule] 80, 
     ColorFunction \[Rule] "Rainbow"]}}],
 {{p1, {-1, -1}}, Locator}, {{p2, {0, 1}}, Locator}]

The right panel does not then work: enter image description here

My question is, why is this so? As you can see, it complains that "DensityPlot::pllim: Range specification {x,-1,0} is not of the form {x, xmin, xmax}. " which I find puzzling. In fact I am generally puzzled. What is going on? Some sort of scoping issue? Evaluation issue? And how can I get it to work? This is probably simple, but I never really understood this frontend stuff.

EDIT: It turns out that this question was due to a (hopefully momentary) sharp increase in stupidity on my part. As pointed out by Simon in a comment, removing the two Dynamics (which I had added in a blind effort to make this work) makes everything work fine. That is,

    Manipulate[
 Grid[
  {{DensityPlot[mndpt[x + y*I, 200],
        {x, -2, 1}, {y, -1.5, 1.5},
        PlotRange \[Rule] {0, 1}, PlotPoints \[Rule] 80, 
     ColorFunction \[Rule] "Rainbow"],
    DensityPlot[mndpt[x + y*I, 200],
        {x, p1[[1]], p2[[1]]},{y, p1[[2]], p2[[2]]},
        PlotRange \[Rule] {0, 1}, PlotPoints \[Rule] 80, 
     ColorFunction \[Rule] "Rainbow"]}}],
 {{p1, {-1, -1}}, Locator}, {{p2, {0, 1}}, Locator}]

does the right thing:

enter image description here

So, who knows why else I did the first few times so that it didn't work.

On the other hand, the message in the original case, namely, "DensityPlot::pllim: Range specification {x,-1,0} is not of the form {x, xmin, xmax}. " was more puzzling. I think it's been explained by Leonid, also in a comment (in brief, try ClearAttributes[Dynamic, ReadProtected] then ??Dynamic and you can see that there is a definition Dynamic/:MakeBoxes[BoxForm`x$_Dynamic,StandardForm]:= etc). As my understanding of frontend programming is negligible I won't try to explain it here, so if anybody does post an answer explaining that, it would be appreciated.

dynamic interactivity problem

1 Answers