How can I make an animated demonstration of the Wigner semicircle distribution?

Question

With Mathematica 10, it's possible to draw the semicircle distribution of R. Wigner:

data = RandomVariate[WignerSemicircleDistribution[1, 3], 10^4];

Show[
  Histogram[data, 20, "PDF"],
  Plot[PDF[WignerSemicircleDistribution[1, 3], x], {x, -2, 4}, PlotStyle -> Thick]]

Wignersemicircledistribution

My question is: how can I make an animated version of Wigner semicircle distribution as shown below?

Please edit your question to reflect that. Also, if you show what you already tried, you might get more answers. — Yves Klett, Feb 23 '15 at 07:43
Ok, serious now, do you want to export gif? Have a loop with precalculated frames? Dynamic random frame? Interactive Manipualte? — Kuba, Feb 23 '15 at 08:41
`data := RandomVariate[WignerSemicircleDistribution[0, 1], 10^2];
Dynamic[

Show[ Histogram[data, 10, "PDF"], Plot[PDF[WignerSemicircleDistribution[0, 1], x], {x, -2, 4}, PlotStyle -> Thick] , PlotRange -> 2] , UpdateInterval -> .2]` — Kuba, Feb 23 '15 at 08:42
Since it is not clear whether an exported GIF is also desired, or just an embedded movie, I would say this could be a duplicate of Is it possible to insert an animated image into Mathematica notebook?. The workflow would simply be to first create a GIF from within Mathematica, then re-import that using the function makeAnimation in my answer. That function fixes a bug which leads to a hard crash when you right-click on the animation created using Kuba's method (in version 8). — Jens, Feb 23 '15 at 17:10
To illustrate the workflow I just described, see my answer to How to create animated snowfall? — Jens, Feb 23 '15 at 17:11
This is probably a duplicate of other how-to-animate-X question; I recommend that an original be found and it be marked as such. — Mr.Wizard, Feb 23 '15 at 18:06

m_goldberg · Answer 1 · 2015-02-23T21:33:20.487

5

Kuba answered this question in a comment, but I think it needs to be recorded as a formal answer.

You can animate your static plot by wrapping it with Dynamic and supplying the option UpdateInterval.

data := RandomVariate[WignerSemicircleDistribution[1, 3], 10^4];
Dynamic[
  Show[
    Histogram[data, 20, "PDF"], 
    Plot[PDF[WignerSemicircleDistribution[1, 3], x], {x, -2, 4}, PlotStyle -> Thick]],
  UpdateInterval -> .5]

The output will look exactly like the static plot you show in your question, but it will update every 0.5 seconds.

edited Feb 23 '15 at 21:33

answered Feb 23 '15 at 14:07

m_goldberg

107,779
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Just a warning: Unfortunately, this crashes (in version 8) when you right-click on the animation. See my answer here where I work around this problem in the function makeAnimation. – Jens Feb 23 '15 at 17:07
1

The crash bug has been fixed in version 10. But in version 8, don't use this, or the user will lose all their unsaved changes in the crash. – Jens Feb 23 '15 at 17:14

kglr · Accepted Answer · 2020-10-09T17:10:18.523

2

data := RandomVariate[WignerSemicircleDistribution[1, 3], 10^4];

Dynamic[
 Clock[{0, 5, 1}, 1]; 
 Histogram[data, 20, "PDF", 
  ChartStyle -> EdgeForm[White],
  Axes -> False, 
  PlotRange -> {{-4, 6}, {0, .25}}, 
  ImageSize -> 400, 
  Frame -> True,
  Epilog- > 
      First[Plot[PDF[WignerSemicircleDistribution[1, 3], x], {x, -4, 6}, 
        PlotStyle -> Thick]]]]

enter image description here

edited Oct 09 '20 at 17:10

answered Feb 23 '15 at 21:54

kglr

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How can I make an animated demonstration of the Wigner semicircle distribution?

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