Animate does not end (possible bug?)

Question

This test code is working and displays always the same histogram and stops at n=5.

nbars = 20;
data = Array[0 &, nbars];

Animate[
 data = RandomInteger[1, nbars];
 BarChart[data],
 {n, 1, 5, 1}, AnimationRepetitions -> 1
 ]

The following code in which the list data should be added to its previous values runs endless, why is it so?

nbars = 20;
data = Array[0 &, nbars];

Animate[
 data = data + RandomInteger[1, nbars];
 BarChart[data],
 {n, 1, 5, 1}, AnimationRepetitions -> 1
 ]

Answer 1

This is not a bug.

Animate is a Dynamic function, this means that everything within Animate is repeatedly updated, regardless of whether the function of steps {n, 1, 5, 1} is running or not. Note that replacing Animate with Manipulate shows this explicitly.

To understand how this works, try running

a = 2;
Animate[Plot[a x + n, {x, 0, 2}], {n, 1, 5, 1}]

Then evaluate a=-2; in another cell, you will see that the plot output changes.

To update data, and run the code with Animate[] instead of ListAnimate[], you can run:

nbars = 20;
data = ConstantArray[0, {5, nbars}];
Table[data[[i]] = data[[Max[i - 1, 1]]] + RandomInteger[1, nbars], {i,
    5}];
Animate[BarChart[data[[n]]], {n, 1, 5, 1}, AnimationRepetitions -> 1]

Answer 2

armed with knowledge that this is a dynamic/manipulate issue we can fix by telling Manipulate via TrackedSymbols not to track data :

nbars = 20;
data = Array[0 &, nbars];
Animate[
 data = data + RandomInteger[1, nbars];
 BarChart[data], {n, 1, 5, 1}, TrackedSymbols -> {n}, 
 AnimationRepetitions -> 1]

this sort-of works, running through n and stopping, although it updates data 6 times, not 5. (If you set nbars large, say 100, you will consistently get a few bars with value 6. ) Additionally, if you manually move the slider after it stops it will update data with each move. ( not clear what you actually expect )

If you do this,

nbars = 20;
data = Array[0 &, nbars];
ListAnimate[
 Table[data = data + RandomInteger[1, nbars]; 
  BarChart[data], {n, 1, 5, 1}], AnimationRepetitions -> 1]

you get exactly 5 frames, that do not change after the first run though.

Answer 3

Answer from Wolfram Technology Group:

In your second example, the value of data is being changed (data = data + RandomInteger[1, nbars]) while the expression is getting evaluated, and, as you mentioned, for each change the Animation is repeated. This is As Designed. If you look at the FullForm of your expression (you can add //FullForm at the end of your expression and evaluate it), you can see that Animate is basically a Manipulate module (with Animator for ControlType and SynchronousUpdating set to True):

nbars = 20;
data = Array[0 &, nbars];

Manipulate[
 CompoundExpression[Set[data, Plus[data, RandomInteger[1, nbars]]], 
  BarChart[data]],
 List[
  n, 1, 5, 1, Rule[AnimationRepetitions, 1], 
  Rule[AppearanceElements, 
   List["ProgressSlider", "PlayPauseButton", "FasterSlowerButtons", 
    "DirectionButton"]]
  ],
 Rule[ControlType, Animator], Rule[AppearanceElements, None], 
 Rule[DefaultBaseStyle, "Animate"], 
 Rule[DefaultLabelStyle, "AnimateLabel"], 
 Rule[SynchronousUpdating, True], Rule[ShrinkingDelay, 10.`]
 ]

And if you look at the output cell for the first expression (without FullForm) by selecting the cell and pressing Shift+Ctrl+E (or clicking on "Show Expression" in the "Cell" menu in Mathematica), you can see that the output cell is a DynamicModuleBox. It will dynamically update with the updated value of "data".