Function Repository Resource:

SimpleListAnimate

Source Notebook

Create an animation from a list of expressions

Contributed by: Richard Hennigan (Wolfram Research)

ResourceFunction["SimpleListAnimate"][{expr₁,expr₂,…}]

generates an animation whose frames are the successive expr_i.

ResourceFunction["SimpleListAnimate"][list,fps]

displays fps frames per second.

Details and Options

ResourceFunction["SimpleListAnimate"] is similar to ListAnimate, but does not display any controls.

To start/stop the animation, click on the image.

The expr_i can be any expressions, and do not need to be graphics.

ResourceFunction["SimpleListAnimate"] generates an Interpretation object that’s interpreted as list.

If it is not specified, fps will by default be chosen so that the animation lasts a total of 5 seconds.

ResourceFunction["SimpleListAnimate"] has the same options as Manipulate, with the following additions and changes:

Alignment

Automatic

how to align objects in the display area

AnimationDirection

Forward

the direction of the animation

AnimationRepetitions

Infinity

how many times to run before stopping

AnimationRunTime

time elapsed since the animation last started running, or 0 if the animation is not running

AnimationTimeIndex

Automatic

time index for the animation, where 0 is the beginning and the value of DefaultDuration is the end

DefaultDuration

the default duration in seconds

DisplayAllSteps

True

whether to force all expr_i to be displayed

ImageSize

All

the overall image size to use

ResourceFunction["SimpleListAnimate"] by default displays in an area large enough to fit any of the expr_i.

With the option setting ImageSize→Automatic, ResourceFunction["SimpleListAnimate"] leaves space only for the expr_i currently being displayed.

Examples

Basic Examples (2)

Animate a sequence of images:

In[1]:=

Out[1]=

Create an animated bird:

In[2]:=

(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/53c1c4f3-29e8-4ffc-9f76-e90dcfea1871"]

Out[2]=

Use the resource function BirdSay with the bird:

In[3]:=

Out[3]=

Scope (4)

SimpleListAnimate Content (2)

Animate a list of Wolfram Language expressions:

In[4]:=

$ResourceFunction[ "SimpleListAnimate"][{Style["\[MathematicaIcon]", Large], "string", Framed[x + y], Graphics[Rectangle[], ImageSize -> 20]}]$

Out[4]=

Animate a sequence of expressions:

In[5]:=

$ResourceFunction["SimpleListAnimate"][Table[Factor[x^n - 1], {n, 50}]]$

Out[5]=

Force the expressions to wrap at a fixed width:

In[6]:=

$ResourceFunction["SimpleListAnimate"][ Table[Pane[Factor[x^n - 1], 200], {n, 50}]]$

Out[6]=

SimpleListAnimate Control (2)

By default, the animation lasts a total of five seconds:

In[7]:=

Out[7]=

Control the display rate of each frame using a second argument:

In[8]:=

Out[8]=

Options (10)

Alignment (1)

Use preset values:

In[9]:=

Out[9]=

AnimationDirection (1)

Control the direction of animation:

In[10]:=

Out[10]=

AnimationRate (1)

Control the animation rate:

In[11]:=

Out[11]=

AnimationRepetitions (1)

Control the number of animation cycles:

In[12]:=

Out[12]=

AnimationRunning (2)

By default, SimpleListAnimate starts running when evaluated:

In[13]:=

Out[13]=

By setting AnimationRunning→False, SimpleListAnimate starts in a paused state:

In[14]:=

Out[14]=

DefaultDuration (1)

Control the time duration of one animation cycle:

In[15]:=

Out[15]=

ImageSize (3)

By default, SimpleListAnimate leaves enough space for its content without ever having to resize:

In[16]:=

Out[16]=

By setting ImageSize, leave just enough space for the current display:

In[17]:=

Out[17]=

A fully custom image size:

In[18]:=

Out[18]=

Applications (4)

Collect the individual steps in an optimization problem:

In[19]:=

${sol, {steps}} = Reap[FindMinimum[(x - 1)^2 + 100 (y - x^2)^2, {{x, -1}, {y, 1}}, StepMonitor :> Sow[{x, y}]]]$

Out[19]=

Animate the progression of the solver:

In[20]:=

ResourceFunction["SimpleListAnimate"][
Table[ListLinePlot[Take[steps, i], Mesh -> All, PlotRange -> {{-1, 1.1}, {-1, 1.1}}], {i, Length[steps]}]]

Out[20]=

Collect individual steps when solving the sine-Gordon PDE:

In[21]:=

${sol, {steps}} = Reap@NDSolve[{\!$ \*SubscriptBox[\(\[PartialD]$, $t, t$]$u[t, x]$\) == \!$ \*SubscriptBox[\(\[PartialD]$, $x, x$]$u[t, x]$\) + Sin[u[t, x]] , u[0, x] == E^-x^2, \!$\*SuperscriptBox[\(u$, TagBox[ RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}], Derivative], MultilineFunction->None]\)[0, x] == 0, u[t, -10] == u[t, 10]}, u, {t, 0, 8}, {x, -10, 10}, StepMonitor :> Sow[Plot[u[t, x], {x, -10, 10}, PlotRange -> {0, 8}]]]; // Quiet$

Animate the solution progress:

In[22]:=

Out[22]=

An implementation of LU decomposition that uses Sow on all intermediate steps:

In[23]:=

$LU[A_] := Module[{m, n, L, U}, {m, n} = Dimensions[A]; L = IdentityMatrix[n]; Sow[L, "L" ]; U = A; Sow[U, "U"]; Do[ L[[k ;; n, k]] = U[[k ;; n, k]]/U[[k, k]]; Sow[L, "L"]; U[[(k + 1) ;; n, k ;; n]] = U[[(k + 1) ;; n, k ;; n]] - L[[(k + 1) ;; n, {k}]] . U[[{k}, k ;; n]]; Sow[U, "U"]; , {k, 1, n - 1}]; {L, U} ];$

Reap the intermediate results and make an animation:

In[24]:=

$LUAnimate[A_, f_] := Module[ {lu, l, u}, {lu, {{l}, {u}}} = Reap[ LU[ A ], {"L", "U"}]; ResourceFunction["SimpleListAnimate"][ Table[Row[{f[l[[i]]], ".", f[u[[i]]], "==", f[A]}], {i, Length[l]}]] ]$