Animate

Animate[expr,{u,umin,umax}]

generates an animation of expr in which u varies continuously from umin to umax.

Animate[expr,{u,umin,umax,du}]

takes u to vary in steps du.

Animate[expr,{u,{u1,u2,}}]

makes u take on discrete values u1, u2, .

Animate[expr,{u,},{v,},]

varies all the variables u, v, .

Details and Options

  • expr can be any expression; it does not need to be a graphic.
  • Animate evaluates expr only for the specific literal values of u it requires.
  • Animate[expr,{{u,u0},umin,umax}] takes u to have initial value u0.
  • When umax is finite, u is taken to vary at such a rate as to make the animation last for the time given by the setting for DefaultDuration.
  • Animate[expr,{u,umin,Infinity}] makes an infinite animation in which the value of u increases forever at a rate of one unit per second.
  • Animate[expr,{u,-Infinity,Infinity}] also allows u to decrease forever if the animation is run in reverse.
  • Animate generates a Manipulate object containing an Animator.
  • Animate[expr,{{u,u0, ulbl},},] uses ulbl as the label for the u animator etc.
  • Animate has the same options as Manipulate, with the following additions and changes:
  • AnimationDirectionForwardthe direction of the animation
    AnimationRateAutomaticthe rate at which to take variables to vary
    AnimationRepetitionsInfinityhow many times to run before stopping
    AnimationRunningTruewhether the animation is running
    AnimationRunTime0time elapsed since the animation last started running, or 0 if the animation is not running
    AnimationTimeIndexAutomatictime index for the animation, where 0 is the beginning and the value of DefaultDuration is the end
    AppearanceElementsAutomaticcontrol elements to include
    BaseStyle{}base style specifications for the animator
    DefaultDuration5.the default duration in seconds
    DeinitializationNonean expression to evaluate if the output from the Animate is deleted
    DisplayAllStepsFalsewhether to force all discrete steps to be displayed
    Exclusions{}specific values to be excluded
    InitializationNonean expression to evaluate when output is first generated
    LabelStyle{}style specifications for the label area
    RefreshRateAutomaticthe default number of times per second to refresh
    ShrinkingDelayAutomatichow long to delay before shrinking if the displayed object gets smaller
  • The default for du is determined by the setting for the RefreshRate option, and is negative if umin is larger than umax.
  • If du is given as 0, it is taken to be the minimum positive or negative value determined by the setting for RefreshRate.
  • If an explicit setting is specified for AnimationRate, it takes precedence over the setting for DefaultDuration.
  • The following elements are included by default: "ProgressSlider", "PlayPauseButton", "FasterSlowerButtons", "DirectionButton". These elements can be specified in any order in a list given as the setting for AppearanceElements.
  • The settings for BaseStyle and LabelStyle are appended to the default styles typically given by the "Animate" and "AnimateLabel" styles in the current stylesheet.

Examples

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Basic Examples  (3)

Animate by continuously changing the value of a:

Animate by varying n in discrete steps:

Animate by continuously changing two parameters a and b:

Scope  (8)

Animate Content  (2)

Animate a plot:

Animate any expression, not just a graphic:

Animate Control  (6)

Specify a range for animation:

Specify the animator controls using AppearanceElements:

Specify animation steps:

Specify an infinite animation, where the animation variable increases at unit speed:

Animate, using a discrete set of values:

Animate several variables at once:

Options  (23)

Alignment  (1)

Use preset values:

AnimationDirection  (1)

Control the direction of animation:

AnimationRate  (1)

Control the rate of animation:

AnimationRepetitions  (1)

Control the number of animation cycles:

AnimationRunning  (2)

By default Animate starts running when evaluated:

By setting AnimationRunning->False, Animate starts in a paused state:

AppearanceElements  (2)

By default Animate only contains an Animator:

Use AppearanceElements to get additional controls:

BaselinePosition  (1)

Align with the surrounding text:

ControlPlacement  (1)

Specify the location of the controls:

DefaultDuration  (1)

Control the time duration of one animation cycle:

Deinitialization  (1)

Specify expressions to be evaluated when Animate is no longer displayed:

Deployed  (2)

By default the contents can be selected and edited:

Use Deployed to restrict the interactivity of the contents:

DisplayAllSteps  (1)

With the default setting, some steps may be skipped:

Use DisplayAllSteps to prevent skipping:

Exclusions  (1)

Exclude values from the range:

FrameMargins  (2)

Use preset values:

Or use any values:

ImageMargins  (2)

Use preset values:

Or use any values:

Initialization  (1)

Specify expression to be evaluated before displaying the animation:

RefreshRate  (1)

Control the refresh rate of the animation:

TrackedSymbols  (1)

Specify symbols that will trigger the animation update:

Applications  (9)

Animate a rolling circle:

Animate the Taylor series of :

Animate the series:

Scan through a large space of cellular automata:

Animate nonlinear slider motion:

Display the superposition of two waves:

Animate a complex map of the plane for different values of :

Display a sphere-torus morphing:

Animate the roots of :

Animate point light positions:

Properties & Relations  (2)

Animated behavior can also be built using Animator as a building block:

Animating a fixed list of expressions can be done directly with ListAnimate:

Possible Issues  (2)

Fix PlotRange to stop animations from jiggling:

Use ImagePadding to make sure different labels do not make the image size change:

Neat Examples  (2)

Wolfram Research (2007), Animate, Wolfram Language function, https://reference.wolfram.com/language/ref/Animate.html (updated 2014).

Text

Wolfram Research (2007), Animate, Wolfram Language function, https://reference.wolfram.com/language/ref/Animate.html (updated 2014).

BibTeX

@misc{reference.wolfram_2021_animate, author="Wolfram Research", title="{Animate}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/Animate.html}", note=[Accessed: 29-July-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_animate, organization={Wolfram Research}, title={Animate}, year={2014}, url={https://reference.wolfram.com/language/ref/Animate.html}, note=[Accessed: 29-July-2021 ]}

CMS

Wolfram Language. 2007. "Animate." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Animate.html.

APA

Wolfram Language. (2007). Animate. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Animate.html