Animate

Animate[expr,{u,u_min,u_max}]

generates an animation of expr in which u varies continuously from u_min to u_max.

Animate[expr,{u,u_min,u_max,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},u_min,u_max}] takes u to have initial value u₀.
When u_max 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,u_min,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, u_lbl},…},…] uses u_lbl as the label for the u animator etc.
Animate has the same options as Manipulate, with the following additions and changes:

AnimationDirection	Forward	the direction of the animation
AnimationRate	Automatic	the rate at which to take variables to vary
AnimationRepetitions	Infinity	how many times to run before stopping
AnimationRunning	True	whether the animation is running
AnimationRunTime	0	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
AppearanceElements	Automatic	control elements to include
BaseStyle	{}	base style specifications for the animator
DefaultDuration	5.	the default duration in seconds
Deinitialization	None	an expression to evaluate if the output from the Animate is deleted
DisplayAllSteps	False	whether to force all discrete steps to be displayed
Exclusions	{}	specific values to be excluded
Initialization	None	an expression to evaluate when output is first generated
LabelStyle	{}	style specifications for the label area
RefreshRate	Automatic	the default number of times per second to refresh
ShrinkingDelay	Automatic	how 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 u_min is larger than u_max.
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)

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Animate

Details and Options

Examples

Basic Examples (3)