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based on an earlier version of the Wolfram Language.
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Animate

Animate
generates an animation of expr in which u varies continuously from to .
Animate
takes u to vary in steps du.
Animate
makes u take on discrete values , , ....
Animate
varies all the variables u, v, ....
  • 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 takes u to have initial value .
  • When 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 uses 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
AppearanceElementsNonecontrol 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 is larger than .
  • If du is given as , it is taken to be the minimum positive or negative value determined by the setting for RefreshRate.
  • The following elements are included by default: , , , . 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 and styles in the current stylesheet.
Animate by continuously changing the value of :
Animate by varying in discrete steps:
Animate by continuously changing two parameters and :
Animate by continuously changing the value of :
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Animate by varying in discrete steps:
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Animate by continuously changing two parameters and :
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Animate a plot:
Animate any expression, not just a graphic:
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:
Use preset values:
Control the direction of animation:
Control the rate of animation:
Control the number of animation cycles:
By default Animate starts running when evaluated:
By setting AnimationRunning->False, Animate starts in a paused state:
By default Animate only contains an Animator:
Use AppearanceElements to get additional controls:
Specify the location of the controls:
Control the time duration of one animation cycle:
Specify expressions to be evaluated when Animate is no longer displayed:
By default the contents can be selected and edited:
Use Deployed to restrict the interactivity of the contents:
With the default setting, some steps may be skipped:
Use DisplayAllSteps to prevent skipping:
Exclude values from the range:
Use preset values:
Or use any values:
Use preset values:
Or use any values:
Specify expression to be evaluated before displaying the animation:
Control the refresh rate of the animation:
Specify symbols that will trigger the animation update:
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:
Animated behavior can also be built using Animator as a building block:
Animating a fixed list of expressions can be done directly with ListAnimate:
Fix PlotRange to stop animations from jiggling:
Use ImagePadding to make sure different labels do not make the image size change:
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