generates a version of expr with controls added to allow interactive manipulation of the value of u.


allows the value of u to vary between umin and umax in steps du.


takes the initial value of u to be uinit.


labels the controls for u with ulbl.


allows u to take on discrete values u1,u2,.


provides controls to manipulate each of the u,v,.


links the controls to the specified controllers on an external device.

Details and Options

  • The expression expr can be any graphic or other expression. If it is None, only the controls are displayed.
  • The following forms by default yield particular forms of controls:
  • {u,umin,umax}manipulator (slider, animator, etc.)
    {u,umin,umax,du}discrete manipulator with step du
    {u,{xmin,ymin},{xmax,ymax}}2D slider
    {u,Locator}a locator in a graphic
    {u,{u1,u2,}}setter bar for few elements; popup menu for more
    {u,{u1->lbl1,u2->lbl2,}}setter bar or popup menu with labels for elements
    {u,{True, False}}checkbox
    {u,color}color slider
    {u}blank input field
    {u,FormObject[]}form with specified fields
    {u,func}create an arbitrary control from a function
    {{u,uinit},}control with initial value uinit
    {{u,uinit,ulbl},}control with label ulbl
    {{u,},,opts}control with particular options
    Control[]general control object
    Delimiterhorizontal delimiter
    string, view, cell expression, etc.explicit text, view, cell, etc. annotations
  • Possible annotations given in place of controls include expressions with heads String, Style, Row, Item, Text, ExpressionCell, TextCell as well as views and layout constructs such as TabView, Grid, and Multicolumn.
  • Inside annotations, controls can be specified using Control.
  • The label ulbl for a control can be any expression.
  • The option setting ControlType->type attempts to use controls of the specified type.
  • Possible control types include: Animator, Checkbox, CheckboxBar, ColorSetter, ColorSlider, FormControl, InputField, IntervalSlider, Manipulator, PopupMenu, RadioButton or RadioButtonBar, Setter or SetterBar, Slider, Slider2D, TogglerBar, Trigger, and VerticalSlider. None can also be used.
  • ControlType options can be given separately for each variable. Options for the controls can also be given within the specification for the variables.
  • ControlType->Trigger specifies that a particular variable should be controlled by a trigger.
  • The control specification {u,umin,umax,,Appearance->"Labeled"} yields a slider with the value displayed as a label.
  • In the form {u,func}, Dynamic[u] is given as the first argument to func.
  • The form {u,umin,umax,func} can also be used; what is evaluated is then func[Dynamic[u],{umin,umax}].
  • The form {u} is equivalent to {u, InputField}. {u, ColorSlider} gives a default color slider as a control.
  • In the form {u,Locator}, the value of u is a list giving x and y coordinates. The coordinates refer either to the first graphic in expr, or range from 0 to 1 in each direction across expr.
  • The form {{u,{{x1,y1},{x2,y2},}},Locator} sets up a locator for each of the {xi,yi}, and makes the value of u be the list of all {xi,yi}.
  • The form {{u,uinit},{xmin,ymin},{xmax,ymax},Locator} specifies a range for the locators.
  • The option setting LocatorAutoCreate->All specifies that new locators should be added for clicks that do not hit existing locators. Click deletes locators.
  • {{u,{}},Locator,LocatorAutoCreate->All} starts with no locators, but allows locators to be created.
  • If a variable u is used more than once, linked controls for it are given.
  • The option setting ControlPlacement->pos specifies that controls should be placed at position pos relative to expr. Possible settings for pos are Bottom, Left, Right, and Top.
  • The placement of an annotation can be specified by enclosing it in an Item that has a ControlPlacement option.
  • The following overall options can be given:
  • AlignmentAutomatichow to align the output in the display area
    AppearanceElementsAutomaticoverall control elements to include in the displayed output
    AutoActionFalsewhether to change controls automatically when the mouse is over them
    AutorunSequencingAutomatichow autorun should use the controls
    BaselinePositionAutomaticalignment relative to surrounding text
    BaseStyle{}base style specifications for the Manipulate
    Bookmarks{}bookmark settings
    ContentSizeAutomaticthe absolute size for the content area
    ContinuousActionAutomaticwhether to update continuously when controls are changed
    ControllerLinkingAutomaticwhen to activate links to external controllers
    ControllerMethodAutomatichow external controllers should operate
    ControllerPathAutomaticwhat external controllers to try to use
    ControlPlacementAutomaticplacement of controls
    ControlTypeAutomatictype of controls to use
    DeinitializationNonean expression to be evaluated if the output from the Manipulate is deleted
    DeployedFalsewhether to make the displayed output deployed
    EvaluatorAutomaticthe kernel to use for evaluations
    FrameLabelNonelabels for the outer frame
    FrameMarginsAutomaticmargins inside the overall frame
    ImageMargins0margins around the whole Manipulate
    InitializationNonean expression to be evaluated when output is first displayed
    InterpolationOrderAutomaticinterpolation order for animating transitions between bookmarks
    LabelStyle{}style specifications for the controls area
    LocalizeVariablesTruewhether to localize the variables
    PaneledTruewhether to put the displayed output in a panel
    PreserveImageOptionsTruewhether to preserve image size and other options when regenerating graphics
    RotateLabelFalsewhether to rotate y labels on the frame
    SaveDefinitionsFalsewhether to save all definitions associated with expr
    ShrinkingDelay0how long to delay before shrinking if the displayed object gets smaller
    SynchronousInitializationTruewhether to perform initialization synchronously
    SynchronousUpdatingAutomaticwhether to update synchronously
    TouchscreenAutoZoomFalsewhether to zoom to fullscreen when activated on a touchscreen
    TouchscreenControlPlacementAutomaticplacement of controls on a touchscreen
    TrackedSymbolsFullsymbols whose changes trigger updates in the output
    UndoTrackedVariablesNonevariables that, when changed, should be tracked by the front end's undo mechanism
    UnsavedVariablesNonevariables whose values should not be saved
  • The options ControlPlacement and ControlType can be given separately for each variable, in the form {u,spec,opts}.
  • Manipulate is a scoping construct that implements lexical scoping.
  • Manipulate generates a DynamicModule object, with the variables u, v, etc. specified as local.
  • With the default setting UnsavedVariables->{}, values of the variables u, v, etc. are automatically saved in notebooks, and restored when the notebooks are reopened.
  • With a setting Initialization:>expr, the expression expr is evaluated when Manipulate is executed, or when the result is first displayed in a particular session.
  • The setting for AppearanceElements can be a list in any order of the following: "ContentResizeArea", "HideControlsButton", "ManipulateMenu", "SnapshotButton". By default, only "ManipulateMenu" is included.
  • Clicking the snapshot button creates a cell directly below the Manipulate output, containing input of the form With[{u=uval,},expr] specifying current values of all variables.
  • With the setting ContinuousAction->None, an explicit Update button is displayed, and expr is not reevaluated until this is clicked.
  • With the default setting TrackedSymbols->Automatic, only symbols that appear explicitly in expr are tracked.
  • TrackedSymbols->True tracks symbols that appear in the controls of Manipulate.
  • With TrackedSymbols->All, the output is updated whenever any symbol encountered in its evaluation is changed.
  • With the default setting ControllerLinking->Automatic, controls in a Manipulate respond to specified controllers on an external device whenever the Manipulate is part of the current selection.
  • Controllers on an external device such as a gamepad can include joysticks, buttons, etc.
  • Typical external controller specifications include:
  • "X" or "X1"xprimary x value
    "Y" or "Y1"yprimary y value
    "Z" or "Z1"zprimary z value
    "XY" or "XY1"{x,y}primary 2-axis controller value
    "XYZ" or "XYZ1"{x,y,z}primary 3-axis controller value
    "X2", "Y2", "XY2", etc.x, y, {x,y}, etc.values from a secondary controller
    "XCyclic", etc.x, etc.values taken to be cyclic
    "XAbsolute", etc.x, etc.values from absolute control positions
    "B1", "B2", etc.b1, b2, etc.toggling button states
    "B1Absolute", "B2Absolute", etc.b1, b2, etc.instantaneous button states
  • Raw external controller specification names for devices active in a particular Wolfram System session can typically be found using ControllerInformation.
  • With the default setting ControllerMethod->Automatic, a controller specification such as "X" means that the displacement of a control such as a joystick by default determines the rate of change of the corresponding variable x. If an alternate state is selected, for example by depressing the joystick, then the absolute position of the control directly determines the value of x.
  • With a controller specification such as "XAbsolute", the absolute position of a control such as a joystick determines the value of the corresponding variable x.
  • With a controller specification such as "XCyclic", the value of the corresponding variable x is typically taken to wrap around cyclically when the control reaches the end of its range.
  • A controller specification such as "XYZ" may be associated with multiple controls on an external device, such as axes on two distinct joysticks on a single controller.
  • On a gamepad or other device with two joysticks, "XY1" typically refers to the left joystick, and "XY2" to the right one. If a gamepad has a "hat" control, this is typically referred to as "XY3".
  • Button controller specifications such as "B1" toggle between True and False whenever the corresponding button is pressed.
  • Absolute specifications such as "B1Absolute" yield True while the button is being pressed, and False otherwise.
  • The settings for BaseStyle and LabelStyle are appended to the default styles typically given by the "Manipulate" and "ManipulateLabel" styles in the current stylesheet.


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Basic Examples  (4)

Manipulate a continuous parameter:

Click for copyable input

Manipulate a parameter in discrete steps:

Click for copyable input

Manipulate two parameters:

Click for copyable input

Give defaults and names for parameters:

Click for copyable input

Scope  (29)

Generalizations & Extensions  (2)

Options  (66)

Applications  (3)

Properties & Relations  (5)

Possible Issues  (4)

Neat Examples  (4)

Introduced in 2007
Updated in 2019