BUILT-IN MATHEMATICA SYMBOL

# Manipulate

Manipulate[expr, {u, umin, umax}]
generates a version of expr with controls added to allow interactive manipulation of the value of u.

Manipulate[expr, {u, umin, umax, du}]
allows the value of u to vary between and in steps du.

Manipulate[expr, {{u, uinit}, umin, umax, ...}]
takes the initial value of u to be .

Manipulate[expr, {{u, uinit, ulbl}, ...}]
labels the controls for u with .

Manipulate[expr, {u, {u1, u2, ...}}]
allows u to take on discrete values .

Manipulate[expr, {u, ...}, {v, ...}, ...]
provides controls to manipulate each of the .

Manipulate[expr, "cu"->{u, ...}, "cv"->{v, ...}, ...]
links the controls to the specified controllers on an external device.

## Details and OptionsDetails 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,func} create an arbitrary control from a function {{u,uinit},...} control with initial value {{u,uinit,ulbl},...} control with label {{u,...},...,opts} control with particular options Control[...] general control object Delimiter horizontal 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 and Grid.
• Inside annotations, controls can be specified using Control.
• The label 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, InputField, 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 , Dynamic[u] is given as the first argument to func.
• The form 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 , and makes the value of u be the list of all .
• 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. Alt+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:
•  Alignment Automatic how to align the output in the display area AppearanceElements Automatic overall control elements to include in the displayed output AutoAction False whether to change controls automatically when the mouse is over them AutorunSequencing Automatic how autorun should use the controls BaselinePosition Automatic alignment relative to surrounding text BaseStyle {} base style specifications for the Manipulate Bookmarks {} bookmark settings ContentSize Automatic the absolute size for the content area ContinuousAction Automatic whether to update continuously when controls are changed ControllerLinking Automatic when to activate links to external controllers ControllerMethod Automatic how external controllers should operate ControllerPath Automatic what external controllers to try to use ControlPlacement Automatic placement of controls ControlType Automatic type of controls to use Deinitialization None an expression to be evaluated if the output from the Manipulate is deleted Deployed False whether to make the displayed output deployed Evaluator Automatic the kernel to use for evaluations FrameLabel None labels for the outer frame FrameMargins Automatic margins inside the overall frame ImageMargins 0 margins around the whole Manipulate Initialization None an expression to be evaluated when output is first displayed InterpolationOrder Automatic interpolation order for animating transitions between bookmarks LabelStyle {} style specifications for the controls area LocalizeVariables True whether to localize the variables Paneled True whether to put the displayed output in a panel PreserveImageOptions True whether to preserve image size and other options when regenerating graphics UnsavedVariables None variables whose values should not be saved RotateLabel False whether to rotate y labels on the frame SaveDefinitions False whether to save all definitions associated with expr ShrinkingDelay 0 how long to delay before shrinking if the displayed object gets smaller SynchronousInitialization True whether to perform initialization synchronously SynchronousUpdating Automatic whether to update synchronously TouchscreenAutoZoom False whether to zoom to fullscreen when activated on a touchscreen TouchscreenControlPlacement Automatic placement of controls on a touchscreen TrackedSymbols Full symbols whose changes trigger updates in the output
• The options ControlPlacement and ControlType can be given separately for each variable, in the form .
• 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: , , , . By default, only 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 , an explicit Update button is displayed, and expr is not reevaluated until this is clicked.
• With the default setting , only symbols that appear explicitly in expr are tracked.
• tracks symbols that appear in the controls of Manipulate.
• With , the output is updated whenever any symbol encountered in its evaluation is changed.
• With the default setting , 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:
•  or x primary x value or y primary y value or z primary z value or {x,y} primary 2-axis controller value or {x,y,z} primary 3-axis controller value , , , etc. x, y, , etc. values from a secondary controller , etc. x, etc. values taken to be cyclic , etc. x, etc. values from absolute control positions , , etc. , , etc. toggling button states , , etc. , , etc. instantaneous button states
• Raw external controller specification names for devices active in a particular Mathematica session can typically be found using ControllerInformation.
• With the default setting , a controller specification such as 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 , the absolute position of a control such as a joystick determines the value of the corresponding variable x.
• With a controller specification such as , 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 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, typically refers to the left joystick, and to the right one. If a gamepad has a "hat" control, this is typically referred to as .
• Button controller specifications such as toggle between True and False whenever the corresponding button is pressed.
• Absolute specifications such as 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 and styles in the current stylesheet.

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Manipulate a continuous parameter:

 Out[1]= Play Animation ▪

Manipulate a parameter in discrete steps:

 Out[1]= Play Animation ▪

Manipulate two parameters:

 Out[1]= Play Animation ▪

Give defaults and names for parameters:

 Out[1]= Play Animation ▪