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keywords=applets, bookmarks button, click-interactive panels, controls, direct manipulation, gamepad, graphical user interface, GUI, hide controls button, instant interface, interactive, interactive panels, interface builder, joystick, Manipulate, mouse interactive, reset button, slider, snapshot button, universal interface, user interfaces;
description=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 umin and umax in steps du. Manipulate[expr, u, uinit , umin, umax, ... ] takes the initial value of u to be uinit. Manipulate[expr, u, uinit, ulbl , ... ] labels the controls for u with ulbl. Manipulate[expr, u, u1, u2, ... ] allows u to take on discrete values u1, u2, .... Manipulate[expr, u, ... , v, ... , ...] provides controls to manipulate each of the u, v, .... Manipulate[expr, SubscriptBox[c, u] - u, ... , SubscriptBox[c, v] - v, ... , ...] links the controls to the specified controllers on an external device.;

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for, educational, wolfram, science, technology, education, programs, options, examples, related, initiatives, tech, products, data, finance, business, engineering, get, started, grow, your, skills, work, with, us, adults, youth, read, manipulate, details, and, see, also, notes, guides, workflows, links, history, alpha, ai, core, technologies, of, additional, deployment, more, learning, support, resources, events, basic, scope, 29, generalizations, extensions, 68, applications, properties, relations, possible, issues, neat, content, controls, 12, presentation, controller, devices, alignment, appearanceelements, autoaction, autorunsequencing, baselineposition, contentsize, continuousaction, controllerlinking, controllermethod, controllerpath, controlplacement, controltype, 11, deinitialization, deployed, excludedcontexts, framelabel, framemargins, imagemargins, includedcontexts, initialization, labelstyle, localizevariables, paneled, rotatelabel, savedefinitions, synchronousinitialization, synchronousupdating, trackedsymbols, undotrackedvariables, text, cms, apa, bibtex, biblatex,

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Text of the page (random words):
m language code manipulate u u 0 1 controllerpath builtin controlplacement 2 specify the location of the controls wolfram language code column table manipulate u u 0 1 controlplacement p p left right bottom top controlplacement also affects annotations whether or not they contain control objects wolfram language code manipulate u v w row control u true false control v true false control w true false spacer 20 controlplacement bottom controltype 11 by default manipulate chooses a manipulator to control the specified variable wolfram language code manipulate u u 0 1 use controltype to specify the type of control to use including none wolfram language code manipulate u u 0 1 controltype none slider and verticalslider wolfram language code manipulate u u 0 1 controltype slider wolfram language code manipulate u u 0 1 imagesize small controltype verticalslider controlplacement left slider2d and locator wolfram language code manipulate u u 0 0 1 1 controltype slider2d controlplacement left wolfram language code manipulate graphics plotrange 1 imagesize tiny u 1 1 1 1 controltype locator radiobutton setter checkbox and popupmenu wolfram language code table manipulate u u 0 1 controltype c c radiobutton setter checkbox popupmenu colorsetter and colorslider wolfram language code table manipulate u u blue controltype c c colorsetter colorslider inputfield wolfram language code manipulate u u xxx controltype inputfield specify the control type for each manipulate variable separately wolfram language code manipulate u v w u 0 1 slider v red colorslider w xxx inputfield controltype can be combined with individual variable control specifications wolfram language code manipulate u v w u 0 1 v 0 1 checkbox w 0 1 controltype setter controltype affects controls specified by control in the same way wolfram language code manipulate u v w row control u 0 1 control v 0 1 checkbox control w 0 1 spacer 20 controltype setter in the automatic setting an appropriate controller is selected wolfram language code manipulate t u v w x y z t u 0 1 v 0 0 1 1 w red x false true y range 5 z range 10 controltype automatic deinitialization 1 use deinitialization to evaluate expressions when manipulate is no longer displayed wolfram language code with nb createwindow createdialog manipulate setoptions nb background c windowopacity o column c o c green o 0 5 0 1 deinitialization setoptions nb background inherited windowopacity inherited deployed 2 by default both the content and the controls are interactive wolfram language code manipulate graphics disk u 0 plotrange 5 u 4 4 manipulate graphics3d cuboid u 0 0 plotrange 5 u 4 4 use deployed to restrict interactivity to the controls wolfram language code manipulate graphics disk u 0 plotrange 5 u 4 4 deployed true manipulate graphics3d cuboid u 0 0 plotrange 5 u 4 4 deployed true excludedcontexts 1 by default certain system internal contexts are not saved in the initialization option wolfram language code x timezone cases manipulate x savedefinitions true toboxes holdpattern initialization _ 1 use excludedcontexts to save definitions of all non protected symbols wolfram language code cases manipulate x savedefinitions true excludedcontexts toboxes holdpattern initialization _ 1 framelabel 3 specify a label at the bottom wolfram language code manipulate u u 0 1 framelabel xxx specify different labels at the bottom and on the left wolfram language code manipulate u u 0 1 framelabel xxx yyy specify labels on each side wolfram language code manipulate u u 0 1 framelabel xxx yyy zzz www framemargins 2 use preset values for the margins around the content area wolfram language code table manipulate framed u u 0 1 framemargins f f tiny small medium large or use explicit values wolfram language code table manipulate framed u u 0 1 framemargins m m 5 15 imagemargins 2 use symbolic values wolfram language code table framed manipulate u u 0 1 imagemargins f framemargins 0 f tiny small medium large or use explicit values wolfram language code framed manipulate u u 0 1 imagemargins 30 framemargins 0 includedcontexts 1 limit recursive inclusion of symbol definitions to the contexts c1 and c2 only wolfram language code c1 x c1 private bar c2 baz c1 private bar 1 c2 baz 3 wolfram language code cases manipulate c1 x includedcontexts c1 c2 savedefinitions true toboxes holdpattern initialization _ 1 initialization 1 use initialization to specify evaluations necessary for the manipulate output wolfram language code manipulate f x x 0 6 initialization f z_ range z labelstyle 3 specify stylistic details for labels wolfram language code table manipulate u u 0 1 labelstyle c c red bold large use compound styles wolfram language code manipulate u u 0 1 labelstyle directive blue italic medium frame labels are affected by labelstyle wolfram language code manipulate u u 0 1 framelabel style xxx large labelstyle red localizevariables 2 by default the variables are localized wolfram language code manipulate u u 0 1 dynamic u by setting localizevariables the variables are treated as global wolfram language code manipulate x x 0 1 localizevariables false dynamic x paneled 1 specify whether the output should be wrapped in a panel wolfram language code table manipulate u u 0 1 paneled t t true false rotatelabel 1 specify whether frame labels should be rotated in the vertical position wolfram language code table manipulate u u 0 1 framelabel xxxxx yyyyy rotatelabel t t true false savedefinitions 2 by default external definitions are lost between kernel sessions wolfram language code f x_ x wolfram language code manipulate f u u 0 1 by setting savedefinitions to true the external definitions are saved with the output wolfram language code f x_ x wolfram language code manipulate f u u 0 1 savedefinitions true synchronousinitialization 2 by default the initializations are done synchronously wolfram language code manipulate pause 1 f x x 0 1 initialization f x_ sin x force asynchronous initialization wolfram language code manipulate pause 1 f x x 0 1 initialization f x_ sin x synchronousinitialization false synchronousupdating 2 by default the evaluation will time out after five seconds wolfram language code manipulate pause 6 x x 0 1 synchronousupdating is disabled the evaluation will not time out wolfram language code manipulate pause 6 x x 0 1 synchronousupdating false trackedsymbols 1 specify symbols that will be used for updating wolfram language code manipulate u v u 0 1 v 1 2 trackedsymbols u undotrackedvariables 1 specify local variables which when changed respond to the undo menu command wolfram language code manipulate u v u 0 1 v 1 2 undotrackedvariables u applications 3 define an operations table wolfram language code optable o_ n_ tableform table o n1 n2 n1 1 n n2 1 n tableheadings range n range n manipulate the operations tables for wolfram language code manipulate optable o n n 1 10 o plus times subtract divide savedefinitions true a general linear transformation of a graphics object wolfram language code manipulate graphics geometrictransformation first arrayplot cellularautomaton 30 1 0 20 a b c d plotlabel numberform matrixform a b c d 2 a 1 2 2 b 0 2 2 c 0 2 2 d 1 2 2 solve a boundary value problem by interactively manipulating the initial values wolfram language code manipulate plot evaluate y t first ndsolve y x x y x y 0 a y 0 b y x 0 4 t 0 4 epilog point 4 1 2 green arrow 0 a 1 b a red point 0 a imagepadding 25 plotrange 3 a 1 traditionalform y 0 3 3 b 0 traditionalform y 0 3 3 properties relations 5 use inputform to get manipulate input wolfram language code manipulate x x x 0 1 inputform on the actual object also reflects the current state wolfram language code dynamicmodule 7 inputform use setting on the output to access the displayed expression wolfram language code manipulate x 2 x 0 1 wolfram language code setting dynamicmodule 7 use dynamic to localize updates and prevent the entire expression from updating wolfram language code manipulate randomreal u u 0 1 wolfram language code manipulate randomreal dynamic u u 0 1 use appearance open to display all the manipulator controls wolfram language code manipulate u u 0 1 appearance open use intervalslider options to change the behavior of the control wolfram language code manipulate int int 0 3 0 7 0 1 controltype intervalslider method push minintervalsize 0 1 possible issues 6 when manipulating plots the plotrange may vary and cause resizing wolfram language code manipulate plot sinc x t x 0 10 t 0 2 use a fixed plotrange to prevent resizing wolfram language code manipulate plot sinc x t x 0 10 plotrange 1 1 t 0 2 when manipulating plots the tick sizes may vary and cause resizing wolfram language code manipulate plot x n sin x x 0 10 n 1 4 use either a fixed plotrange or imagepadding to prevent resizing wolfram language code manipulate plot x n sin x x 0 10 imagepadding 25 n 1 4 manipulate only notices explicit visible parameters wolfram language code f max_ plot sin a x x 0 max the parameter a is not explicitly visible in f wolfram language code manipulate f max a 1 5 max 10 20 savedefinitions true redefine f to include the parameter a explicitly wolfram language code f a_ max_ plot sin a x x 0 max wolfram language code manipulate f a max a 1 5 max 10 20 savedefinitions true manipulate can support any number of locator controls as long as the initial value of each one is a single point wolfram language code manipulate graphics polygon pt1 pt2 pt3 plotrange 1 pt1 0 0 locator pt2 1 0 locator pt3 1 1 locator if a manipulate contains a locator control whose initial value is a list of points then that manipulate can contain no other locator controls wolfram language code manipulate graphics polygon pts plotrange 2 pts 0 0 1 0 1 1 0 1 1 1 locator mixing single point locators and multi point locators in the same manipulate will generate a warning wolfram language code manipulate graphics polygon pts point pt plotrange 2 pts 0 0 1 0 1 1 0 1 1 1 locator pt 1 1 locator by default definitions attached to system symbols are not pulled in wolfram language code x subscript y 1 subscript y 1 17 cases manipulate x savedefinitions true toboxes holdpattern initialization _ 1 use excludedcontexts to pull in definitions from all contexts wolfram language code cases manipulate x excludedcontexts savedefinitions true toboxes holdpattern initialization _ 1 alternatively attach definitions to your own symbols wolfram language code clear subscript y subscript y 1 17 cases manipulate x savedefinitions true toboxes holdpattern initialization _ 1 evaluations producing side effects such as messages sometimes print to the messages notebook wolfram language code createdocument documentnotebook manipulate print val val val true false deployed true neat examples 4 manipulate the electrostatic potential built from point charges wolfram language code manipulate contourplot q1 norm x y p 1 q2 norm x y p 2 x 2 2 y 2 2 contours 10 q1 1 3 3 q2 1 3 3 p 1 0 1 0 1 1 1 1 locator deployed true create a simple polyhedron property explorer wolfram language code manipulate column polyhedrondata g polyhedrondata g p g polyhedrondata all p complement polyhedrondata properties classes visualize solutions to a linear system of differential equations wolfram language code a 1 1 0 9 1 4 0 3 wolfram language code manipulate parametricplot evaluate matrixexp a t pt t 0 10 plotrange 5 pt 2 0 0 1 3 0 locator savedefinitions true create a variable number of controls wolfram language code manipulate arrayplot take data h w data randominteger 0 1 10 20 controltype none h 5 1 10 1 w 5 1 20 1 dynamic panel grid outer checkbox dynamic data 1 2 0 1 range h range w see also controllermanipulate control animate table manipulator dynamic deploy controlactive controlsrendering formobject formfunction formcontrol function repository manipulateplot tech notes introduction to manipulate introduction to dynamic advanced manipulate functionality advanced dynamic functionality introduction to control objects related guides interactive manipulation dynamic visualization custom interface construction graphics interactivity drawing click interactive panels dynamic graphics elements gamepad device interface control objects video computation update history tabular communication setting up user interactions gauges video creation standalone interfaces creating web pages generalized input options styling for interactive manipulation creating importing images creating form interfaces apps creating instant apis tabular processing overview related workflows related workflows build a manipulate use the manipulate interface create interactive content for the web control interactive content with a gamepad avoid dynamic content warnings related links fast introduction for programmers interactive interfaces an elementary introduction to the wolfram language interactive manipulation an elementary introduction to the wolfram language creating websites and apps wolfram demonstrations project history introduced in 2007 6 0 updated in 2008 7 0 2012 9 0 2014 10 0 2019 12 0 2020 12 1 2021 12 3 2024 14 1 cite this as wolfram research 2007 manipulate wolfram language function https reference wolfram com language ref manipulate html updated 2024 text wolfram research 2007 manipulate wolfram language function https reference wolfram com language ref manipulate html updated 2024 cms wolfram language 2007 manipulate wolfram language system documentation center wolfram research last modified 2024 https reference wolfram com language ref manipulate html apa wolfram language 2007 manipulate wolfram language system documentation center retrieved from https reference wolfram com language ref manipulate html bibtex misc reference wolfram_2026_manipulate author wolfram research title manipulate year 2024 howpublished url https reference wolfram com language ref manipulate html note accessed 02 october 2026 biblatex online reference wolfram_2026_manipulate organization wolfram research title manipulate year 2024 url https reference wolfram com language ref manipulate html note accessed 02 october 2026 give feedback top introduction for programmers introductory book wolfram function repository wolfram data repository wolfram data drop wolfram language products top products wolfram one mathematica ai access compute services system modeler wolfram alpha notebook edition wolfram alpha pro mobile apps wolfram engine wolfram player volume site licensing server deployment options consulting wolfram consulting repositories data repository function repository community paclet repository neural net repository prompt repository wolfram language example repository notebook archive wolfram github learning wolfram u wolfram language documentation webinars training educational programs wolfram language introduction fast introduction for programmers fast introduction for math students books wolfram community wolfram blog public resources wolfram alpha 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