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Dynamic
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Dynamic

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Dynamic[expr]

represents an object that displays as the dynamically updated current value of expr. If the displayed form of Dynamic[expr] is interactively changed or edited, an assignment expr=val is done to give expr the new value val that corresponds to the displayed form.

✖
Dynamic[expr,None]

does not allow interactive changing or editing.

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Dynamic[expr,f]

continually evaluates f[val,expr] during interactive changing or editing of val.

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Dynamic[expr,{f,fend}]

also evaluates fend[val,expr] when interactive changing or editing is complete.

✖
Dynamic[expr,{fstart,f,fend}]

also evaluates fstart[val,expr] when interactive changing or editing begins.

Details and Options

  • Dynamic[expr] can appear not only directly as an expression to display, but also for example as a coordinate in a graphics primitive or an object such as a slider, or as a setting for an option.
  • When used to assign values to expr through interactive operations, the expression in Dynamic[expr] will most often be a symbol x, an object x[i], a part e[[i]], or a list {x,y,…}.
  • In graphics, for example, Point[Dynamic[{x,y}]] represents a point whose position is dynamically updated to be given by the current values of x and y. Whenever the point is interactively moved, assignments of the form {x,y}={valx,valy} are done. Point[Dynamic[{x,y}]] can be moved interactively; Dynamic[Point[{x,y}]] cannot.
  • Dynamic[expr] evaluates expr whenever it needs its value and it determines that any type of value of symbols on which it depends might have changed.
  • If Refresh or Clock objects appear in the evaluation of the expression in Dynamic[expr], then expr will always continually be reevaluated.
  • Dynamic has attribute HoldFirst, so that expr is not evaluated until its value is needed for display.
  • Dynamic[expr] is equivalent to Dynamic[expr,(expr=#)&].
  • Dynamic[expr,f] makes interactive operations not change expr except by virtue of the evaluation of f[val,expr].
  • Objects represented by Dynamic[expr,None] cannot be changed interactively, but will change if the value of expr changes for other reasons.
  • Dynamic[expr,Temporary] allows the displayed form of an object to change in the course of interactive operations, but assigns an updated value to expr only when the operations are complete.
  • For interactive mouse operations, Dynamic[expr,{fstart,f,fend}] typically evaluates fstart[val,expr] once when the mouse is pressed, then evaluates f[val,expr] whenever the mouse is moved, and then evaluates fend[val,expr] once when the mouse is released.
  • If the mouse is not moved, fstart, f, and fend are each evaluated exactly once.
  • f[val,expr] is always evaluated once immediately after the evaluation of fstart[val,expr], and when it is last evaluated, the value of val is always the same as in fend[val,expr].
  • Interactive operations that can affect Dynamic objects include dragging of elements in graphics or in objects such as Slider, as well as editing of fields in objects such as InputField.
  • The functions fstart, f, and fend can be the following:
  • Automaticassign values using Set
    Noneperform no action
    Temporaryallow interactive operations to make temporary changes
    funcevaluate func[val,expr]
  • Dynamic[expr,f] is equivalent to Dynamic[expr,{None,f,None}].
  • Dynamic[expr,Temporary] is equivalent to Dynamic[expr,{None,Temporary,Automatic}].
  • Dynamic[expr,f] can be used to enforce constraints on values assigned to expr.
  • Dynamic[expr,f] can be used to do assignments for individual variables when expr is an expression like x+y.
  • A function func[val,expr] should have attribute HoldRest if it is going to perform an assignment to expr. This can be achieved with Function[{v,e},body,HoldRest].
  • The following options can be given:
  • BaseStyle {}base style specifications for the displayed object
    Deinitialization Nonean expression to evaluate when the Dynamic can no longer be displayed
    Evaluator Automaticthe kernel to use for evaluations
    Initialization Nonean expression to evaluate when the Dynamic is first displayed
    ShrinkingDelay 0.how long to delay before shrinking if the displayed object gets smaller
    SynchronousUpdating Truewhether to evaluate contents synchronously
    TrackedSymbols Allsymbols whose changes trigger an update
    UpdateIntervalInfinitytime interval at which to do updates
  • Dynamic[e] displays as the dynamically updated current value of e in StandardForm and TraditionalForm, but just as Dynamic[e] in InputForm and OutputForm.
  • Dynamic[expr] provides an analog of delayed assignment, where values are implicitly requested by the need to display, rather than by evaluation of an expression.

Examples

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Basic Examples  (1)Summary of the most common use cases

Dynamic simply returns the current value of its argument:

In[1]:=1
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https://wolfram.com/xid/0mrdma-cp2a8f
Out[1]=1

Assign a value to to update the output above:

In[2]:=2
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https://wolfram.com/xid/0mrdma-egto16
Out[2]=2

Tie the symbol to a Slider:

In[3]:=3
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https://wolfram.com/xid/0mrdma-imk66i
Out[3]=3

Scope  (24)Survey of the scope of standard use cases

Basic Dynamic  (6)

Any expression can be wrapped with Dynamic:

In[1]:=1
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https://wolfram.com/xid/0mrdma-d0sqfe
Out[1]=1

Dynamic is not shown in StandardForm, but is still present:

In[2]:=2
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https://wolfram.com/xid/0mrdma-d6hoy4
Out[2]=2

Use Dynamic to link the currently displayed value depending on :

In[1]:=1
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https://wolfram.com/xid/0mrdma-615ryl
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mrdma-lmmzzi
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0mrdma-5f2070
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0mrdma-2q9y1g
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0mrdma-256w2p
Out[5]=5

By default, variables inside Dynamic are not localized:

In[1]:=1
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https://wolfram.com/xid/0mrdma-wns1lv
Out[1]=1

Use DynamicModule to localize variables:

In[2]:=2
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https://wolfram.com/xid/0mrdma-w3xs5m
Out[2]=2

And to initialize variables:

In[3]:=3
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https://wolfram.com/xid/0mrdma-z5uu6l
Out[3]=3

A Dynamic expression can be self-triggering:

In[1]:=1
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https://wolfram.com/xid/0mrdma-lgmr9y
Out[1]=1

Use with Slider:

In[2]:=2
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https://wolfram.com/xid/0mrdma-p3qs1d
Out[2]=2

Expressions such as RandomReal and DateString do not automatically update:

In[1]:=1
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https://wolfram.com/xid/0mrdma-qp18n1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mrdma-dajf7h
Out[2]=2

Use UpdateInterval to force dynamic updating:

In[3]:=3
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https://wolfram.com/xid/0mrdma-cce67d
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0mrdma-gl615s
Out[4]=4

Dynamic holds its argument and never evaluates it unless it displays as output:

In[1]:=1
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https://wolfram.com/xid/0mrdma-mvhwc9

Since the above Dynamic was never displayed, the assignment was never executed:

In[2]:=2
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https://wolfram.com/xid/0mrdma-bk4u5i
Out[2]=2

Placing Dynamic  (3)

Plot needs specific numerical values to create the output:

In[1]:=1
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https://wolfram.com/xid/0mrdma-hfnpry
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mrdma-izckjh
Out[2]=2

Separate Dynamic expressions update independently, allowing for efficiency:

In[1]:=1
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https://wolfram.com/xid/0mrdma-y6gyx7
In[2]:=2
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https://wolfram.com/xid/0mrdma-dckwju
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0mrdma-whv6kh
Out[3]=3

Use graphics coordinates as control input by placing Dynamic around them:

In[1]:=1
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https://wolfram.com/xid/0mrdma-ei91r7
Out[1]=1

Use the graphics coordinates as control input and see the effects on 2D sliders:

In[2]:=2
✖
https://wolfram.com/xid/0mrdma-lisf83
Out[2]=2

Interactive Dynamic  (8)

Use Dynamic to connect variables with interactive controls, such as Slider:

In[1]:=1
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https://wolfram.com/xid/0mrdma-g14irb
Out[1]=1

Slider2D:

In[1]:=1
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https://wolfram.com/xid/0mrdma-u9g39n
Out[1]=1

InputField:

In[1]:=1
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https://wolfram.com/xid/0mrdma-mlz4xm
Out[1]=1

TemplateBox[{ColorSlider, paclet:ref/ColorSlider}, RefLink, BaseStyle -> {InlineFormula}]:

In[1]:=1
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https://wolfram.com/xid/0mrdma-7j8swp
Out[1]=1

PopupMenu:

In[1]:=1
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https://wolfram.com/xid/0mrdma-wndx6k
Out[1]=1

Locator:

In[1]:=1
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https://wolfram.com/xid/0mrdma-rmk19f
Out[1]=1

Use Dynamic to control view elements, such as TabView:

In[1]:=1
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https://wolfram.com/xid/0mrdma-g5sc0r
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0mrdma-jipojg
Out[2]=2

FlipView:

In[3]:=3
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https://wolfram.com/xid/0mrdma-fzvxy
Out[3]=3

PopupView:

In[4]:=4
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https://wolfram.com/xid/0mrdma-lp81ca
Out[4]=4

OpenerView:

In[5]:=5
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https://wolfram.com/xid/0mrdma-r7tiru
Out[5]=5

Use Dynamic to set a front end option, such as ImageSize:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-b8ftef
Out[1]=1

Advanced Dynamic  (7)

By default, Dynamic performs an assignment operation when used in an interactive element:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-0f3t4u
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0mrdma-sigivm
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0mrdma-e7a0mp
Out[3]=3

Use the second argument to specify a function to be evaluated during interaction:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-bhphjr
Out[1]=1

Supply a list of two functions to be evaluated during and after interaction:

In[1]:=1
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https://wolfram.com/xid/0mrdma-21ohvi
Out[1]=1

Supply a list of three functions to be evaluated before, during, and after interaction:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-ncr2j2
Out[1]=1

Use Temporary to update the dynamic variable at the end of interaction:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-5r90se
Out[1]=1

Use None to disallow updating the dynamic variable:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-h2eg00
Out[1]=1

Dynamic also performs assignment operations for interactively settable front end options:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-ezxbrl
Out[1]=1

Options  (8)Common values & functionality for each option

BaseStyle  (1)

Set the base style:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-t2702w
Out[1]=1

Deinitialization  (1)

Specify expressions to be evaluated when output is no longer displayed:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-6uj7m5

Evaluator  (1)

Specify a Dynamic that will only run in the kernel named "Local":

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-8o5qyf
Out[1]=1

Initialization  (2)

By default, external definitions are lost between kernel sessions:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-fgp9g3
In[2]:=2
✖
https://wolfram.com/xid/0mrdma-bmdhst
Out[2]=2

Use Initialization to evaluate expressions necessary for displaying the output:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-04g9jo
Out[1]=1

ShrinkingDelay  (1)

Assign a number or graphics to :

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-p5g02x
Out[1]=1

Use ShrinkingDelay to allow lapse time before shrinking the size of the output:

In[2]:=2
✖
https://wolfram.com/xid/0mrdma-rd62w0
Out[2]=2

SynchronousUpdating  (1)

Prevent a lengthy evaluation from timing out or hanging the system:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-lli1bo
Out[1]=1

TrackedSymbols  (1)

Updates y only when x changes:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-i4ikp3
Out[1]=1

Applications  (5)Sample problems that can be solved with this function

Constrain the coordinates of a point to lie on a circle:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-l1va85
Out[1]=1

Construct a dynamic calculating interface:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-dv1
Out[1]=1

Create a timer to track lapsed minutes and seconds, with Trigger for the controls:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-hmct2
Out[1]=1

Create a simple interface that looks up the shapes of countries:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-e10gc0
Out[1]=1

Construct custom controls, e.g. an angular slider with range :

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-lnuxzl
Out[1]=1

An angular slider with range :

In[2]:=2
✖
https://wolfram.com/xid/0mrdma-sk4vsb
Out[2]=2

Properties & Relations  (4)Properties of the function, and connections to other functions

Dynamic may be used to directly display its contents:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-bzyczz
Out[1]=1

A Dynamic that simply displays has no interactivity, and the second argument does not affect it:

In[2]:=2
✖
https://wolfram.com/xid/0mrdma-blb6xg
Out[2]=2

Alternatively, Dynamic may be fed as a value to an interactive control, object or option:

In[3]:=3
✖
https://wolfram.com/xid/0mrdma-rp89i
Out[3]=3

A value-style Dynamic invokes its second argument when the value is interactively changed:

In[4]:=4
✖
https://wolfram.com/xid/0mrdma-ny8sx
Out[4]=4

Dynamic expressions do not evaluate their contents until the result is displayed onscreen:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-3vzgrq

Even showing the result is not a guarantee that it will resolve immediately:

In[2]:=2
✖
https://wolfram.com/xid/0mrdma-sdzijg
Out[2]=2

Use FinishDynamic when timing is important:

In[3]:=3
✖
https://wolfram.com/xid/0mrdma-rrrcgn
Out[3]=3

Synchronous dynamics are time-limited according to the value of DynamicEvaluationTimeout:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-xzyiyv
Out[1]=1

An evaluation can detect if it's being dynamically evaluated by using $DynamicEvaluation:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-se52fy
Out[1]=1

Possible Issues  (4)Common pitfalls and unexpected behavior

The following example does not work because the assignment operation fails:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-7a20bz
Out[1]=1

Use the second argument of Dynamic to control the assignment operation:

In[2]:=2
✖
https://wolfram.com/xid/0mrdma-yeu4ug
Out[2]=2

Self-triggering Dynamic can easily cause infinite loops (delete the output to stop it):

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-ufr6lq

By default, view elements generate the entire contents before displaying:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-d5ja6f
Out[1]=1

Use Dynamic and ImageSize->Automatic to generate the contents only when displayed:

In[2]:=2
✖
https://wolfram.com/xid/0mrdma-rqjwor
Out[2]=2

Module variables are not initialized, and returning a Module variable leaks the symbol name:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-dnsaz2
Out[1]=1

Generally, variables should be initialized and localized using DynamicModule instead:

In[2]:=2
✖
https://wolfram.com/xid/0mrdma-jhc5lc
Out[2]=2

It is also acceptable to wrap Dynamic entirely around a Module:

In[3]:=3
✖
https://wolfram.com/xid/0mrdma-hwl4m9
Out[3]=3

Neat Examples  (6)Surprising or curious use cases

Coupled Slider:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-nj1dzk
Out[1]=1

Coupled Slider2D:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-iuthrj
Out[1]=1

A "droopy" Slider:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-va58uu
Out[1]=1

Center a disk at the mouse position as it moves over the graphics area:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-p48mbv
Out[1]=1

Remember the last mouse position as it leaves the graphics area:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-hy5sqh
Out[1]=1

Click inside the framed area to see bouncing balls:

In[1]:=1
✖
https://wolfram.com/xid/0mrdma-89yysa
Out[1]=1
Wolfram Research (2007), Dynamic, Wolfram Language function, https://reference.wolfram.com/language/ref/Dynamic.html.
✖
Wolfram Research (2007), Dynamic, Wolfram Language function, https://reference.wolfram.com/language/ref/Dynamic.html.

Text

Wolfram Research (2007), Dynamic, Wolfram Language function, https://reference.wolfram.com/language/ref/Dynamic.html.

✖
Wolfram Research (2007), Dynamic, Wolfram Language function, https://reference.wolfram.com/language/ref/Dynamic.html.

CMS

Wolfram Language. 2007. "Dynamic." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Dynamic.html.

✖
Wolfram Language. 2007. "Dynamic." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Dynamic.html.

APA

Wolfram Language. (2007). Dynamic. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Dynamic.html

✖
Wolfram Language. (2007). Dynamic. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Dynamic.html

BibTeX

@misc{reference.wolfram_2025_dynamic, author="Wolfram Research", title="{Dynamic}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/Dynamic.html}", note=[Accessed: 22-June-2025 ]}

✖
@misc{reference.wolfram_2025_dynamic, author="Wolfram Research", title="{Dynamic}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/Dynamic.html}", note=[Accessed: 22-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_dynamic, organization={Wolfram Research}, title={Dynamic}, year={2007}, url={https://reference.wolfram.com/language/ref/Dynamic.html}, note=[Accessed: 22-June-2025 ]}

✖
@online{reference.wolfram_2025_dynamic, organization={Wolfram Research}, title={Dynamic}, year={2007}, url={https://reference.wolfram.com/language/ref/Dynamic.html}, note=[Accessed: 22-June-2025 ]}