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Wolfram Language & System Documentation Center
DiscretePlot3D
  • See Also
    • ListPointPlot3D
    • ListPlot3D
    • ListDensityPlot
    • ListContourPlot
    • Plot3D
    • ArrayPlot
    • MatrixPlot
    • Table
  • Related Guides
    • Function Visualization
    • Discrete Calculus
    • Statistical Visualization
    • See Also
      • ListPointPlot3D
      • ListPlot3D
      • ListDensityPlot
      • ListContourPlot
      • Plot3D
      • ArrayPlot
      • MatrixPlot
      • Table
    • Related Guides
      • Function Visualization
      • Discrete Calculus
      • Statistical Visualization

DiscretePlot3D[f,{i,imin,imax},{j,jmin,jmax}]

generates a plot of f when i runs from imin to imax and j runs from jmin to jmax.

DiscretePlot3D[f,{i,imin,imax,di},{j,jmin,jmax,dj}]

uses steps di and dj.

DiscretePlot3D[f,{i,{i1,…,im}},{j,{j1,…,jn}}]

uses successive i values i1, …, jm and j values j1, …, jn.

DiscretePlot3D[{f1,f2,…},…,…]

plots the values of all the fk.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data and Layouts  
Labeling and Legending  
Styling and Appearance  
Options  
Axes  
AxesLabel  
AxesOrigin  
Show More Show More
AxesStyle  
ColorFunction  
ColorFunctionScaling  
EvaluationMonitor  
ExtentElementFunction  
ExtentMarkers  
ExtentSize  
Filling  
FillingStyle  
ImageSize  
Joined  
LabelingFunction  
LabelingSize  
PlotLegends  
PlotMarkers  
PlotStyle  
PlotTheme  
RegionFunction  
ScalingFunctions  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • ListPointPlot3D
    • ListPlot3D
    • ListDensityPlot
    • ListContourPlot
    • Plot3D
    • ArrayPlot
    • MatrixPlot
    • Table
  • Related Guides
    • Function Visualization
    • Discrete Calculus
    • Statistical Visualization
    • See Also
      • ListPointPlot3D
      • ListPlot3D
      • ListDensityPlot
      • ListContourPlot
      • Plot3D
      • ArrayPlot
      • MatrixPlot
      • Table
    • Related Guides
      • Function Visualization
      • Discrete Calculus
      • Statistical Visualization

DiscretePlot3D

DiscretePlot3D[f,{i,imin,imax},{j,jmin,jmax}]

generates a plot of f when i runs from imin to imax and j runs from jmin to jmax.

DiscretePlot3D[f,{i,imin,imax,di},{j,jmin,jmax,dj}]

uses steps di and dj.

DiscretePlot3D[f,{i,{i1,…,im}},{j,{j1,…,jn}}]

uses successive i values i1, …, jm and j values j1, …, jn.

DiscretePlot3D[{f1,f2,…},…,…]

plots the values of all the fk.

Details and Options

  • DiscretePlot3D is typically used to visualize bivariate sequences.
  • DiscretePlot3D plots the variable i along the axis and j along the axis.
  • DiscretePlot3D uses the standard Wolfram Language iterator specification.
  • DiscretePlot3D treats the variables i and j as local, effectively using Block.
  • DiscretePlot3D has attribute HoldAll, and evaluates f only after assigning specific numerical values to i and j.
  • In some cases, it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to i and j.
  • The precision used in evaluating f is the minimum precision used in the iterators.
  • The form w[f] provides a wrapper w to be applied to the resulting graphics primitives.
  • The following wrappers can be used:
  • Annotation[f,label]provide an annotation
    Button[f,action]define an action to execute when the element is clicked
    Callout[f,label]label the element with a callout
    Callout[f,label,pos]place the callout at relative position pos
    EventHandler[f,…]define a general event handler for the element
    Hyperlink[f,uri]make the element act as a hyperlink
    Labeled[f,label]make the data a hyperlink
    Labeled[f,label,pos]place the label at relative position pos
    Legended[f,label]identify the element in a legend
    PopupWindow[f,cont]attach a popup window to the element
    StatusArea[f,label]display in the status area when the element is moused over
    Style[f,opts]show the element using the specified styles
    Tooltip[f,label]attach an arbitrary tooltip to the element
  • Callout and Labeled can use the following positions pos:
  • Automaticautomatically placed labels
    Above, Below, Before, Afterpositions around the data
    xnear the data at a position x
    {s,Above},{s,Below},…relative position at position s along the data
    {pos,epos}epos in label placed at relative position pos of the data
  • Labels that depend on {i,j} will be applied for each plot element, while labels that are independent of {i,j} will only occur once.
  • DiscretePlot3D has the same options as Graphics3D, with the following additions and changes: [List of all options]
  • Axes Truewhether to draw axes
    BoxRatios{1,1,0.4}bounding 3D box ratios
    ClippingStyleAutomatichow to draw clipped parts of surfaces
    ColorFunction Automatichow to determine the color of surfaces
    ColorFunctionScaling Truewhether to scale arguments to ColorFunction
    EvaluationMonitor Noneexpression to evaluate at every function evaluation
    ExtentElementFunction Automatichow to generate raw graphics for extent fills
    ExtentMarkers Nonemarkers to use for extent boundaries
    ExtentSize Automaticwidth and depth to extend from plot point
    Filling Automaticfilling under each surface
    FillingStyle Opacity[0.5]style to use for filling
    Joined Falsewhether to join
    LabelingFunction Automatichow to label points
    LabelingSize Automaticmaximum size of callouts and labels
    MethodAutomaticthe methods to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotLegends Nonelegends for sequences
    PlotMarkers Nonemarkers to use for plot points
    PlotRange{Full,Full,Automatic}the range of or other values to include
    PlotStyle Automaticgraphics directives for the style for each surface
    PlotTheme $PlotThemeoverall theme for the plot
    RegionFunction (True&)how to determine whether a point should be included
    ScalingFunctions Nonehow to scale individual coordinates
    WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • The arguments supplied to ColorFunction are , , .
  • With the setting ExtentSize->{{sxl,sxr},{syl,syr}} a horizontal plane is drawn around each plot point extending sxl to the left and sxr to the right along the axis and syl to the left and syr to the right along the axis. With ExtentMarkers->{{mxl,mxr},{myl,myr}}, the markers mxl and mxr will be used as left and right markers along the axis and myl and myr as left and right markers along the axis.
  • The arguments supplied to ExtentElementFunction are the element region {{xmin,xmax},{ymin,ymax},{zmin,zmax}} and the sample point {xi,yi,zi}.
  • With the setting ExtentSize->None, xmin is equal to xmax and ymin is equal to ymax. With the setting Filling->None, zmin is equal to zmax.
  • Possible settings for PlotMarkers include:
  • Noneomit markers when drawing surfaces
    "Point"use 2D points as markers
    "Sphere"use 3D spheres as markers
    {"Point",s},{"Sphere",s}specify the size s of the markers
    {spec1,spec2,…}use specification speci for expression expri
  • The marker size s can be a symbolic value such as Tiny, Small, Medium and Large or a scaled fraction of the width of the graphic.
  • Possible settings for ScalingFunctions include:
  • szscale the z axis
    {sx,sy}scale x and y axes
    {sx,sy,sz}scale x, y and z axes
  • Each scaling function si is either a string "scale" or {g,g-1}, where g-1 is the inverse of g.
  • List of all options

    • AlignmentPointCenterthe default point in the graphic to align with
      AspectRatioAutomaticratio of height to width
      AxesTruewhether to draw axes
      AxesEdgeAutomaticon which edges to put axes
      AxesLabelNoneaxes labels
      AxesOriginAutomaticwhere axes should cross
      AxesStyle{}graphics directives to specify the style for axes
      BackgroundNonebackground color for the plot
      BaselinePositionAutomatichow to align with a surrounding text baseline
      BaseStyle{}base style specifications for the graphic
      BoxedTruewhether to draw the bounding box
      BoxRatios{1,1,0.4}bounding 3D box ratios
      BoxStyle{}style specifications for the box
      ClippingStyleAutomatichow to draw clipped parts of surfaces
      ClipPlanesNoneclipping planes
      ClipPlanesStyleAutomaticstyle specifications for clipping planes
      ColorFunctionAutomatichow to determine the color of surfaces
      ColorFunctionScalingTruewhether to scale arguments to ColorFunction
      ContentSelectableAutomaticwhether to allow contents to be selected
      ControllerLinkingFalsewhen to link to external rotation controllers
      ControllerPathAutomaticwhat external controllers to try to use
      Epilog{}2D graphics primitives to be rendered after the main plot
      EvaluationMonitorNoneexpression to evaluate at every function evaluation
      ExtentElementFunctionAutomatichow to generate raw graphics for extent fills
      ExtentMarkersNonemarkers to use for extent boundaries
      ExtentSizeAutomaticwidth and depth to extend from plot point
      FaceGridsNonegrid lines to draw on the bounding box
      FaceGridsStyle{}style specifications for face grids
      FillingAutomaticfilling under each surface
      FillingStyleOpacity[0.5]style to use for filling
      FormatTypeTraditionalFormdefault format type for text
      ImageMargins0.the margins to leave around the graphic
      ImagePaddingAllwhat extra padding to allow for labels, etc.
      ImageSizeAutomaticabsolute size at which to render the graphic
      JoinedFalsewhether to join
      LabelingFunctionAutomatichow to label points
      LabelingSizeAutomaticmaximum size of callouts and labels
      LabelStyle{}style specifications for labels
      LightingAutomaticsimulated light sources to use
      MethodAutomaticthe methods to use
      PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
      PlotLabelNonea label for the plot
      PlotLegendsNonelegends for sequences
      PlotMarkersNonemarkers to use for plot points
      PlotRange{Full,Full,Automatic}the range of or other values to include
      PlotRangePaddingAutomatichow much to pad the range of values
      PlotRegionAutomaticfinal display region to be filled
      PlotStyleAutomaticgraphics directives for the style for each surface
      PlotTheme$PlotThemeoverall theme for the plot
      PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
      Prolog{}2D graphics primitives to be rendered before the main plot
      RegionFunction(True&)how to determine whether a point should be included
      RotationAction"Fit"how to render after interactive rotation
      ScalingFunctionsNonehow to scale individual coordinates
      SphericalRegionAutomaticwhether to make the circumscribing sphere fit in the final display area
      TicksAutomaticspecification for ticks
      TicksStyle{}style specification for ticks
      TouchscreenAutoZoomFalsewhether to zoom to fullscreen when activated on a touchscreen
      ViewAngleAutomaticangle of the field of view
      ViewCenterAutomaticpoint to display at the center
      ViewMatrixAutomaticexplicit transformation matrix
      ViewPoint{1.3,-2.4,2.}viewing position
      ViewProjectionAutomaticprojection method for rendering objects distant from the viewer
      ViewRangeAllrange of viewing distances to include
      ViewVectorAutomaticposition and direction of a simulated camera
      ViewVertical{0,0,1}direction to make vertical
      WorkingPrecisionMachinePrecisionthe precision used in internal computations

Examples

open all close all

Basic Examples  (3)

Plot a bivariate sequence:

Associate a region with the points:

Plot several sequences:

Scope  (12)

Data and Layouts  (4)

Plot multiple datasets:

Use wrappers on individual data, datasets, or collections of datasets:

Wrappers can be nested:

Override the default tooltips:

Use PopupWindow to provide additional drilldown information:

Button can be used to trigger any action:

Use ScalingFunctions to scale the axes:

Labeling and Legending  (3)

Label individual points:

Use tooltips instead:

Specify label names with LabelingFunction:

Styling and Appearance  (5)

Use ExtentSize to associate a region with a point:

Use an explicit list of styles for the plots:

Use any gradient color schemes from ColorData:

Style can be used to override styles:

Show plot markers:

Show extent region boundaries:

Use a theme with dark background in a high-contrast color scheme:

Options  (90)

Axes  (3)

By default, Axes are drawn for DiscretePlot3D:

Use AxesFalse to turn off axes:

Turn each axis on individually:

AxesLabel  (4)

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

Use labels based on variables specified in DiscretePlot3D:

AxesOrigin  (2)

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

AxesStyle  (4)

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

ColorFunction  (6)

Color the points by scaled , , or value:

Color the surface by scaled , , or value:

Color the regions by scaled , , or value:

Use a named color gradient:

ColorFunction has higher priority than PlotStyle:

Use black when two numbers are relatively prime:

ColorFunctionScaling  (1)

Color by absolute height:

EvaluationMonitor  (1)

Gather the plotted heights:

Show the plot and a histogram of the heights:

ExtentElementFunction  (5)

Get a list of built-in settings for ExtentElementFunction:

For detailed settings, use Palettes ▶ Chart Element Schemes:

This ChartElementFunction is appropriate to show the global scale:

Write a custom ExtentElementFunction:

A built-in element function may have options; use Palettes ▶ Chart Element Schemes to set them:

ExtentMarkers  (4)

Do not show the extent edges:

Use lines to show the extent edges:

Use varying sized tubes to show the extent edges:

Place tubes along the front and left edges of the extent region:

ExtentSize  (6)

Show heights as points:

Draw full regions around the heights:

With unevenly spaced points:

Use fixed-size regions:

With unevenly spaced points:

Use sizes relative to the distance between points:

With unevenly spaced points:

Use equally sized regions that do not overlap:

With unevenly spaced points:

Control the placement of the region around the points:

Filling  (3)

DiscretePlot3D fills to :

Turn off filling:

Fill to different levels:

FillingStyle  (3)

Fill to the bottom with a variety of styles:

With expanded point regions:

Use different colors above and below the filling level:

Only fill below the filling level:

ImageSize  (7)

Use named sizes such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull to fill the available space in an object:

Specify the image size as a fraction of the available space:

Joined  (2)

Join the points into a surface:

Combine a surface with extent regions:

LabelingFunction  (4)

Put the labels above the points:

Put them in a tooltip:

Use callouts to label the points:

Label the points with their values:

Label the points with their indices:

LabelingSize  (1)

Specify a maximum size for textual labels:

Use the full label:

PlotLegends  (6)

Use automatic legends:

Specify a list of labels for legends:

Use named legends:

PlotLegends automatically picks up PlotStyle values:

Use Placed to control legend placement:

Use SwatchLegend to change legend appearance:

PlotMarkers  (4)

Change the size of the default plot markers:

Markers are not usually shown when surfaces are used:

Use points with surfaces:

Use spheres for markers:

Vary the size of the spheres:

PlotStyle  (7)

Use different style directives:

By default, different styles are chosen for multiple functions:

Explicitly specify the style for different functions:

PlotStyle applies to points, lines, and surfaces:

PlotStyle can be combined with ColorFunction:

PlotStyle can be combined with FillingStyle:

FillingStyle by default uses the same style as PlotStyle with transparency:

PlotTheme  (4)

Use a theme with simple ticks and grid lines:

Change the color scheme:

Use a theme with dark background in a high-contrast color scheme:

Turn off the ticks:

RegionFunction  (4)

Restrict the region plotted:

Extended regions are treated as the underlying point without additional clipping:

Regions can have several unconnected components:

Define regions using logical combinations of constraints:

ScalingFunctions  (9)

By default, plots have linear scales in each direction:

Use a log scale in the direction:

Use a linear scale in the direction that shows smaller numbers at the front:

Use a reciprocal scale in the direction:

Use different scales in the and directions:

Reverse the axis without changing the axis:

Use a scale defined by a function and its inverse:

Positions in Ticks and FaceGrids are automatically scaled:

PlotRange is automatically scaled:

Applications  (2)

Visualize properties of discrete distributions, such as probability density function:

Cumulative distribution function:

Survival function:

Approximate the volume under a surface using Riemann sums:

Properties & Relations  (4)

Plot3D generates continuous surfaces:

Use ListPointPlot3D to plot lists of values:

Use BarChart3D to show bars for lists of values:

Use DiscretePlot to plot functions of single discrete variables:

See Also

ListPointPlot3D  ListPlot3D  ListDensityPlot  ListContourPlot  Plot3D  ArrayPlot  MatrixPlot  Table

Related Guides

    ▪
  • Function Visualization
  • ▪
  • Discrete Calculus
  • ▪
  • Statistical Visualization

History

Introduced in 2010 (8.0) | Updated in 2012 (9.0) ▪ 2014 (10.0) ▪ 2019 (12.0)

Wolfram Research (2010), DiscretePlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscretePlot3D.html (updated 2019).

Text

Wolfram Research (2010), DiscretePlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscretePlot3D.html (updated 2019).

CMS

Wolfram Language. 2010. "DiscretePlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/DiscretePlot3D.html.

APA

Wolfram Language. (2010). DiscretePlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscretePlot3D.html

BibTeX

@misc{reference.wolfram_2025_discreteplot3d, author="Wolfram Research", title="{DiscretePlot3D}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/DiscretePlot3D.html}", note=[Accessed: 01-May-2026]}

BibLaTeX

@online{reference.wolfram_2025_discreteplot3d, organization={Wolfram Research}, title={DiscretePlot3D}, year={2019}, url={https://reference.wolfram.com/language/ref/DiscretePlot3D.html}, note=[Accessed: 01-May-2026]}

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