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Wolfram Language & System Documentation Center
DiscretePlot
  • See Also
    • ListPlot
    • ListLinePlot
    • ListLogPlot
    • DateListPlot
    • ListStepPlot
    • Plot
    • Table
  • Related Guides
    • Function Visualization
    • Discrete Calculus
    • Data Visualization
    • Nonparametric Statistical Distributions
    • Statistical Visualization
    • See Also
      • ListPlot
      • ListLinePlot
      • ListLogPlot
      • DateListPlot
      • ListStepPlot
      • Plot
      • Table
    • Related Guides
      • Function Visualization
      • Discrete Calculus
      • Data Visualization
      • Nonparametric Statistical Distributions
      • Statistical Visualization

DiscretePlot[f,{n,nmax}]

generates a plot of f as a function of n when n=1,…,nmax.

DiscretePlot[f,{n,nmin,nmax}]

generates a plot when n runs from nmin to nmax.

DiscretePlot[f,{n,nmin,nmax,dn}]

uses steps dn.

DiscretePlot[f,{n,{n1,…,nm}}]

uses the successive values n1, …, nm.

DiscretePlot[{f1,f2,…},…]

plots the values of all the fi.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data and Wrappers  
Labeling and Legending  
Styling and Appearance  
Options  
AspectRatio  
ColorFunction  
ColorFunctionScaling  
Show More Show More
EvaluationMonitor  
ExtentElementFunction  
ExtentMarkers  
ExtentSize  
Filling  
FillingStyle  
Joined  
LabelingFunction  
LabelingSize  
PlotLabels  
PlotLegends  
PlotMarkers  
PlotStyle  
PlotTheme  
RegionFunction  
ScalingFunctions  
WorkingPrecision  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • ListPlot
    • ListLinePlot
    • ListLogPlot
    • DateListPlot
    • ListStepPlot
    • Plot
    • Table
  • Related Guides
    • Function Visualization
    • Discrete Calculus
    • Data Visualization
    • Nonparametric Statistical Distributions
    • Statistical Visualization
    • See Also
      • ListPlot
      • ListLinePlot
      • ListLogPlot
      • DateListPlot
      • ListStepPlot
      • Plot
      • Table
    • Related Guides
      • Function Visualization
      • Discrete Calculus
      • Data Visualization
      • Nonparametric Statistical Distributions
      • Statistical Visualization

DiscretePlot

DiscretePlot[f,{n,nmax}]

generates a plot of f as a function of n when n=1,…,nmax.

DiscretePlot[f,{n,nmin,nmax}]

generates a plot when n runs from nmin to nmax.

DiscretePlot[f,{n,nmin,nmax,dn}]

uses steps dn.

DiscretePlot[f,{n,{n1,…,nm}}]

uses the successive values n1, …, nm.

DiscretePlot[{f1,f2,…},…]

plots the values of all the fi.

Details and Options

  • DiscretePlot is typically used to visualize sequences.
  • DiscretePlot uses the standard Wolfram Language iterator specification.
  • DiscretePlot treats the variable n as local, effectively using Block.
  • DiscretePlot has attribute HoldAll and evaluates f only after assigning specific numerical values to n.
  • In some cases, it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to n.
  • The precision used in evaluating f is the minimum precision used in the iterator.
  • 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 n will be applied for each plot element, while labels that are independent of n will only occur once.
  • DiscretePlot has the same options as Graphics, with the following additions and changes: [List of all options]
  • AspectRatio 1/GoldenRatioratio of height to width
    AxesTruewhether to draw axes
    ClippingStyleNonewhat to draw when lines are clipped
    ColorFunction Automatichow to determine the coloring of lines
    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 Nonewidth to extend from plot point
    Filling Axisfilling from extent
    FillingStyle Automaticstyle to use for filling
    Joined Automaticwhether to join points
    LabelingFunction Automatichow to label points
    LabelingSize Automaticmaximum size of callouts and labels
    MethodAutomaticwhat method to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotLabels Nonelabels for elements
    PlotLegends Nonelegends for sequences
    PlotMarkers Nonemarkers to use for plot points
    PlotRangeAutomaticrange of values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotStyle Automaticgraphics directives to determine the style of each line
    PlotTheme $PlotThemeoverall theme for the plot
    RegionFunction (True &)how to determine whether a point should be included
    ScalingFunctions Nonehow to scale individual coordinates
    WorkingPrecision MachinePrecisionprecision for internal computation
  • The arguments supplied to ColorFunction are , .
  • With the setting ExtentSize->{sl,sr}, a horizontal line is drawn around each plot point, extending sl to the left and sr to the right. With ExtentMarkers->{ml,mr}, the markers ml and mr will be used as left and right extent boundary markers.
  • With the default settings Joined->Automatic and Filling->Axis, DiscretePlot switches between drawing points with a stem filling when there are few points and lines with a solid filling when there are many points.
  • The arguments supplied to ExtentElementFunction are the element region {{xmin,xmax},{ymin,ymax}} and the sample point {xi,yi}.
  • With the setting ExtentSize->None, xmin is equal to xmax. With the setting Filling->None, ymin is equal to ymax.
  • ColorData["DefaultPlotColors"] gives the default sequence of colors used by PlotStyle.
  • Possible settings for ScalingFunctions include:
  • syscale the y axis
    {sx,sy}scale x and y 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
      AspectRatio1/GoldenRatioratio of height to width
      AxesTruewhether to draw axes
      AxesLabelNoneaxes labels
      AxesOriginAutomaticwhere axes should cross
      AxesStyle{}style specifications for the axes
      BackgroundNonebackground color for the plot
      BaselinePositionAutomatichow to align with a surrounding text baseline
      BaseStyle{}base style specifications for the graphic
      ClippingStyleNonewhat to draw when lines are clipped
      ColorFunctionAutomatichow to determine the coloring of lines
      ColorFunctionScalingTruewhether to scale arguments to ColorFunction
      ContentSelectableAutomaticwhether to allow contents to be selected
      CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
      Epilog{}primitives 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
      ExtentSizeNonewidth to extend from plot point
      FillingAxisfilling from extent
      FillingStyleAutomaticstyle to use for filling
      FormatTypeTraditionalFormthe default format type for text
      FrameFalsewhether to put a frame around the plot
      FrameLabelNoneframe labels
      FrameStyle{}style specifications for the frame
      FrameTicksAutomaticframe ticks
      FrameTicksStyle{}style specifications for frame ticks
      GridLinesNonegrid lines to draw
      GridLinesStyle{}style specifications for grid lines
      ImageMargins0.the margins to leave around the graphic
      ImagePaddingAllwhat extra padding to allow for labels etc.
      ImageSizeAutomaticthe absolute size at which to render the graphic
      JoinedAutomaticwhether to join points
      LabelingFunctionAutomatichow to label points
      LabelingSizeAutomaticmaximum size of callouts and labels
      LabelStyle{}style specifications for labels
      MethodAutomaticwhat method to use
      PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
      PlotLabelNonean overall label for the plot
      PlotLabelsNonelabels for elements
      PlotLegendsNonelegends for sequences
      PlotMarkersNonemarkers to use for plot points
      PlotRangeAutomaticrange of values to include
      PlotRangeClippingTruewhether to clip at the plot range
      PlotRangePaddingAutomatichow much to pad the range of values
      PlotRegionAutomaticthe final display region to be filled
      PlotStyleAutomaticgraphics directives to determine the style of each line
      PlotTheme$PlotThemeoverall theme for the plot
      PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
      Prolog{}primitives rendered before the main plot
      RegionFunction(True &)how to determine whether a point should be included
      RotateLabelTruewhether to rotate y labels on the frame
      ScalingFunctionsNonehow to scale individual coordinates
      TicksAutomaticaxes ticks
      TicksStyle{}style specifications for axes ticks
      WorkingPrecisionMachinePrecisionprecision for internal computation

Examples

open all close all

Basic Examples  (4)

Plot a sequence:

Plot several sequences:

Show a Riemann sum approximation to the area under a curve:

With bars to the left and right of the sample points:

Use legends to identify functions:

Scope  (19)

Data and Wrappers  (4)

Plot multiple functions:

Use wrappers on functions or sets of functions:

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  (8)

Label functions:

Label individual points:

Use callouts:

Apply callouts to extended regions:

Use Legended to provide a legend for a specific dataset:

Use Placed to change the legend location:

Use Callout to label datasets:

Use Callout to label elements:

Use Callout to label elements even when they are joined:

Specify a location for labels:

Specify label names with LabelingFunction:

Styling and Appearance  (7)

Use an explicit list of styles for the plots:

Style can be used to override styles:

Use any graphic for PlotMarkers:

Use any gradient or indexed color schemes from ColorData:

Use ExtentSize to associate a region with a point:

Show extent markers:

Use a theme with a frame and grid lines:

Options  (80)

AspectRatio  (4)

By default, DiscretePlot uses a fixed height to width ratio for the plot:

Make the height the same as the width with AspectRatio1:

AspectRatioAutomatic determines the ratio from the plot ranges:

AspectRatioFull adjusts the height and width to tightly fit inside other constructs:

ColorFunction  (6)

Color by scaled and coordinates, respectively:

Color joined plots:

Color filling element functions:

Color by height with a named color scheme:

Identify where TemplateBox[{n}, PrimePi] jumps:

ColorFunction has higher priority than PlotStyle:

ColorFunctionScaling  (2)

No argument scaling on the left; automatic scaling on the right:

Identify where TemplateBox[{n}, PrimePi] jumps:

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:

Built-in element functions may have options; use Palettes ▶ Chart Element Schemes to set them:

ExtentMarkers  (6)

Do not show the extent endpoints:

Use points to show the extent endpoints:

Show TemplateBox[{n}, Floor] with appropriate continuity markers:

Show TemplateBox[{n}, Ceiling] with appropriate continuity markers:

Control the size of markers:

Use custom shapes for the markers:

Markers use the settings for PlotStyle:

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  (6)

DiscretePlot automatically fills to the axis:

Turn off filling:

Use symbolic or explicit values:

With Joined->True:

With ExtentSize->Full:

Fill between curves 1 and 2:

Fill between curves 1 and 2 with a specific style:

Fill between curves 1 and 2; use red when 1 is below 2 and blue when 1 is above 2:

FillingStyle  (4)

Use different fill colors:

Fill with opacity 0.5 orange:

Fill with red below the axis and blue above:

Use a variable filling style obtained from a ColorFunction:

Joined  (3)

Plots are automatically joined when there are many points:

Join the points:

Do not join the points:

LabelingFunction  (3)

Put labels above the points:

Put them in a tooltip:

Use callouts to label the points:

Label the points with their values:

LabelingSize  (1)

Specify a maximum size for textual labels:

Use the full label:

PlotLabels  (4)

Specify text to label sets of points:

Place the labels above the points:

Use callouts to identify the points:

Use None to not add a label:

PlotLegends  (6)

Generate a legend using labels:

Generate a legend using placeholders:

Use PlotLegends->"Expressions" to use the actual equations:

PlotLegends matches PlotStyle and PlotMarkers in the plot:

Use Placed to change legend position:

Use PointLegend to change legend appearance:

PlotMarkers  (8)

DiscretePlot normally uses distinct colors to distinguish different sets of data:

Automatically use colors and shapes to distinguish sets of data:

Markers are placed at the plot points regardless of the setting for ExtentSize:

Change the size of the default plot markers:

Use arbitrary text for plot markers:

Use explicit graphics for plot markers:

Use the same symbol for all the sets of data:

Explicitly use a symbol and size:

PlotStyle  (4)

Use different style directives:

By default, different styles are chosen for multiple curves and regions:

Explicitly specify the style for different curves and regions:

PlotStyle can be combined with ColorFunction:

PlotTheme  (1)

Use a theme with a frame and grid lines:

Change the style for the grid lines:

RegionFunction  (1)

Draw over the region where :

ScalingFunctions  (7)

By default, plots have linear scales in each direction:

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

Use a log scale in the direction:

Reverse the axis without changing the axis:

Use different scales in the and directions:

Use a scale defined by a function and its inverse:

PlotRange and AxesOrigin are automatically scaled:

WorkingPrecision  (2)

Evaluate functions using machine-precision arithmetic:

Evaluate functions using arbitrary-precision arithmetic:

Applications  (4)

Plot the PDF of the empirical distribution of univariate data:

The CDF is a piecewise constant function:

Visualize the PDF and CDF for a discrete distribution:

Show Riemann sum approximations to the area under a curve:

Plot how many primes are below a number:

Properties & Relations  (4)

Plot generates continuous curves:

Use ListPlot to plot lists of values:

Use BarChart to show bars for lists of values:

Use DiscretePlot3D to plot functions of two discrete variables:

See Also

ListPlot  ListLinePlot  ListLogPlot  DateListPlot  ListStepPlot  Plot  Table

Related Guides

    ▪
  • Function Visualization
  • ▪
  • Discrete Calculus
  • ▪
  • Data Visualization
  • ▪
  • Nonparametric Statistical Distributions
  • ▪
  • Statistical Visualization

History

Introduced in 2008 (7.0) | Updated in 2010 (8.0) ▪ 2012 (9.0) ▪ 2014 (10.0) ▪ 2019 (12.0)

Wolfram Research (2008), DiscretePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscretePlot.html (updated 2019).

Text

Wolfram Research (2008), DiscretePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscretePlot.html (updated 2019).

CMS

Wolfram Language. 2008. "DiscretePlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/DiscretePlot.html.

APA

Wolfram Language. (2008). DiscretePlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscretePlot.html

BibTeX

@misc{reference.wolfram_2025_discreteplot, author="Wolfram Research", title="{DiscretePlot}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/DiscretePlot.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_discreteplot, organization={Wolfram Research}, title={DiscretePlot}, year={2019}, url={https://reference.wolfram.com/language/ref/DiscretePlot.html}, note=[Accessed: 01-December-2025]}

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