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


uses steps di and dj.


uses successive i values i1, i2, and j values j1, j2, .


plots the values of all the expri.

Details and Options


open allclose 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  (72)

AxesLabel  (2)

Use labels based on variables specified in DiscretePlot3D:

Specify a label for each axis:

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:

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:

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:

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:

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:

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


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


@misc{reference.wolfram_2020_discreteplot3d, author="Wolfram Research", title="{DiscretePlot3D}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/DiscretePlot3D.html}", note=[Accessed: 03-March-2021 ]}


@online{reference.wolfram_2020_discreteplot3d, organization={Wolfram Research}, title={DiscretePlot3D}, year={2019}, url={https://reference.wolfram.com/language/ref/DiscretePlot3D.html}, note=[Accessed: 03-March-2021 ]}


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


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