This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


generates a plot of the values of expr when i runs from to and j runs from to .
uses steps di and dj.
uses successive i values , , ... and j values , , ....
plots the values of all the .
  • DiscretePlot3D plots the variable i along the axis and j along the axis.
  • DiscretePlot3D has attribute HoldAll, and evaluates expr only after assigning specific numerical values to i and j.
  • In some cases it may be more efficient to use Evaluate to evaluate expr symbolically before specific numerical values are assigned to i and j.
  • The precision used in evaluating expr is the minimum precision used in the iterators.
  • The form provides a wrapper w to be applied to the resulting graphics primitives.
  • The following wrappers can be used:
Annotation[expr,label]provide an annotation
Button[expr,action]define an action to execute when the element is clicked
EventHandler[expr,...]define a general event handler for the element
Hyperlink[expr,uri]make the element act as a hyperlink
PopupWindow[expr,cont]attach a popup window to the element
StatusArea[expr,label]display in the status area when the element is moused over
Style[expr,opts]show the element using the specified styles
Tooltip[expr,label]attach an arbitrary tooltip to the element
AxesTruewhether to draw axes
BoxRatios{1,1,0.4}bounding 3D box ratios
ClippingStyleAutomatichow to draw clipped parts of surfaces
ColorFunctionAutomatichow to determine the color of surfaces
ColorFunctionScalingTruewhether to scale arguments to ColorFunction
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
FillingAutomaticfilling under each surface
FillingStyleOpacity[0.5]style to use for filling
JoinedFalsewhether to join
MethodAutomaticthe methods to use
NormalsFunctionAutomatichow to determine effective surface normals
PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
PlotRange{Full,Full,Automatic}the range of or other values to include
PlotStyleAutomaticgraphics directives for the style for each surface
RegionFunction(True&)how to determine whether a point should be included
WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • With the setting ExtentSize a horizontal plane is drawn around each plot point extending to the left and to the right along the axis and to the left and to the right along the axis. With ExtentMarkers, the markers and will be used as left and right markers along the axis and and as left and right markers along the axis.
Plot a bivariate sequence:
Associate a region with the points:
Plot several sequences:
Plot a bivariate sequence:
Click for copyable input
Associate a region with the points:
Click for copyable input
Plot several sequences:
Click for copyable input
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 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 labels based on variables specified in DiscretePlot3D:
Specify a label for each axis:
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:
Color by absolute height:
Gather the plotted heights:
Show the plot and a histogram of the heights:
Get a list of built-in settings for ExtentElementFunction:
For detailed settings, use PalettesChartElementSchemes:
This ChartElementFunction is appropriate to show the global scale:
Write a custom ExtentElementFunction:
A built-in element function may have options; use PalettesChartElementSchemes to set them:
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:
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:
DiscretePlot3D fills to :
Turn off filling:
Fill to different levels:
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:
Join the points into a surface:
Combine a surface with extent regions:
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:
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:
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:
Visualize properties of discrete distributions, such as probability density function:
Cumulative distribution function:
Survival function:
Approximate the volume under a surface using Riemann sums:
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:
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