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DensityPlot
  • See Also
    • ListDensityPlot
    • DensityPlot3D
    • SliceDensityPlot3D
    • ContourPlot
    • ArrayPlot
    • Plot3D
    • StreamPlot
    • VectorPlot
    • StreamDensityPlot
    • VectorDensityPlot
    • ColorFunction
    • RegionPlot
    • ComplexPlot
  • Related Guides
    • Function Visualization
    • Solvers over Regions
  • Tech Notes
    • Density and Contour Plots
    • See Also
      • ListDensityPlot
      • DensityPlot3D
      • SliceDensityPlot3D
      • ContourPlot
      • ArrayPlot
      • Plot3D
      • StreamPlot
      • VectorPlot
      • StreamDensityPlot
      • VectorDensityPlot
      • ColorFunction
      • RegionPlot
      • ComplexPlot
    • Related Guides
      • Function Visualization
      • Solvers over Regions
    • Tech Notes
      • Density and Contour Plots

DensityPlot[f,{x,xmin,xmax},{y,ymin,ymax}]

makes a density plot of f as a function of x and y.

DensityPlot[f,{x,y}∈reg]

takes the variables {x,y} to be in the geometric region reg.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Sampling  
Presentation  
Options  
AspectRatio  
Axes  
AxesLabel  
Show More Show More
AxesOrigin  
AxesStyle  
BoundaryStyle  
ClippingStyle  
ColorFunction  
ColorFunctionScaling  
EvaluationMonitor  
Exclusions  
ExclusionsStyle  
ImageSize  
MaxRecursion  
Mesh  
MeshFunctions  
MeshStyle  
PerformanceGoal  
PlotLayout  
PlotLegends  
PlotPoints  
PlotRange  
PlotTheme  
RegionFunction  
ScalingFunctions  
WorkingPrecision  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Tech Notes
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • ListDensityPlot
    • DensityPlot3D
    • SliceDensityPlot3D
    • ContourPlot
    • ArrayPlot
    • Plot3D
    • StreamPlot
    • VectorPlot
    • StreamDensityPlot
    • VectorDensityPlot
    • ColorFunction
    • RegionPlot
    • ComplexPlot
  • Related Guides
    • Function Visualization
    • Solvers over Regions
  • Tech Notes
    • Density and Contour Plots
    • See Also
      • ListDensityPlot
      • DensityPlot3D
      • SliceDensityPlot3D
      • ContourPlot
      • ArrayPlot
      • Plot3D
      • StreamPlot
      • VectorPlot
      • StreamDensityPlot
      • VectorDensityPlot
      • ColorFunction
      • RegionPlot
      • ComplexPlot
    • Related Guides
      • Function Visualization
      • Solvers over Regions
    • Tech Notes
      • Density and Contour Plots

DensityPlot

DensityPlot[f,{x,xmin,xmax},{y,ymin,ymax}]

makes a density plot of f as a function of x and y.

DensityPlot[f,{x,y}∈reg]

takes the variables {x,y} to be in the geometric region reg.

Details and Options

  • DensityPlot is also known as heat map.
  • It evaluates f at values of x and y in the domain being plotted over and uses a color function to map each value f[x,y] to a color.
  • The plot visualizes the set where is a color function mapping -values to colors.
  • At positions where f does not evaluate to a real number, holes are left so that the background to the density plot shows through.
  • DensityPlot treats the variables x and y as local, effectively using Block.
  • DensityPlot has attribute HoldAll, and evaluates f only after assigning specific numerical values to x and y.
  • In some cases, it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to x and y.
  • DensityPlot has the same options as Graphics, with the following additions and changes: [List of all options]
  • AspectRatio 1ratio of height to width
    BoundaryStyle Nonehow to draw RegionFunction boundaries
    BoxRatiosAutomaticeffective 3D bounding box ratios
    ClippingStyle Nonehow to draw values clipped by PlotRange
    ColorFunction Automatichow to color the plot
    ColorFunctionScaling Truewhether to scale the argument to ColorFunction
    EvaluationMonitor Noneexpression to evaluate at every function evaluation
    Exclusions Automaticx, y curves to exclude
    ExclusionsStyle Nonewhat to draw at excluded curves
    FrameTruewhether to draw a frame around the plot
    FrameTicksAutomaticframe tick marks
    LightingAngleNoneeffective angle of the simulated light source
    MaxRecursion Automaticthe maximum number of recursive subdivisions allowed
    Mesh Nonehow many mesh lines in each direction to draw
    MeshFunctions {#1&,#2&}how to determine the placement of mesh lines
    MeshStyle Automaticthe style for mesh lines
    MethodAutomaticthe method to use for refining the plot
    PerformanceGoal $PerformanceGoalaspects of performance to try to optimize
    PlotLayout Automatichow to position densities
    PlotLegends Nonelegends for color gradients
    PlotPoints Automaticthe initial number of sample points for the function in each direction
    PlotRange {Full,Full,Automatic}the range of f or other values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotRangePaddingAutomatichow much to pad the range of values
    PlotTheme $PlotThemeoverall theme for the plot
    RegionFunction (True&)how to determine whether a point should be included
    ScalingFunctions Nonehow to scale individual coordinates
    WorkingPrecision MachinePrecisionthe precision used in internal computations
  • Typical settings for PlotLegends include:
  • Noneno legend
    Automaticautomatically determine legend from ColorFunction
    Placed[lspec,…]specify placement for legend
  • Possible settings for PlotLayout that show single densities in multiple plot panels include:
  • "Column"use separate densities in a column of panels
    "Row"use separate densities in a row of panels
    {"Column",k},{"Row",k}use k columns or rows
    {"Column",UpTo[k]},{"Row",UpTo[k]}use at most k columns or rows
  • DensityPlot initially evaluates f at a grid of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to subdivide at most MaxRecursion times to generate smooth contours.
  • You should realize that since it uses only a finite number of sample points, it is possible for DensityPlot to miss features of your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.
  • With the setting Mesh->All, DensityPlot draws mesh lines to show all the subdivisions it uses.
  • The default setting MeshFunctions->{#1&,#2&} draws an x, y mesh.
  • The arguments supplied to functions in MeshFunctions and RegionFunction are x, y, f.
  • ColorFunction is supplied with a single argument, given by default by the scaled value of f.
  • With the default settings Exclusions->Automatic and ExclusionsStyle->None, DensityPlot breaks continuity in the density it displays at any discontinuity curve it detects.
  • Possible settings for ScalingFunctions include:
  • sfscale the f values
    {sx,sy}scale x and y axes
    {sx,sy,sf}scale x and y axes and f values
  • Each scaling function si is either a string "scale" or {g,g-1} where g-1 is the inverse of g.
  • DensityPlot returns Graphics[GraphicsComplex[data]].
  • List of all options

    • AlignmentPointCenterthe default point in the graphic to align with
      AspectRatio1ratio of height to width
      AxesFalsewhether 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
      BoundaryStyleNonehow to draw RegionFunction boundaries
      BoxRatiosAutomaticeffective 3D bounding box ratios
      ClippingStyleNonehow to draw values clipped by PlotRange
      ColorFunctionAutomatichow to color the plot
      ColorFunctionScalingTruewhether to scale the argument 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
      ExclusionsAutomaticx, y curves to exclude
      ExclusionsStyleNonewhat to draw at excluded curves
      FormatTypeTraditionalFormthe default format type for text
      FrameTruewhether to draw a frame around the plot
      FrameLabelNoneframe labels
      FrameStyle{}style specifications for the frame
      FrameTicksAutomaticframe tick marks
      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
      LabelStyle{}style specifications for labels
      LightingAngleNoneeffective angle of the simulated light source
      MaxRecursionAutomaticthe maximum number of recursive subdivisions allowed
      MeshNonehow many mesh lines in each direction to draw
      MeshFunctions{#1&,#2&}how to determine the placement of mesh lines
      MeshStyleAutomaticthe style for mesh lines
      MethodAutomaticthe method to use for refining the plot
      PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
      PlotLabelNonean overall label for the plot
      PlotLayoutAutomatichow to position densities
      PlotLegendsNonelegends for color gradients
      PlotPointsAutomaticthe initial number of sample points for the function in each direction
      PlotRange{Full,Full,Automatic}the range of f or other values to include
      PlotRangeClippingTruewhether to clip at the plot range
      PlotRangePaddingAutomatichow much to pad the range of values
      PlotRegionAutomaticthe final display region to be filled
      PlotTheme$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
      WorkingPrecisionMachinePrecisionthe precision used in internal computations

Examples

open all close all

Basic Examples  (4)

Plot a function:

Use a different color scheme and legend:

Create a contouring overlay mesh:

Use a multi-panel layout to show multiple functions at the same time:

Scope  (19)

Sampling  (11)

More points are sampled where the function changes quickly:

The plot range is selected automatically:

Areas where the function becomes nonreal are excluded:

The region is split when there are discontinuities in the function:

Use PlotPoints and MaxRecursion to control adaptive sampling:

Use PlotRange to focus in on areas of interest:

Use Exclusions to remove curves or split the resulting surface:

Use RegionFunction to restrict the surface to a region given by inequalities:

The domain may be specified by a region:

The domain may be specified by a MeshRegion:

Plot over an infinite domain:

Presentation  (8)

Add labels:

Color the surface by height:

Add a legend:

Provide an interactive Tooltip for a surface:

Style the overlay mesh:

Create a contouring overlay mesh:

Use a theme with simple ticks in a high-contrast color scheme:

Show multiple functions as densities in separate panels:

Use a column instead of a row:

Options  (89)

AspectRatio  (4)

By default, DensityPlot uses the same width and height:

Use a numerical value to specify the height to width ratio:

AspectRatioAutomatic determines the ratio from the plot ranges:

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

Axes  (4)

By default, DensityPlot uses a frame instead of axes:

Use axes instead of a frame:

Use AxesOrigin to specify where the axes intersect:

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 DensityPlot:

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:

BoundaryStyle  (3)

Use a red boundary around the edges of the surface:

BoundaryStyle applies to regions cut by RegionFunction:

BoundaryStyle does not apply to cuts made by Exclusions:

Use ExclusionsStyle instead:

ClippingStyle  (4)

Show clipped regions like the rest of the surface:

Leave clipped regions empty:

Use pink to fill the clipped regions:

Use light red where the surface is clipped above and pink below:

ColorFunction  (5)

Color by scaled coordinate:

Specify gray-level intensity by scaled coordinate:

Named color gradients color in the direction:

Use brightness to correspond to height or density of a function:

Use the interpolation between two colors to indicate the height or density of a function:

ColorFunctionScaling  (1)

Get the natural range of values by setting ColorFunctionScaling to False:

EvaluationMonitor  (2)

Show where DensityPlot samples a function:

Count how many times is evaluated:

Exclusions  (6)

This uses automatic methods to compute exclusions:

Indicate that no exclusions should be computed:

Give exclusions as an equation:

Give multiple exclusion sets:

Use a condition with the exclusion equation:

Use both automatically computed and explicit exclusions:

ExclusionsStyle  (1)

Use a red boundary to indicate the excluded curves:

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:

MaxRecursion  (1)

Refine the function where it changes quickly:

Mesh  (6)

Use no mesh:

Show the initial and final sampling mesh:

Use 5 mesh lines in each direction:

Use 3 mesh lines in the direction and 6 mesh lines in the direction:

Use mesh lines at specific values:

Use different styles for different mesh lines:

MeshFunctions  (3)

Use the value as the mesh function:

Use mesh lines in the and directions:

Use mesh lines corresponding to fixed distances from the origin:

MeshStyle  (2)

Use red mesh lines:

Use red mesh lines in the direction and dashed mesh lines in the direction:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLayout  (3)

Place each density in a separate panel using shared axes:

Use a row instead of a column:

Use multiple columns or rows:

Prefer full columns or rows:

PlotLegends  (4)

Show a legend for the heights:

PlotLegends automatically matches the color function:

Use Placed to change legend position:

Use BarLegend to change legend appearance:

PlotPoints  (2)

Use more initial points to get a smoother density:

Use 20 initial points in the direction and 5 in the direction:

PlotRange  (4)

Automatically compute the range:

Use all points to compute the range:

Show the surface over the full , range:

Automatically compute the , range:

Use an explicit range to emphasize features:

PlotTheme  (1)

Use a theme with detailed ticks and a legend:

Change the color function:

RegionFunction  (3)

Plot over an annulus region in and :

Regions do not have to be connected:

Use any logical combination of conditions:

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 top:

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 GridLines are automatically scaled:

PlotRange is automatically scaled:

WorkingPrecision  (2)

Evaluate functions using machine-precision arithmetic:

Evaluate functions using arbitrary-precision arithmetic:

Applications  (7)

Plot a sum of 5 sine waves in random directions:

This shows the solution to the heat equation in one dimension:

Plot a saddle surface; the mesh curves show where the function is zero:

The 1, 2, 3, and norms, with the iso-norm mesh lines at 1/2, 1, and 3/2:

Show argument variation for sin, cos, tan, and cot over the complex plane:

Show the different complex components for a function:

Transform a function to expose more features:

Properties & Relations  (9)

DensityPlot samples more points where it needs to:

Use ContourPlot to get segmented iso curves and contour regions:

Use ListDensityPlot for plotting continuous data:

Use Plot3D to get 3D surfaces:

Add a ColorFunction to get an overlay density:

ComplexPlot plots the phase of a function using color and shades by the magnitude:

Use ArrayPlot or MatrixPlot for discrete data:

Use Plot for univariate functions:

Use ParametricPlot for plane parametric curves and regions:

Use ContourPlot3D and RegionPlot3D for implicit surfaces and regions:

Possible Issues  (2)

With segmenting or piecewise color functions, the transition color borders may not be sharp:

Use ContourPlot for segmenting problems instead:

Color functions or densities that change quickly may show artifacts:

Use PlotPoints to increase the sampling density:

Neat Examples  (2)

Branch cuts for inverse trigonometric functions:

Real and imaginary part overlay mesh:

See Also

ListDensityPlot  DensityPlot3D  SliceDensityPlot3D  ContourPlot  ArrayPlot  Plot3D  StreamPlot  VectorPlot  StreamDensityPlot  VectorDensityPlot  ColorFunction  RegionPlot  ComplexPlot

Tech Notes

    ▪
  • Density and Contour Plots

Related Guides

    ▪
  • Function Visualization
  • ▪
  • Solvers over Regions

History

Introduced in 1988 (1.0) | Updated in 2007 (6.0) ▪ 2008 (7.0) ▪ 2012 (9.0) ▪ 2014 (10.0) ▪ 2017 (11.1) ▪ 2021 (13.0)

Wolfram Research (1988), DensityPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/DensityPlot.html (updated 2021).

Text

Wolfram Research (1988), DensityPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/DensityPlot.html (updated 2021).

CMS

Wolfram Language. 1988. "DensityPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/DensityPlot.html.

APA

Wolfram Language. (1988). DensityPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DensityPlot.html

BibTeX

@misc{reference.wolfram_2025_densityplot, author="Wolfram Research", title="{DensityPlot}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/DensityPlot.html}", note=[Accessed: 01-March-2026]}

BibLaTeX

@online{reference.wolfram_2025_densityplot, organization={Wolfram Research}, title={DensityPlot}, year={2021}, url={https://reference.wolfram.com/language/ref/DensityPlot.html}, note=[Accessed: 01-March-2026]}

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