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ListDensityPlot [{{f11,,f1n},,{fm1,,fmn}}]

generates a smooth density plot from an array of values fij.

ListDensityPlot [{{x1,y1,f1},,{xk,yk,fk}}]

generates a density plot with values fi defined at specified points {xi,yi}.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Tabular Data  
Presentation  
Options  
AspectRatio  
Axes  
AxesLabel  
Show More Show More
AxesOrigin  
AxesStyle  
BoundaryStyle  
ClippingStyle  
ColorFunction  
ColorFunctionScaling  
DataRange  
ImageSize  
InterpolationOrder  
MaxPlotPoints  
Mesh  
MeshFunctions  
MeshStyle  
PerformanceGoal  
PlotFit  
PlotLayout  
PlotLegends  
PlotRange  
PlotTheme  
RegionFunction  
ScalingFunctions  
VertexColors  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Tech Notes
Related Guides
History
Cite this Page

ListDensityPlot [{{f11,,f1n},,{fm1,,fmn}}]

generates a smooth density plot from an array of values fij.

ListDensityPlot [{{x1,y1,f1},,{xk,yk,fk}}]

generates a density plot with values fi defined at specified points {xi,yi}.

Details and Options

Examples

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Basic Examples  (4)

Use an array of values to define heights for a density:

Give explicit , , coordinates for points in a density:

A larger set of , , samples:

Use a multipanel layout to show multiple datasets at the same time:

Use different interpolations of data:

Scope  (16)

Data  (8)

For regular data consisting of values, the and data ranges are taken to be integer values:

Provide explicit and data ranges by using DataRange :

For irregular data consisting of triples, the and data ranges are inferred from data:

Areas around where the data is nonreal are excluded:

Use MaxPlotPoints to limit the number of points used:

PlotRange is selected automatically:

Use PlotRange to focus in on areas of interest:

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

Tabular Data  (1)

Get tabular data:

Plot a shaded density plot of column f over columns x and y:

Plot multiple sets of columns, arranging the plots in a row:

Include color bar legends for the plot:

Presentation  (7)

Add labels:

Color the density by height:

Include a legend:

Provide overlay meshes:

Provide an interactive Tooltip for the density:

Use a theme with simple ticks and a legend in a bold color scheme:

Use a multipanel layout to show multiple datasets at the same time:

Use a column instead of a row:

Options  (98)

AspectRatio  (4)

By default, ListDensityPlot 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, ListDensityPlot 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 units as labels:

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  (4)

No boundary is used by default:

Use a red boundary around the edges of the surface:

BoundaryStyle applies to holes cut by RegionFunction :

BoundaryStyle applies between Voronoi regions associated with the data:

ClippingStyle  (4)

Clipped regions are not shown by default:

Color clipped regions like the rest of the density:

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 the 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 :

DataRange  (4)

Arrays of height values are displayed against the number of elements in each direction:

Rescale to the sampling space:

Triples are interpreted as , , coordinates:

Force interpretation as arrays of height values:

The dataset is normally interpreted as a list of triples:

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:

InterpolationOrder  (5)

Densities are normally blended across polygons:

Use zero-order or piecewise constant interpolation:

Use third-order spline interpolation to fit the data:

Interpolation order 0 to 5:

For irregular data, zero-order interpolation gives Voronoi regions for each point:

MaxPlotPoints  (4)

ListDensityPlot normally uses all the points in the dataset:

Limit the number of points used in each direction:

MaxPlotPoints imposes a regular grid on irregular data:

The grid does not extend beyond the convex hull of the original data:

Mesh  (7)

No mesh is used by default:

Show the initial and final sampling mesh:

The entire mesh for irregular data is a Delaunay triangulation:

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, giving a continuously colored contour plot:

Use mesh lines in the and directions:

Show where the real and imaginary parts of a function are constant over the complex plane:

MeshStyle  (3)

Mesh lines are partially transparent by default:

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:

PlotFit  (4)

By default, density gradients can be very detailed:

Fitting the data results in smoother plots:

Fit a quadratic surface to the data:

Use KernelModelFit to approximate the data:

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  (5)

No legend is used, by default:

Include a legend:

Legends automatically use the same colors as the density plot:

Use Placed to change legend placement:

Use BarLegend to customize the legend:

PlotRange  (2)

Automatically compute the range and clip extreme portions of it:

Use all points to compute the range:

PlotTheme  (2)

Use a theme with simple ticks and a legend in a bright color scheme:

Change the color scheme:

RegionFunction  (4)

Plot over a region in :

The region depends on DataRange :

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:

VertexColors  (2)

ListDensityPlot usually colors the density using a color function:

Specify random colors for each vertex:

Applications  (3)

Plot a probability density function of two variables:

Compare to the empirical density function:

Show the regions closest to a set of points:

Show ozone density around the world:

Use CountryData to add country outlines:

Properties & Relations  (16)

ListDensityPlot is similar to ListPlot3D viewed from above:

ListDensityPlot and ListPlot3D view as a function of and :

The data has only one value for each , pair:

The data has two values for each , pair:

Use ListDensityPlot3D to plot 3D data:

ListDensityPlot associates colors with the vertices of polygons:

Raster , ArrayPlot , MatrixPlot , and ReliefPlot associate colors with the whole polygon:

Use ArrayPlot for arrays of discrete data:

Use MatrixPlot for structural plots of matrices:

Use ReliefPlot for matrices corresponding to medical and geographic values:

Use DensityPlot for functions:

Smoothly shade a map using color with GeoDensityPlot :

Use ListPointPlot3D to show three-dimensional points:

ListDensityPlot produces smooth color variations:

Use ListContourPlot to get segmented colors:

Use ListPlot3D to create surfaces from continuous data:

Use ListLogPlot , ListLogLogPlot , and ListLogLinearPlot for logarithmic plots:

Use ListPolarPlot for polar plots:

Use DateListPlot to show data over time:

Use ParametricPlot3D for three-dimensional parametric curves and surfaces:

Possible Issues  (2)

The appearance may depend on the source of the data:

An ×3 matrix is by default interpreted as a list of triples:

Use DataRange->All to force interpretation as a matrix of values:

Or provide an explicit list of data ranges to force interpretation as a matrix of values:

Neat Examples  (1)

Tech Notes

History

Introduced in 1988 (1.0) | Updated in 2007 (6.0) 2008 (7.0) 2012 (9.0) 2014 (10.0) 2016 (11.0) 2017 (11.1) 2021 (13.0) 2025 (14.2) 2025 (14.3)

Wolfram Research (1988), ListDensityPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ListDensityPlot.html (updated 2025).

Text

Wolfram Research (1988), ListDensityPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ListDensityPlot.html (updated 2025).

CMS

Wolfram Language. 1988. "ListDensityPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/ListDensityPlot.html.

APA

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

BibTeX

@misc{reference.wolfram_2025_listdensityplot, author="Wolfram Research", title="{ListDensityPlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ListDensityPlot.html}", note=[Accessed: 17-November-2025]}

BibLaTeX

@online{reference.wolfram_2025_listdensityplot, organization={Wolfram Research}, title={ListDensityPlot}, year={2025}, url={https://reference.wolfram.com/language/ref/ListDensityPlot.html}, note=[Accessed: 17-November-2025]}

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