Built-in Mathematica Symbol

ListContourPlot

ListContourPlot[array]
generates a contour plot from an array of height values.

ListContourPlot[{{x₁, y₁, f₁}, {x₂, y₂, f₂}, ...}]
generates a contour plot from values defined at specified points.

MORE INFORMATION

ListContourPlot[array] arranges successive rows of array up the page, and successive columns across.

ListContourPlot by default generates grayscale output, in which larger values are shown lighter.

ListContourPlot has the same options as Graphics, with the following additions and changes:

AspectRatio	1	ratio of height to width
BoundaryStyle	None	how to draw RegionFunction boundaries
BoxRatios	Automatic	effective 3D bounding box ratios
ClippingStyle	None	how to draw values clipped by PlotRange
ColorFunction	Automatic	how to determine the color of regions between contour lines
ColorFunctionScaling	True	whether to scale the argument to ColorFunction
ContourLabels	Automatic	how to label contour levels
Contours	Automatic	how many or what contours to use
ContourShading	Automatic	how to shade regions between contours
ContourStyle	Automatic	the style for contour lines
DataRange	Automatic	the range of x and y values to assume for data
Frame	True	whether to draw a frame around the plot
FrameTicks	Automatic	frame tick marks
InterpolationOrder	None	the polynomial degree in each variable of the function interpolated between data points
LightingAngle	None	effective angle of the simulated light source
MaxPlotPoints	Automatic	the maximum number of points to include
Mesh	None	how many mesh lines in each direction to draw
MeshFunctions	{}	how to determine the placement of mesh lines
MeshStyle	Automatic	the style for mesh lines
Method	Automatic	the method to use for interpolation and data reduction
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotRange	{Full,Full,Automatic}	the range of f or other values to include
PlotRangeClipping	True	whether to clip at the plot range
PlotRangePadding	Automatic	how much to pad the range of values
RegionFunction	(True&)	how to determine whether a point should be included

ListContourPlot linearly interpolates values to give smooth contours.

array should be a rectangular array of real numbers; holes will be left in the plot whenever there are elements that are not real numbers.

ListContourPlot[array] by default takes the x and y coordinate values for each data point to be successive integers starting at 1.

The setting DataRange->{{x_min, x_max}, {y_min, y_max}} specifies other ranges of coordinate values to use.

With the default setting DataRange->Automatic, ListContourPlot[{{a₁₁, a₁₂, a₁₃}, ..., {a_n1, a_n2, a_n3}}] will assume that the data being given is {{x₁, y₁, f₁}, ...}, rather than an n×3 array of values.

ListContourPlot[list, DataRange->All] always takes list to represent an array of values.

For ListContourPlot[array], Mesh->Full draws a mesh that crosses at the position of each data point.

In determining how to color regions between contour levels, ListContourPlot looks first at any explicit setting given for ContourShading, then at the setting for ColorFunction.

ListContourPlot works with SparseArray objects.

The arguments supplied to functions in MeshFunctions and RegionFunction are x, y, f.

ColorFunction is by default supplied with a single argument, given by the average of the scaled values of f for each pair of successive contour levels.

ListContourPlot returns Graphics[GraphicsComplex[data]].

EXAMPLES

CLOSE ALL

Basic Examples (3)

Generate contours from an array of heights:

Give explicit

coordinates for the data:

Generate contours over interpolated data:

Generate contours from an array of heights:

In[1]:=

Out[1]=

Give explicit

coordinates for the data:

In[1]:=

In[2]:=

Out[2]=

Generate contours over interpolated data:

In[1]:=

Out[1]=

Scope (13)

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:

Add labels:

Color the density by height:

Label the contours:

Use specific colors between contours:

Use different styles for the contours:

Options (57)

No boundary is used by default:

Use a red boundary around the edges of the contours:

BoundaryStyle applies to holes cut by RegionFunction:

BoundaryStyle applies where there are jumps in the surface:

Clipped regions are not shown by default:

Color clipped regions like the rest of the surface:

Use pink to fill the clipped regions:

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

Color by scaled z coordinate:

Named color gradients color in the

direction:

Color with blue if contour values are negative, and with red otherwise:

Add labels to contour lines:

Label with values in a frame:

Use 7 equally spaced contours:

Use automatic contour selection:

Use at most 5 automatically selected contours:

Use specific contours:

Use specific contours with specific styles:

Use a function to generate a set of contours:

Have contours at the 10% and 90% percentile values:

The automatic shading is darker at low values and lighter at high values:

Use None to only show the contour lines:

Shade between contours using a color function:

Use an explicit list of colors between contours:

The default contour style is a partially transparent line:

Use black contour lines:

Use None to not show contour lines:

Alternate between red and dashed contour lines:

Use dashed red contour lines:

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

Rescale to the sampling space:

Triples are interpreted as

coordinates:

Generate an array of triples:

Force interpretation as an array of height values:

Contours are normally based on a linear interpolation of the data:

Use zero-order or piecewise constant interpolation:

Use third-order spline interpolation to fit the data:

Interpolation order zero to 5:

With a limited number of points, irregular data is linearly interpolated:

Irregular data with InterpolationOrder->1 uses natural neighbor interpolation:

ListContourPlot normally uses all of the points in the data set:

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:

Show the initial and final sampling mesh:

Use 5 mesh levels in each direction:

Use mesh lines in the

and

directions:

Use mesh levels corresponding to real and imaginary parts of a complex-valued function:

Use red mesh lines:

Use red mesh lines in the

direction and dashed mesh lines in the

direction:

Generate a higher quality plot:

Emphasize performance, possibly at the cost of quality:

Automatically compute the z range:

Use all points to compute the range:

Use an explicit

range to emphasize features:

Plot over a region in

:

The region depends on DataRange:

Regions do not have to be connected:

Use any logical combination of conditions:

Applications (2)

The contours for a probability density function:

Compare to the empirical density function:

Contouring medical data:

Properties & Relations (14)

ListContourPlot is similar to ListDensityPlot, but with bands of discrete colors:

ListContourPlot 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 ArrayPlot for arrays of discrete data:

Use MatrixPlot for structural plots of matrices:

Use ReliefPlot for matrices corresponding to medical and geographic values:

Use ListContourPlot3D to generate contour surfaces from four-dimensional data:

Use ContourPlot for functions:

Use ListPointPlot3D to show three-dimensional points:

Use ListDensityPlot to create densities from continuous data:

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: