ListDensityPlot

ListDensityPlot[array]

generates a smooth density plot from an array of values.

ListDensityPlot[{{x₁,y₁,f₁},{x₂,y₂,f₂},…}]

generates a density plot with values defined at specified points.

Details and Options

ListDensityPlot[array] arranges successive rows of array up the page, and successive columns across.
ListDensityPlot linearly interpolates values so as to give smooth shading.
ListDensityPlot is mainly intended for discrete samplings of continuous data; ArrayPlot is intended for purely discrete data.
ListDensityPlot by default generates output in which larger values are shown lighter.
ListDensityPlot 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 color the plot
ColorFunctionScaling	True	whether to scale the argument to ColorFunction
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 interpolated density 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	{#1&,#2&}	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
PlotLegends	None	legends for color gradients
PlotRange	{Full,Full,Automatic}	the range of f or other values to include
PlotRangePadding	Automatic	how much to pad the range of values
PlotRangeClipping	True	whether to clip at the plot range
PlotTheme	$PlotTheme	overall theme for the plot
RegionFunction	(True&)	how to determine whether a point should be included
ScalingFunctions	None	how to scale individual coordinates
VertexColors	Automatic	colors to assume at every point

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.
ListDensityPlot[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, ListDensityPlot[{{a₁₁,a₁₂,a₁₃},…,{a_n1,a_n2,a_n3}}] will assume that the data being given is {{x₁,y₁,f₁},…}, rather than an ×3 array of values.
ListDensityPlot[list,DataRange->All] always takes list to represent an array of values.
Possible settings for ScalingFunctions include:
s_f scale the f-values

{s_x,s_y} scale x and y axes

{s_x,s_y,s_f} scale x and y axes and f-values
Each scaling function s_i is either a string "scale" or {g,g^-1}, where g^-1 is the inverse of g.
For ListDensityPlot[array], Mesh->Full draws a mesh that crosses at the position of each data point.
ListDensityPlot works with SparseArray objects.
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.
Typical settings for PlotLegends include:
None no legend

Automatic automatically determine legend from ColorFunction

Placed[lspec,…] specify placement for legend
The setting for VertexColors must be an array or list with the same structure as the array or list of values.
An explicit setting for VertexColors overrides colors determined from ColorFunction.
ListDensityPlot returns Graphics[GraphicsComplex[data]].