Built-in Mathematica Symbol

DensityPlot

DensityPlot[f, {x, x_min, x_max}, {y, y_min, y_max}]
makes a density plot of f as a function of x and y.

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

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 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:

AspectRatio	1	ratio of height to width
BoundaryStyle	None	how to draw RegionFunction boundaries
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
EvaluationMonitor	None	expression to evaluate at every function evaluation
Exclusions	Automatic	x, y curves to exclude
ExclusionsStyle	None	what to draw at excluded curves
Frame	True	whether to draw a frame around the plot
FrameTicks	Automatic	frame tick marks
MaxRecursion	Automatic	the maximum number of recursive subdivisions allowed
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 refining the plot
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotPoints	Automatic	the initial number of sample points for the function in each direction
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
WorkingPrecision	MachinePrecision	the precision used in internal computations

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 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.