Built-in Mathematica Symbol

ContourPlot

ContourPlot[f, {x, x_min, x_max}, {y, y_min, y_max}]
generates a contour plot of f as a function of x and y.

g, {x, x_min, x_max}, {y, y_min, y_max}]
plots contour lines for which f=g.

g₁, f₂

g₂, ...}, {x, x_min, x_max}, {y, y_min, y_max}]
plots several contour lines.

ContourPlot 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 contour plot shows through.

ContourPlot has attribute HoldAll, and evaluates the f_i and g_i only after assigning specific numerical values to x and y.

In some cases it may be more efficient to use Evaluate to evaluate the f_i and g_i symbolically before specific numerical values are assigned to x and y.

ContourPlot 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 regions between contour lines
ColorFunctionScaling	True	whether to scale the argument to ColorFunction
ContourLabels	None	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
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 put 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	{}	how to determine the placement of mesh lines
MeshStyle	Automatic	the style for mesh lines
Method	Automatic	the method to use for refining contours
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotPoints	Automatic	the initial number of sample points 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

With the default setting ContourShading->Automatic, shading is used for ContourPlot[f, ...] but not for ContourPlot[fg, ...].

ContourPlot[{f₁g₁, f₂g₂, ...}, ...] superimposes the contour lines associated with all of the equalities f_ig_i.

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

ContourPlot 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 ContourPlot to miss features of your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.

With some settings for PerformanceGoal, other specific option settings may be overridden.

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 average of the scaled values of f for each pair of successive contour levels.

With the default settings Exclusions->Automatic and ExclusionsStyle->None, ContourPlot breaks continuity in its sampling at any discontinuity curve it detects. The discontinuity is immediately visible only if it jumps out of a particular contour level.