2.10.7 Density and Contour Plots

DensityGraphics[array]	density plot
ContourGraphics[array]	contour plot

The functions DensityPlot and ContourPlot discussed in Section 1.9.5 work by creating ContourGraphics and DensityGraphics objects containing arrays of values.

Most of the options for density and contour plots are the same as those for ordinary two-dimensional plots. There are, however, a few additional options.

option name	default value
ColorFunction	Automatic	how to assign colors to each cell
ColorFunctionScaling	True	whether to scale values before applying a color function
Mesh	True	whether to draw a mesh
MeshStyle	Automatic	a style for the mesh

In a density plot, the color of each cell represents its value. By default, each cell is assigned a gray level, running from black to white as the value of the cell increases. In general, however, you can specify other "color maps" for the relation between the value of a cell and its color. The option ColorFunction allows you to specify a function which is applied to each cell value to find the color of the cell. With ColorFunctionScaling->True the cell values are scaled so as to run between 0 and 1 in a particular density plot; with ColorFunctionScaling->False no such scaling is performed. The function you give as the setting for ColorFunction may return any Mathematica color directive, such as GrayLevel, Hue or RGBColor. A common setting to use is ColorFunction -> Hue.

option name	default value
Contours	10	what contours to use
ContourLines	True	whether to draw contour lines
ContourStyle	Automatic	style to use for contour lines
ContourShading	True	whether to shade regions in the plot
ColorFunction	Automatic	how to assign colors to contour levels
ColorFunctionScaling	True	whether to scale values before applying a color function

In constructing a contour plot, the first issue is what contours to use. With the default setting Contours -> 10, Mathematica uses a sequence of 10 contour levels equally spaced between the minimum and maximum values defined by the PlotRange option.

Contours -> n	use a sequence of n equally spaced contours
Contours -> {, , ... }	use contours with values , , ...

There are some slight subtleties associated with labeling density and contour plots. Both the Axes and Frame options from ordinary two-dimensional graphics can be used. But setting AxesOrigin -> Automatic keeps the axes outside the plot in both cases.