More points are sampled where the function changes quickly:

The plot range is selected automatically:

Areas where the function becomes nonreal are excluded:

The surface is split when there are discontinuities in the function:

Use PlotPoints and MaxRecursion to control adaptive sampling:

Use PlotRange to focus in on areas of interest:

Use Exclusions to remove curves or split the resulting surface:

Use RegionFunction to restrict the surface to a region given by inequalities:

The domain may be specified by a region:

The domain may be specified by a MeshRegion :

Plot over an infinite domain:

Label surfaces with Labeled :

Label surfaces with PlotLabels :

Place the label near the surface at an {x,y} value:

Use Callout :

Place a label with a specific location:

Include legends for each surface:

Use Legended to provide a legend for a specific curve:

Use Placed to change the legend location:

Provide an explicit PlotStyle for the surface:

Provide separate styles for different surfaces:

Add labels:

Color the surface by height:

Add a legend:

Use a theme with bright colors and height-based mesh lines:

Style the areas between mesh lines:

Provide an interactive Tooltip for a surface:

Fill below a surface:

Use colored backgrounds:

Use a black boundary around the edges of the surface:

Use a thick boundary around the edges of the surface:

Use a thick, red boundary around the edges of the surface:

Do not use any boundary:

BoundaryStyle applies to holes cut by RegionFunction :

BoundaryStyle does not apply to holes cut by Exclusions :

Automatic uses the natural scale from PlotRange :

Use BoxRatios to emphasize some particular feature, in this case a saddle surface:

Clipped regions use different surface colors by default:

Do not draw clipped regions:

Make clipped regions partially transparent:

Color clipped regions red at the bottom and blue at the top:

Color according to the and coordinates:

Color by scaled coordinate:

Use ColorData for predefined color gradients:

Named color gradients color in the direction:

ColorFunction has higher priority than PlotStyle :

ColorFunction has lower priority than MeshShading :

Use unscaled coordinates:

Use scaled coordinates in the direction and unscaled coordinates in the and directions:

Show where Plot3D samples a function:

Count how many times is evaluated:

This uses automatic methods to compute exclusions, in this case from branch cuts:

Indicate that no exclusions should be computed:

Give a set of exclusions as list of equations:

Use a condition with the exclusion equation:

Use both automatically computed and explicit exclusions:

Style the boundary with a thick, blue line:

Style the boundary with a thick, blue line and the surface in between transparent:

Use a transparent surface in the exclusion cuts:

Fill to the bottom:

Filling occurs along the region cut by the RegionFunction :

Fill to both top and bottom:

Fill surface 1 to the bottom with blue and surface 2 to the top with red:

Fill to the bottom with a variety of styles:

Fill to the plane with red below and blue above:

Fill to the plane from below only:

Textual labels are shown at their actual sizes:

Specify a maximum size for textual labels:

Image labels are automatically resized:

Specify a maximum size for image labels:

Show image labels at their natural sizes:

Refine the surface where it changes quickly:

Use no mesh:

Show the initial and final sampling meshes:

Use 5 mesh lines in each direction:

Use 3 mesh lines in the direction and 6 mesh lines in the direction:

Use mesh lines at specific values:

Use different styles for different mesh lines:

Use the value as the mesh function:

Use mesh lines in the and directions:

Use mesh lines corresponding to fixed distances from the origin:

Use None to remove regions:

Lay a checkerboard pattern over a surface:

MeshShading has a higher priority than PlotStyle :

MeshShading has a higher priority than ColorFunction :

Use red mesh lines:

Use red mesh lines in the direction and thick mesh lines in the direction:

Normals are automatically calculated:

Use None to get flat shading for all the polygons:

Vary the effective normals used on the surface:

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

Specify text to label surfaces:

Specify a label:

Use callouts to identify the curves:

Use placeholders to identify plot styles:

Use specific labels:

Use the respective expressions:

Use Placed to control legend position:

Use SwatchLegend to change the appearance:

Create a legend based on a color function:

Use BarLegend to change the appearance:

Use more initial points to get a smoother surface:

Use 20 initial points in the direction and 5 in the direction:

Automatically compute the range:

Use all points to compute the range:

Show the surface over the full , range:

Automatically compute the , range:

Use an explicit range to emphasize features:

Color a surface with diffuse orange:

Use Specularity to get highlights:

Use Opacity to get transparent surfaces:

Use separate styles for each of the surfaces:

Produce a wire mesh:

Use a theme with grid lines and a legend:

Turn off the grid lines:

Create a thick surface for 3D printing:

Plot over an annulus region in and :

Filling will fill from the region boundary:

Regions do not have to be connected:

Use any logical combination of conditions:

By default, plots have linear scales in each direction:

Use a log scale in the direction:

Use a linear scale in the direction that shows smaller numbers at the top:

Use a reciprocal scale in the direction:

Use different scales in the and directions:

Reverse the axis without changing the axis:

Use a scale defined by a function and its inverse:

Positions in Ticks are automatically scaled:

PlotRange is automatically scaled:

Textures use scaled and coordinates by default:

Use the and parameters:

Use unscaled coordinates:

Use textures to highlight how parameters map onto a surface:

Use scaled or unscaled coordinates for textures:

Evaluate functions using machine-precision arithmetic:

Evaluate functions using arbitrary-precision arithmetic:

Make the surface partially transparent to see its inner structure:

Use MeshShading to create holes in the surface to see its inner structure:

Use MeshFunctions to also specify the slices to use:

Plot and together and guess that :

This is indeed true:

Show that TemplateBox[{p, infty}, Norm2]<=TemplateBox[{p, 2}, Norm2]<=TemplateBox[{p, 1}, Norm2] by plotting their surfaces:

Prove it:

Understand how a family of functions relate to each other:

The , , , and norms, with the unit norm mesh line:

Plot a saddle surface; the mesh curves show where the function is zero:

Use a RegionFunction to create a cutout to understand limit behavior:

There are different limits when approaching along different lines:

Highlight the local extrema for a function using MeshFunctions :

The red curves where indicate local extrema for each fixed :

Similarly the blue curves where indicate local extrema for each fixed :

The intersections of the red and blue curves are the points where and :

Plot the stream lines of the gradient field on top of the surface:

Plot the gradient vector field on top of the function surface:

The epigraph of a function is given by . You can visualize the epigraph using Filling :

The hypograph of a function is given by . You can visualize the hypograph using Filling :

Show the real and imaginary parts of :

Show the different complex components for a function:

This shows the solution to the heat equation in one dimension:

Plot an iterated logistic map as a function of parameter and initial value: