This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# StreamDensityPlot

 StreamDensityPlot generates a stream plot of the vector field as a function of x and y, superimposed on a background density plot of the scalar field s. StreamDensityPlottakes the scalar field to be the norm of the vector field. StreamDensityPlotgenerates plots of several vector fields.
• StreamDensityPlot plots streamlines that show the local direction of the vector field at every point.
• StreamDensityPlot by default shows enough streamlines to achieve a roughly uniform density throughout the plot.
• StreamDensityPlot does not show streamlines at any positions for which the etc. do not evaluate to real numbers.
• StreamDensityPlot has attribute HoldAll, and evaluates the , etc. only after assigning specific numerical values to x and y.
• In some cases it may be more efficient to use Evaluate to evaluate the , etc. symbolically before specific numerical values are assigned to x and y.
 AspectRatio 1 ratio of height to width BoundaryStyle None how to draw RegionFunction boundaries BoxRatios Automatic effective 3D box ratios for simulated lighting ColorFunction Automatic how to color background densities ColorFunctionScaling True whether to scale arguments to ColorFunction EvaluationMonitor None expression to evaluate at every function evaluation Frame True whether to draw a frame around the plot FrameTicks Automatic frame tick marks LightingAngle None effective angle for simulated lighting MaxRecursion Automatic the maximum number of recursive subdivisions allowed for the scalar field Mesh None how many mesh lines to draw in the background MeshFunctions {#5&} how to determine the placement of mesh lines MeshShading None how to shade regions between mesh lines MeshStyle Automatic the style of mesh lines Method Automatic methods to use for the plot PerformanceGoal \$PerformanceGoal aspects of performance to try to optimize PlotRange {Full,Full} range of x, y values to include PlotRangePadding Automatic how much to pad the range of values RegionFunction True& determine what region to include StreamColorFunction None how to color streamlines StreamColorFunctionScaling True whether to scale the argument to StreamColorFunction StreamPoints Automatic determine number, placement and closeness of streamlines StreamScale Automatic determine sizes and segmenting of individual streamlines StreamStyle Automatic how to draw streamlines WorkingPrecision MachinePrecision precision to use in internal computations
• The default setting MeshFunctions draws mesh lines for the scalar field s.
Plot the streamlines for a vector field with background based on field magnitude:
Plot the streamlines for a vector field with background based on a logarithm of field magnitude:
Plot the streamlines for two fields with a background based on the first field's magnitude:
Plot the streamlines for a vector field with background based on field magnitude:
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Plot the streamlines for a vector field with background based on a logarithm of field magnitude:
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Plot the streamlines for two fields with a background based on the first field's magnitude:
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 Scope   (19)
Visualize a vector field with the background based on :
Plot two vector fields with background color based on the first field's magnitude:
Use Evaluate to evaluate the vector field symbolically before numeric assignment:
Plot a vector field with streamlines placed with specified densities:
Plot the streamlines that go through a set of seed points:
Use both automatic and explicit seeding with styles for explicitly seeded streamlines:
Plot streamlines over a specified region:
Use a specific number of mesh lines:
Specify mesh lines:
Specify different dashings and arrowheads by settings to StreamScale:
Color the background scalar field with a color function:
Plot the streamlines with arrows colored according to field magnitude:
Apply a variety of streamline styles:
Plot vectors and streamlines together:
Specify mesh lines with different styles:
Specify global mesh line styles:
Apply a variety of styles to region boundaries:
Fix the lighting angle at 0 (right of the plot), and vary the altitude from 0 to /2:
 Options   (116)
By default, the aspect ratio is 1:
Set the aspect ratio:
Use colored backgrounds:
By default, region boundaries have no style:
Apply a variety of styles to region boundaries:
Color the field magnitude using Hue:
Color using Hue based on :
Use any named color gradient from ColorData:
Use ColorData for predefined color gradients:
Specify a color function that blends two colors by the coordinate:
Use ColorFunctionScaling->False to get unscaled values:
By default, scaled values are used:
Use ColorFunctionScaling->False to get unscaled values:
Use unscaled coordinates in the direction and scaled coordinates in the directions:
Explicitly specify the scaling for each color function argument:
Show where the vector field function is sampled:
Count the number of times the vector field function is evaluated:
Label the axes:
Vary the lighting angle from 0 (right of the plot) to /2 (top of the plot):
Fix the lighting angle at 0 (right of the plot), and vary the altitude from 0 to /2:
Refine the plot where it changes quickly:
By default, no mesh lines are displayed:
Show the final sampling mesh:
Use a specific number of mesh lines:
Specify mesh lines:
Use different styles for different mesh lines:
By default, mesh lines correspond to the magnitude of the field:
Use the value as the mesh function:
Use mesh lines corresponding to fixed distances from the origin:
Use None to remove regions:
Styles are used cyclically:
Use indexed colors from ColorData cyclically:
Apply a variety of styles to the mesh lines:
Do not use normals in shading:
Randomly vary the effective normals:
Generate a higher-quality plot:
Emphasize performance, possibly at the cost of quality:
The full plot range is used by default:
Specify an explicit limit for both and ranges:
Specify an explicit range that applies to both and ranges:
Specify an explicit range:
Specify an explicit minimum range:
Specify an explicit range:
Specify an explicit maximum range:
Specify different and ranges:
Plot streamlines only over certain quadrants:
Plot streamlines only over regions where the field magnitude is above a given threshold:
Use any logical combination of conditions:
Color streamlines according to the norm of the vector field:
Use any named color gradient from ColorData:
Use ColorData for predefined color gradients:
Specify a color function that blends two colors by the coordinate:
Use StreamColorFunctionScaling->False to get unscaled values:
By default, scaled values are used:
Use StreamColorFunctionScaling->False to get unscaled values:
Use unscaled coordinates in the direction and scaled coordinates in the direction:
Explicitly specify the scaling for each color function argument:
Specify a maximum number of streamlines:
Use symbolic names to specify the number of streamlines:
Use both automatic and explicit seeding with styles for explicitly seeded streamlines:
Specify the minimum distance between streamlines:
Specify the minimum distance between streamlines at the start and end of a streamline:
Control the maximum length that each streamline can have:
Create full streamlines without segmentation:
Use curves for streamlines:
Use symbolic names to control the lengths of streamlines:
Specify segment lengths:
Specify an explicit dashing pattern for streamlines:
Specify the number of points rendered on each streamline segment:
Specify absolute aspect ratios relative to the longest line segment:
Specify relative aspect ratios relative to each line segment:
Scale the length of the arrows by the coordinate:
Apply a variety of styles to the streamlines:
Set the style for multiple vector fields:
Use named styles:
Named arrow styles:
Named dot styles:
Named pointer styles:
Named dart styles:
Color the vectors according to their norm:
Use any named color gradient from ColorData:
Color the vectors according to their value:
Use VectorColorFunctionScaling->False to get unscaled values:
By default, scaled values are used:
Use VectorColorFunctionScaling->False to get unscaled values:
Use unscaled coordinates in the direction and scaled coordinates in the direction:
Explicitly specify the scaling for each color function argument:
Use automatically determined vector points:
Use symbolic names to specify the set of field vectors:
Create a regular grid of field vectors with the same number of arrows for and :
Create a regular grid of field vectors with a different number of arrows for and :
Specify a list of points for showing field vectors:
Use a different number of field vectors on a regular grid:
The location for vectors is given in the middle of the drawn vector:
Use automatically determined vector scale:
Specify the relative size of vectors as a fraction of the diagonal of the plot range:
Use symbolic names to control the size of vectors:
With the vector scaling function set to None, all vectors have the same size:
Specify an absolute size for the arrowheads:
Specify arrowhead size relative to the length of the arrow:
Scale the vector length by the absolute value of the coordinate:
By default, the vector length is scaled by the norm of the vector field:
Set the style for the vectors:
Set the style for multiple vector fields:
Plot the vector fields without arrowheads:
Plot the vector field with a named vector style:
Arrow vector styles:
Circular vector styles:
Dart vector styles:
Dot vector styles:
Pointer vector styles:
Specify both arrow tail and head:
Graphics primitives without Arrowheads are scaled based on the vector scale:
Change the scaling using the VectorScale option:
 Applications   (16)
Visualize a vector field with the background based on the field's divergence:
Visualize a vector field with the background based on the magnitude of the field's curl:
Show streamlines superimposed on the Hamiltonian for a 2D Hamiltonian system:
Check how closely NDSolve conserves the invariant:
Characterize linear planar systems interactively:
Use a stream plot as a background for an interactive differential equation demo:
Combine several examples into a tabbed view:
Mouse over the tabs to get a description of the field:
Quadratic system with two limit cycles:
Homoclinic loops:
Unfolding a double zero eigenvalue with odd symmetry:
Explore a parameterized vector field using Manipulate:
Vibrating membranes:
Unfolding a function and its gradient field:
Generate a list of rasterized plots for animation:
Animating a list of rasters instead of the original vector graphics may reduce memory usage:
Create an animation that shifts the streamline colors in the direction of the vector norms:
Explore various streamline styles and scales with several examples:
Generate icons to graphically represent field choices:
Click on the field icons to switch field plots:
Generate a list of stream plots of varying :
Stack 2D stream plots in 3D:
Use ListStreamDensityPlot for plotting data:
Use StreamPlot for plotting only streamlines without a plot of the scalar field:
Use VectorDensityPlot to plot functions with vectors instead of streamlines:
Use ListVectorDensityPlot to plot data with vectors instead of streamlines:
Use VectorPlot to plot with vectors instead of streamlines without a plot of the scalar field:
Use VectorPlot3D to visualize 3D vector fields:
StreamDensityPlot samples more points where it needs to:
Scalar fields can be plotted by themselves with DensityPlot:
Use LineIntegralConvolutionPlot to plot the line integral convolution of a vector field:
Plot streamlines with the divergence as the background density:
Plot streamlines with the absolute value of the vorticity as the background density:
Constrain the stream plot to a variety of regions:
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