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

StreamPlot

 StreamPlot generates a stream plot of the vector field as a function of x and y. StreamPlotgenerates plots of several vector fields.
• StreamPlot plots streamlines that show the local direction of the vector field at each point.
• StreamPlot by default shows enough streamlines to achieve a roughly uniform density throughout the plot, and shows no background scalar field.
• StreamPlot does not show streamlines at any positions for which the etc. do not evaluate to real numbers.
• StreamPlot 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 EvaluationMonitor None expression to evaluate at every function evaluation Frame True whether to draw a frame around the plot FrameTicks Automatic frame tick marks 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
Plot the streamlines with arrows for the field :
Plot the streamlines with arrows for two fields:
Plot the streamlines with arrows for the field :
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Plot the streamlines with arrows for two fields:
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 Scope   (16)
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:
Plot multiple vector fields:
Use a specific number of mesh lines:
Specify specific mesh lines:
Use Evaluate to evaluate the vector field symbolically before numeric assignment:
Specify different dashings and arrowheads by settings to StreamScale:
Plot the streamlines with arrows colored according to the magnitude of the field:
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:
 Options   (102)
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:
Show where the vector field function is sampled:
Count the number of times the vector field function is evaluated:
Label the axes:
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:
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 directions:
Explicitly specify the scaling for each color function argument:
Specify a specific 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 norms:
Use any named color gradient from ColorData:
Color the vectors according to their values:
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 directions:
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, then 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:
Scale the vector length by the component 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   (17)
Streamlines for the gradient field of over the unit square:
Streamlines for the Hamiltonian vector field of :
Streamlines for the Polya vector field of :
Global attractor of damped conservative system:
Combine several examples into a tabbed view:
Mouseover the tabs to get a description of the vector field:
Quadratic system with two limit cycles:
Van der Pol Oscillator:
Characterize linear planar systems interactively:
Use a stream plot as a background for an interactive differential equation:
Unfolding a double zero eigenvalue:
Rotating pendulum:
A two-parameter potential:
Unfolding the elliptic umbilic:
Generate a list of rasterized stream 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 ListStreamPlot for plotting data:
Use StreamDensityPlot to add a density plot of the scalar field:
Use ListStreamDensityPlot for plotting data with a density plot of the scalar field:
Use VectorPlot to plot with vectors instead of streamlines:
Use LineIntegralConvolutionPlot to plot the line integral convolution of a vector field:
Use VectorPlot3D to visualize 3D vector fields:
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