StreamPlot

StreamPlot[{v_x,v_y},{x,x_min,x_max},{y,y_min,y_max}]

generates a stream plot of the vector field {v_x,v_y} as a function of x and y.

StreamPlot[{{v_x,v_y},{w_x,w_y},…},{x,x_min,x_max},{y,y_min,y_max}]

generates plots of several vector fields.

StreamPlot[…,{x,y}∈reg]

takes the variables {x,y} to be in the geometric region reg.

Details and Options

StreamPlot plots streamlines that show the local direction of the vector field at each point, effectively solving the system of differential equations and then plotting .
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 v_i etc. do not evaluate to real numbers.
StreamPlot treats the variables x and y as local, effectively using Block.
StreamPlot has attribute HoldAll, and evaluates the v_i 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 v_i etc. symbolically before specific numerical values are assigned to x and y.
StreamPlot has the same options as Graphics, with the following additions and changes:

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
PlotLayout	Automatic	how to position fields
PlotLegends	None	legends to include
PlotRange	{Full,Full}	range of x, y values to include
PlotRangePadding	Automatic	how much to pad the range of values
PlotTheme	$PlotTheme	overall theme for the plot
RegionBoundaryStyle	Automatic	how to style plot region boundaries
RegionFillingStyle	Automatic	how to style plot region interiors
RegionFunction	(True&)	determine what region to include
StreamColorFunction	Automatic	how to color streamlines
StreamColorFunctionScaling	True	whether to scale the argument to StreamColorFunction
StreamMarkers	Automatic	shape to use for streams
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 arguments supplied to functions in RegionFunction and StreamColorFunction are x, y, v_x, v_y, Norm[{v_x,v_y}].
Possible settings for PlotLayout that show single streamlines in multiple plot panels include:

	"Column"	use separate streamlines in a column of panels
	"Row"	use separate streamlines in a row of panels
	{"Column",k},{"Row",k}	use k columns or rows
	{"Column",UpTo[k]},{"Row",UpTo[k]}	use at most k columns or rows

Examples

open allclose all

Basic Examples (4)

Plot the streamlines with arrows for the field :

Include a legend for the field magnitude:

Visualize streamlines as unbroken lines:

Use a multi-panel layout to show multiple vector fields at the same time:

Scope (21)

Sampling (10)

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:

The domain may be specified by a region:

The domain may be specified by a MeshRegion:

Presentation (11)

Specify different dashings and arrowheads by setting to StreamScale:

Plot the streamlines with arrows colored according to the magnitude of the field:

Apply a variety of streamline styles:

Use a theme with axes:

Override the style from the theme:

Use a named appearance to draw the streamlines:

Style the streamlines as well:

Specify mesh lines with different styles:

Specify global mesh line styles:

Shade mesh regions cyclically:

Apply a variety of styles to region boundaries:

Show multiple functions as densities in separate panels:

Use a column instead of a row:

Add a legend with placeholder text:

Use the vector fields as legend labels:

Use explicit labels for each vector field:

Options (95)

AspectRatio (3)

By default, StreamPlot uses the same width and height:

Use numerical value to specify the height to width ratio:

AspectRatioAutomatic determines the ratio from the plot ranges:

Axes (4)

By default, StreamPlot uses a frame instead of axes:

Use axes instead of a frame:

Use AxesOrigin to specify where the axes intersect:

Turn each axis on individually:

AxesLabel (3)

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

AxesOrigin (2)

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

AxesStyle (4)

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

Background (1)

Use colored backgrounds:

EvaluationMonitor (2)

Show where the vector field function is sampled:

Count the number of times the vector field function is evaluated:

FrameLabel (1)

Label the axes:

ImageSize (5)

Use named sizes such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Use maximum sizes for the width and height:

Mesh (5)

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:

MeshFunctions (3)

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:

MeshShading (3)

Use None to remove regions:

Styles are used cyclically:

Use indexed colors from ColorData cyclically:

MeshStyle (1)

Apply a variety of styles to the mesh lines:

PerformanceGoal (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLayout (2)

Place each group of vectors in a separate panel using shared axes:

Use a row instead of a column:

Use multiple columns or rows:

Prefer full columns or rows:

PlotLegends (5)

No legends are included by default:

Include a legend to show the color range of field norms:

Control the placement of the legend:

Include a legend for multiple fields:

Use the vector fields as the legend text:

Use placeholder text:

Change the appearance of the legend:

PlotRange (5)

The full plot range is used by default:

Specify an explicit limit for both and ranges:

Specify an explicit range:

Specify different and ranges:

PlotTheme (2)

Use a theme with simpler ticks and brighter colors:

Use a theme with dense streamlines:

Change the stream styles:

RegionBoundaryStyle (2)

By default, region boundaries are styled:

Show no boundaries and filling:

Apply a variety of styles to region boundaries:

RegionFillingStyle (1)

By default, region filling is styled:

Show no filling:

RegionFunction (3)

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:

StreamColorFunction (5)

By default, 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:

StreamColorFunctionScaling (4)

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:

StreamMarkers (7)

Streamlines are drawn as arrows by default:

Use a named appearance to draw the streamlines:

Use different markers for different vector fields:

Named arrow styles:

Named dot styles:

Named pointer styles:

Named dart styles:

StreamPoints (6)

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:

StreamScale (9)

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:

StreamStyle (5)

StreamColorFunction has precedence over colors specified in StreamStyle:

Set StreamColorFunctionNone to specify colors with StreamStyle:

Apply a variety of styles to the streamlines:

Specify a custom arrowhead:

Set the style for multiple vector fields:

Applications (17)

Streamlines for the gradient field of over the unit square:

Streamlines for the Hamiltonian vector field of :

Global attractor of damped conservative system:

Combine several examples into a tabbed view:

Mouse over 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 solution plotter:

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:

Specify the geometry for a fluid flow:

Specify the boundary conditions for a flow that enters at the left-hand channel and exits through the two right-hand channels:

Define the Navier–Stokes equations:

Use the finite element method to solve for the steady flow velocities and pressure:

Use DensityPlot to plot the pressure and StreamPlot to plot the flow:

Properties & Relations (11)

Use ListStreamPlot for plotting data:

Use VectorPlot to plot with vectors instead of streamlines:

Use ListVectorPlot to generate a plot based on data:

Use StreamPlot3D to plot streamlines of 3D vector fields:

Use ListStreamPlot3D to plot streamlines based on data:

Use StreamDensityPlot to add a density plot of the scalar field:

Use VectorDensityPlot to plot vectors instead of streamlines:

Use ListStreamDensityPlot to generate a plot based on data:

Use ListVectorDensityPlot to plot arrows instead of streamlines:

Use LineIntegralConvolutionPlot to plot the line integral convolution of a vector field:

Use VectorDisplacementPlot to visualize the deformation of a region associated with a displacement vector field:

Use ListVectorDisplacementPlot to visualize the same deformation based on data:

Use VectorPlot3D to visualize 3D vector fields:

Use ListVectorPlot3D to generate a plot based on data:

Plot vectors on surfaces with SliceVectorPlot3D:

Plot vectors based on data:

Use VectorDisplacementPlot3D to visualize the deformation of a 3D region associated with a displacement vector field:

Use ListVectorDisplacementPlot3D to visualize the same deformation based on data:

Plot a complex function as a vector field using streamlines:

Use vectors instead of streamlines:

Use GeoVectorPlot to plot vectors on a map:

Use GeoStreamPlot to plot streamlines instead of vectors:

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