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StreamPlot
  • See Also
    • VectorPlot
    • StreamPlot3D
    • StreamDensityPlot
    • ListStreamPlot
    • LineIntegralConvolutionPlot
    • ParametricPlot
    • ContourPlot
    • DensityPlot
    • Plot3D
    • VectorPlot3D
    • SliceVectorPlot3D
  • Related Guides
    • Vector Visualization
    • Function Visualization
    • Vector Analysis
    • Differential Equations
    • Solvers over Regions
    • See Also
      • VectorPlot
      • StreamPlot3D
      • StreamDensityPlot
      • ListStreamPlot
      • LineIntegralConvolutionPlot
      • ParametricPlot
      • ContourPlot
      • DensityPlot
      • Plot3D
      • VectorPlot3D
      • SliceVectorPlot3D
    • Related Guides
      • Vector Visualization
      • Function Visualization
      • Vector Analysis
      • Differential Equations
      • Solvers over Regions

StreamPlot[{vx,vy},{x,xmin,xmax},{y,ymin,ymax}]

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

StreamPlot[{{vx,vy},{wx,wy},…},{x,xmin,xmax},{y,ymin,ymax}]

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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Sampling  
Presentation  
Options  
AspectRatio  
Axes  
AxesLabel  
Show More Show More
AxesOrigin  
AxesStyle  
Background  
EvaluationMonitor  
ImageSize  
Mesh  
MeshFunctions  
MeshShading  
MeshStyle  
PerformanceGoal  
PlotLayout  
PlotLegends  
PlotRange  
PlotTheme  
RegionBoundaryStyle  
RegionFillingStyle  
RegionFunction  
ScalingFunctions  
StreamColorFunction  
StreamColorFunctionScaling  
StreamMarkers  
StreamPoints  
StreamScale  
StreamStyle  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • VectorPlot
    • StreamPlot3D
    • StreamDensityPlot
    • ListStreamPlot
    • LineIntegralConvolutionPlot
    • ParametricPlot
    • ContourPlot
    • DensityPlot
    • Plot3D
    • VectorPlot3D
    • SliceVectorPlot3D
  • Related Guides
    • Vector Visualization
    • Function Visualization
    • Vector Analysis
    • Differential Equations
    • Solvers over Regions
    • See Also
      • VectorPlot
      • StreamPlot3D
      • StreamDensityPlot
      • ListStreamPlot
      • LineIntegralConvolutionPlot
      • ParametricPlot
      • ContourPlot
      • DensityPlot
      • Plot3D
      • VectorPlot3D
      • SliceVectorPlot3D
    • Related Guides
      • Vector Visualization
      • Function Visualization
      • Vector Analysis
      • Differential Equations
      • Solvers over Regions

StreamPlot

StreamPlot[{vx,vy},{x,xmin,xmax},{y,ymin,ymax}]

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

StreamPlot[{{vx,vy},{wx,wy},…},{x,xmin,xmax},{y,ymin,ymax}]

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 is known as a streamline plot.
  • StreamPlot plots streamlines defined by and , where and is an initial stream point. The streamline is the curve passing through point , and whose tangents correspond to the vector field at each point.
  • The streamlines are colored by default according to the magnitude of the vector field and have an arrow in the direction of increasing value of .
  • 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 vi 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 vi 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 vi 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: [List of all options]
  • AspectRatio 1ratio of height to width
    EvaluationMonitor Noneexpression to evaluate at every function evaluation
    FrameTruewhether to draw a frame around the plot
    FrameTicksAutomaticframe tick marks
    MethodAutomaticmethods to use for the plot
    PerformanceGoal $PerformanceGoalaspects of performance to try to optimize
    PlotLayout Automatichow to position fields
    PlotLegends Nonelegends to include
    PlotRange {Full,Full}range of x, y values to include
    PlotRangePaddingAutomatichow much to pad the range of values
    PlotTheme $PlotThemeoverall theme for the plot
    RegionBoundaryStyle Automatichow to style plot region boundaries
    RegionFillingStyle Automatichow to style plot region interiors
    RegionFunction (True&)determine what region to include
    ScalingFunctions Nonehow to scale individual coordinates
    StreamColorFunction Automatichow to color streamlines
    StreamColorFunctionScaling Truewhether to scale the argument to StreamColorFunction
    StreamMarkers Automaticshape to use for streams
    StreamPoints Automaticdetermine number, placement, and closeness of streamlines
    StreamScale Automaticdetermine sizes and segmenting of individual streamlines
    StreamStyle Automatichow to draw streamlines
    WorkingPrecisionMachinePrecisionprecision to use in internal computations
  • The arguments supplied to functions in RegionFunction and StreamColorFunction are x, y, vx, vy, Norm[{vx,vy}].
  • 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
  • Possible settings for ScalingFunctions are:
  • {sx,sy}scale x and y axes
  • Common built-in scaling functions s include:
  • "Log"log scale with automatic tick labeling
    "Log10"base-10 log scale with powers of 10 for ticks
    "SignedLog"log-like scale that includes 0 and negative numbers
    "Reverse"reverse the coordinate direction
    "Infinite"infinite scale
  • List of all options

    • AlignmentPointCenterthe default point in the graphic to align with
      AspectRatio1ratio of height to width
      AxesFalsewhether to draw axes
      AxesLabelNoneaxes labels
      AxesOriginAutomaticwhere axes should cross
      AxesStyle{}style specifications for the axes
      BackgroundNonebackground color for the plot
      BaselinePositionAutomatichow to align with a surrounding text baseline
      BaseStyle{}base style specifications for the graphic
      ContentSelectableAutomaticwhether to allow contents to be selected
      CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
      Epilog{}primitives rendered after the main plot
      EvaluationMonitorNoneexpression to evaluate at every function evaluation
      FormatTypeTraditionalFormthe default format type for text
      FrameTruewhether to draw a frame around the plot
      FrameLabelNoneframe labels
      FrameStyle{}style specifications for the frame
      FrameTicksAutomaticframe tick marks
      FrameTicksStyle{}style specifications for frame ticks
      GridLinesNonegrid lines to draw
      GridLinesStyle{}style specifications for grid lines
      ImageMargins0.the margins to leave around the graphic
      ImagePaddingAllwhat extra padding to allow for labels etc.
      ImageSizeAutomaticthe absolute size at which to render the graphic
      LabelStyle{}style specifications for labels
      MethodAutomaticmethods to use for the plot
      PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
      PlotLabelNonean overall label for the plot
      PlotLayoutAutomatichow to position fields
      PlotLegendsNonelegends to include
      PlotRange{Full,Full}range of x, y values to include
      PlotRangeClippingFalsewhether to clip at the plot range
      PlotRangePaddingAutomatichow much to pad the range of values
      PlotRegionAutomaticthe final display region to be filled
      PlotTheme$PlotThemeoverall theme for the plot
      PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
      Prolog{}primitives rendered before the main plot
      RegionBoundaryStyleAutomatichow to style plot region boundaries
      RegionFillingStyleAutomatichow to style plot region interiors
      RegionFunction(True&)determine what region to include
      RotateLabelTruewhether to rotate y labels on the frame
      ScalingFunctionsNonehow to scale individual coordinates
      StreamColorFunctionAutomatichow to color streamlines
      StreamColorFunctionScalingTruewhether to scale the argument to StreamColorFunction
      StreamMarkersAutomaticshape to use for streams
      StreamPointsAutomaticdetermine number, placement, and closeness of streamlines
      StreamScaleAutomaticdetermine sizes and segmenting of individual streamlines
      StreamStyleAutomatichow to draw streamlines
      TicksAutomaticaxes ticks
      TicksStyle{}style specifications for axes ticks
      WorkingPrecisionMachinePrecisionprecision to use in internal computations

Examples

open all close 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  (22)

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  (12)

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:

Use a log scale for the x axis:

Reverse the y scale so it increases toward the bottom:

Options  (97)

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:

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  (6)

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 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:

ScalingFunctions  (2)

Use a log scale for the x axis:

Reverse the y scale so it increases toward the bottom:

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  (16)

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:

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:

See Also

VectorPlot  StreamPlot3D  StreamDensityPlot  ListStreamPlot  LineIntegralConvolutionPlot  ParametricPlot  ContourPlot  DensityPlot  Plot3D  VectorPlot3D  SliceVectorPlot3D

Related Guides

    ▪
  • Vector Visualization
  • ▪
  • Function Visualization
  • ▪
  • Vector Analysis
  • ▪
  • Differential Equations
  • ▪
  • Solvers over Regions

History

Introduced in 2008 (7.0) | Updated in 2012 (9.0) ▪ 2014 (10.0) ▪ 2018 (11.3) ▪ 2020 (12.1) ▪ 2020 (12.2) ▪ 2021 (13.0) ▪ 2022 (13.1)

Wolfram Research (2008), StreamPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/StreamPlot.html (updated 2022).

Text

Wolfram Research (2008), StreamPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/StreamPlot.html (updated 2022).

CMS

Wolfram Language. 2008. "StreamPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/StreamPlot.html.

APA

Wolfram Language. (2008). StreamPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StreamPlot.html

BibTeX

@misc{reference.wolfram_2025_streamplot, author="Wolfram Research", title="{StreamPlot}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/StreamPlot.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_streamplot, organization={Wolfram Research}, title={StreamPlot}, year={2022}, url={https://reference.wolfram.com/language/ref/StreamPlot.html}, note=[Accessed: 01-December-2025]}

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