WOLFRAM

plots streamlines for the vector field given as an array of vectors.

Details and Options

Examples

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Basic Examples  (4)Summary of the most common use cases

Plot the vector field interpolated from a specified set of vectors:

Out[2]=2

Include a legend showing the field strength:

Out[1]=1

Use tubes to represent the streamlines:

Out[1]=1

Specify the range of the data:

Out[1]=1

Scope  (12)Survey of the scope of standard use cases

Sampling  (3)

Specify the density of seed points for the streamlines:

Out[28]=28

Specify specific seed points for the streamlines:

Out[1]=1

Plot streamlines over a specified region:

Out[1]=1

Presentation  (9)

Streamlines are drawn as lines by default:

Out[44]=44

Use 3D tubes for the streamlines:

Out[17]=17

Use flat ribbons:

Out[1]=1

Use "arrow" versions of the stream markers to indicate the direction of flow along the streamlines:

Out[1]=1

Arrows on tubes:

Out[2]=2

Ribbons are turned into arrows by tapering the heads and notching the tails of the streamlines:

Out[3]=3

Use a single color for the streamlines:

Out[1]=1

Use a named color gradient for the streamlines:

Out[1]=1

Include a legend for the field magnitude:

Out[1]=1

Use StreamScale to split streamlines into multiple shorter line segments:

Out[1]=1
Out[2]=2

Increase the number of points in each segment and increase the marker aspect ratio:

Out[1]=1

Use a theme:

Out[1]=1

Use a log scale in the z direction:

Out[1]=1

Options  (46)Common values & functionality for each option

BoxRatios  (2)

By default, BoxRatios is set to Automatic:

Out[2]=2

Make the box twice as long in the x direction:

Out[1]=1

DataRange  (2)

By default, the data range is taken to be the index range of the data array:

Out[3]=3

Specify the data range for the domain:

Out[1]=1

PlotLegends  (3)

No legends are included by default:

Out[1]=1

Include a legend that indicates the vector field norm:

Out[1]=1

Specify the location of the legend:

Out[1]=1

PlotTheme  (1)

Specify a theme:

Out[19]=19

RegionBoundaryStyle  (4)

Show the region defined by a RegionFunction:

Out[7]=7

Use None to avoid showing the boundary:

Out[1]=1

Specify the color of the region boundary:

Out[1]=1

The boundaries of full rectangular regions are not shown:

Out[1]=1

RegionFunction  (4)

Plot streamlines in a restricted region:

Out[14]=14

Plot streams only where the field magnitude exceeds a given threshold:

Out[1]=1

Region functions depend, in general, on seven arguments:

Out[1]=1

Use RegionBoundaryStyleNone to avoid showing the boundary:

Out[1]=1

ScalingFunctions  (3)

By default, linear scales are used:

Out[2]=2

Use a log scale in the z direction:

Out[1]=1

Reverse the direction of the z direction:

Out[1]=1

StreamColorFunction  (4)

Color the streams by their norm:

Out[2]=2

Use any named color gradient from ColorData:

Out[1]=1

Color the streamlines according to their x value:

Out[1]=1

Use StreamColorFunctionScalingFalse to get unscaled values:

Out[1]=1

StreamColorFunctionScaling  (2)

By default, scaled values are used:

Out[3]=3

Use StreamColorFunctionScalingFalse to get unscaled values:

Out[1]=1

StreamMarkers  (5)

By default, lines are used:

Out[5]=5

Draw the streamlines as tubes:

Out[1]=1

Draw them as flat ribbons:

Out[2]=2

"Arrow" stream markers automatically break the streamlines into shorter segments:

Out[1]=1

Use 3D arrowheads on tubes:

Out[2]=2

Use directional ribbons:

Out[3]=3

Make segmented markers continuous:

Out[1]=1

Break continuous markers into segments:

Out[1]=1

StreamPoints  (4)

Use automatically determined stream points to seed the curves:

Out[7]=7

Specify a maximum number of streamlines:

Out[1]=1

Give specific seed points for the streams:

Out[1]=1

Use coarsely spaced streamlines:

Out[1]=1

Use more finely spaced streamlines:

Out[2]=2

StreamScale  (9)

Segmented markers have default lengths, numbers of points and aspect ratios:

Out[22]=22

Modify the lengths of the segments:

Out[1]=1

Specify the number of sample points in each segment:

Out[1]=1

Modify the aspect ratios for the stream markers:

Out[1]=1

Make segmented markers continuous:

Out[1]=1

Break continuous markers into segments:

Out[1]=1

The aspect ratio controls the thickness of ribbons and tubes:

Out[1]=1
Out[2]=2
Out[3]=3

The aspect ratio controls the sizes of arrowheads:

Out[1]=1

Use three points in each segment:

Out[1]=1

StreamStyle  (3)

Change the appearance of the streamlines:

Out[14]=14

StreamColorFunction takes precedence over StreamStyle:

Out[1]=1

Use StreamColorFunctionNone to specify a streamline color with StreamStyle:

Out[1]=1

Applications  (2)Sample problems that can be solved with this function

Numerically compute the electric field at a sampling of points under the influence of two thin wires of finite length with equal constant charge densities and opposite signs:

Visualize the electric field along with the positively charged (black) and the negatively charged (red) wires:

Out[5]=5

Visualize time-independent heat flow in a unit cube. Consider the steady-state heat equation for the temperature on the unit cube with on the face, insulated on the , , and faces, inside a centered disk of radius 0.3 on the face and outside the disk as shown in the following:

Use finite differences to discretize the heat equation :

Specify boundary conditions for on the and faces:

Specify the insulated boundary conditions for on the other faces:

Solve the system of equations:

Use finite differences to approximate the heat flux:

Generate seed points for the streamlines on the face:

Generate seed points for the streamlines in the red disk on the face:

Visualize the heat flow. The boundary temperatures are specified in the legend, and the blank faces of the cube are insulated:

Out[9]=9

Properties & Relations  (10)Properties of the function, and connections to other functions

Use StreamPlot3D and VectorPlot3D to visualize functions:

Out[1]=1

Use StreamPlot and VectorPlot to visualize functions in 2D:

Out[1]=1

Plot vectors along surfaces with ListSliceVectorPlot3D:

Out[2]=2

Use ListVectorPlot3D to plot a 3D field as discrete vectors:

Out[2]=2

Use ListVectorPlot for plotting 2D vectors:

Out[2]=2

Use ListStreamPlot to plot with streamlines instead of vectors:

Out[2]=2

Use ListVectorDensityPlot or ListStreamDensityPlot to add a density plot of a scalar field:

Out[2]=2

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

Out[3]=3

Use ListVectorDisplacementPlot3D to visualize a deformation in 3D:

Out[4]=4

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

Out[2]=2

Use GeoVectorPlot to plot vectors on a map:

Out[1]=1

Use GeoStreamPlot to plot streamlines instead of vectors:

Out[2]=2

Possible Issues  (2)Common pitfalls and unexpected behavior

Tube StreamMarkers can be distorted by the BoxRatios:

Out[3]=3

Carefully adjusting the BoxRatios can eliminate the tube distortion:

Out[4]=4

The colors of "Arrow" and "Arrow3D" stream markers are determined at the tip of the arrow, which can result in inconsistent colors for long arrows:

Out[1]=1
Out[2]=2
Wolfram Research (2021), ListStreamPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/ListStreamPlot3D.html (updated 2022).
Wolfram Research (2021), ListStreamPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/ListStreamPlot3D.html (updated 2022).

Text

Wolfram Research (2021), ListStreamPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/ListStreamPlot3D.html (updated 2022).

Wolfram Research (2021), ListStreamPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/ListStreamPlot3D.html (updated 2022).

CMS

Wolfram Language. 2021. "ListStreamPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/ListStreamPlot3D.html.

Wolfram Language. 2021. "ListStreamPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/ListStreamPlot3D.html.

APA

Wolfram Language. (2021). ListStreamPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ListStreamPlot3D.html

Wolfram Language. (2021). ListStreamPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ListStreamPlot3D.html

BibTeX

@misc{reference.wolfram_2025_liststreamplot3d, author="Wolfram Research", title="{ListStreamPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/ListStreamPlot3D.html}", note=[Accessed: 04-June-2025 ]}

@misc{reference.wolfram_2025_liststreamplot3d, author="Wolfram Research", title="{ListStreamPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/ListStreamPlot3D.html}", note=[Accessed: 04-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_liststreamplot3d, organization={Wolfram Research}, title={ListStreamPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/ListStreamPlot3D.html}, note=[Accessed: 04-June-2025 ]}

@online{reference.wolfram_2025_liststreamplot3d, organization={Wolfram Research}, title={ListStreamPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/ListStreamPlot3D.html}, note=[Accessed: 04-June-2025 ]}