ListStreamPlot3D

ListStreamPlot3D[varr]

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

Details and Options

Examples

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Basic Examples  (4)

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

Include a legend showing the field strength:

Use tubes to represent the streamlines:

Specify the range of the data:

Scope  (12)

Sampling  (3)

Specify the density of seed points for the streamlines:

Specify specific seed points for the streamlines:

Plot streamlines over a specified region:

Presentation  (9)

Streamlines are drawn as lines by default:

Use 3D tubes for the streamlines:

Use flat ribbons:

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

Arrows on tubes:

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

Use a single color for the streamlines:

Use a named color gradient for the streamlines:

Include a legend for the field magnitude:

Use StreamScale to split streamlines into multiple shorter line segments:

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

Use a theme:

Use a log scale in the z direction:

Options  (46)

BoxRatios  (2)

By default, BoxRatios is set to Automatic:

Make the box twice as long in the x direction:

DataRange  (2)

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

Specify the data range for the domain:

PlotLegends  (3)

No legends are included by default:

Include a legend that indicates the vector field norm:

Specify the location of the legend:

PlotTheme  (1)

Specify a theme:

RegionBoundaryStyle  (4)

Show the region defined by a RegionFunction:

Use None to avoid showing the boundary:

Specify the color of the region boundary:

The boundaries of full rectangular regions are not shown:

RegionFunction  (4)

Plot streamlines in a restricted region:

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

Region functions depend, in general, on seven arguments:

Use RegionBoundaryStyleNone to avoid showing the boundary:

ScalingFunctions  (3)

By default, linear scales are used:

Use a log scale in the z direction:

Reverse the direction of the z direction:

StreamColorFunction  (4)

Color the streams by their norm:

Use any named color gradient from ColorData:

Color the streamlines according to their x value:

Use StreamColorFunctionScalingFalse to get unscaled values:

StreamColorFunctionScaling  (2)

By default, scaled values are used:

Use StreamColorFunctionScalingFalse to get unscaled values:

StreamMarkers  (5)

By default, lines are used:

Draw the streamlines as tubes:

Draw them as flat ribbons:

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

Use 3D arrowheads on tubes:

Use directional ribbons:

Make segmented markers continuous:

Break continuous markers into segments:

StreamPoints  (4)

Use automatically determined stream points to seed the curves:

Specify a maximum number of streamlines:

Give specific seed points for the streams:

Use coarsely spaced streamlines:

Use more finely spaced streamlines:

StreamScale  (9)

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

Modify the lengths of the segments:

Specify the number of sample points in each segment:

Modify the aspect ratios for the stream markers:

Make segmented markers continuous:

Break continuous markers into segments:

The aspect ratio controls the thickness of ribbons and tubes:

The aspect ratio controls the sizes of arrowheads:

Use three points in each segment:

StreamStyle  (3)

Change the appearance of the streamlines:

StreamColorFunction takes precedence over StreamStyle:

Use StreamColorFunctionNone to specify a streamline color with StreamStyle:

Applications  (2)

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:

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:

Properties & Relations  (10)

Use StreamPlot3D and VectorPlot3D to visualize functions:

Use StreamPlot and VectorPlot to visualize functions in 2D:

Plot vectors along surfaces with ListSliceVectorPlot3D:

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

Use ListVectorPlot for plotting 2D vectors:

Use ListStreamPlot to plot with streamlines instead of vectors:

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

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

Use ListVectorDisplacementPlot3D to visualize a deformation in 3D:

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

Use GeoVectorPlot to plot vectors on a map:

Use GeoStreamPlot to plot streamlines instead of vectors:

Possible Issues  (2)

Tube StreamMarkers can be distorted by the BoxRatios:

Carefully adjusting the BoxRatios can eliminate the tube distortion:

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:

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).

CMS

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

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: 25-May-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: 25-May-2025 ]}