StreamPlot3D

StreamPlot3D[{vx,vy,vz},{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]

plots streamlines for the vector field {vx,vy,vz} as functions of x, y and z.

StreamPlot3D[{vx,vy,vz},{x,y,z}reg]

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

Details and Options

Examples

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Basic Examples  (4)

Plot streamlines through a vector field in 3D:

Use tubes to show the streamlines:

Include a legend for the vector field magnitudes:

Plot streamlines over an arbitrary region:

Scope  (11)

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  (8)

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:

Options  (41)

BoxRatios  (2)

By default, BoxRatios is set to Automatic:

Make the box twice as long in the x direction:

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 ball:

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:

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:

Control the number of 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  (10)

Basic Applications  (1)

Consider a vector differential equation where f(x)=If[TemplateBox[{x}, Norm]<=1,x,{1,0,0}] is defined piecewise.

Visualize solutions of using seed points for the streamlines that are inside the unit sphere:

Fluid Flow  (3)

Consider Stokes flow for a point force of the form , where is a constant vector and is a Dirac delta function. For example, a force pointing down:

Define the fluid velocity vector , the pressure and the viscosity :

Confirm that the equations for Stokes flow are satisfied so that and :

Plot streamlines for the flow:

Visualize Stokes flow around a unit sphere. Define the fluid velocity vector , the pressure , the viscosity and the far-field fluid speed :

Confirm that the equations for Stokes flow are satisfied so that and :

Plot streamlines for the flow:

Plot the pressure for the flow:

Specify the NavierStokes equations for a fluid through a pipe with a bulge:

Specify the geometry for the flow:

Specify the boundary conditions for flow from left to right:

Solve for the flow velocities and pressure:

Specify seed points for the streamlines:

Plot the streamlines for the flow:

Electrical Systems  (1)

Visualize electric field lines for a dipole:

The streamlines appear to have uniform color because of the extremely rapid change in the vector field norm near the point charges at . Bounding the magnitude of the vector field norm with a region function makes the colors visible:

Add spheres to indicate the positive (red) and negative (black) point charges:

Arrows can be used to provide more information, but the colors change because arrow markers are colored by the field magnitude at the tip of the arrow:

Use a custom StreamColorFunction to exert more control over the colors:

Miscellaneous  (5)

Lorenz attractor:

Use ribbons or arrow ribbons to visualize the torsion of a twisted cubic:

Visualize solutions of differential equations on manifolds:

Visualize streamlines for Poiseuille flow. The fluid speed is fastest along the central axis:

Visualize solutions of Euler's equations for a rotating rigid body:

Properties & Relations  (10)

Use VectorPlot3D to visualize a field with discrete arrows:

Use StreamPlot to plot streamlines of 2D vector fields:

Use ListVectorPlot3D or ListStreamPlot3D to visualize data:

Plot vectors along surfaces with SliceVectorPlot3D:

Use VectorPlot for plotting 2D vectors:

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

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

Plot a complex function as a vector field:

Plot a complex function as a vector field using streamlines:

GeoStreamPlot plots streamlines on maps of the Earth:

Possible Issues  (3)

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), StreamPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/StreamPlot3D.html.

Text

Wolfram Research (2021), StreamPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/StreamPlot3D.html.

BibTeX

@misc{reference.wolfram_2021_streamplot3d, author="Wolfram Research", title="{StreamPlot3D}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/StreamPlot3D.html}", note=[Accessed: 27-November-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_streamplot3d, organization={Wolfram Research}, title={StreamPlot3D}, year={2021}, url={https://reference.wolfram.com/language/ref/StreamPlot3D.html}, note=[Accessed: 27-November-2021 ]}

CMS

Wolfram Language. 2021. "StreamPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/StreamPlot3D.html.

APA

Wolfram Language. (2021). StreamPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StreamPlot3D.html