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StreamScale—Wolfram Documentation

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StreamScale

is an option to StreamPlot, ListStreamPlot, and related functions that determines the length and arrowhead size of streamlines that are drawn.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
Neat Examples  
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StreamScale

StreamScale

is an option to StreamPlot, ListStreamPlot, and related functions that determines the length and arrowhead size of streamlines that are drawn.

Details

  • StreamPlot and related functions effectively find streamlines by following the flow of the vector field. StreamScale determines how the streamlines found should be segmented for display.
  • Each streamline segment is rendered as an Arrow, with its own arrowhead.
  • The following settings can be given for StreamScale:
  • Automaticautomatically determine streamline scale
    Nonedraw no arrows for streamlines
    Fulluse full streamlines without segmentation
    {seg,npts,aratio,sfun}use explicit specification of streamline scaling
  • The setting StreamScale->{seg,npts,aratio,sfun} allows explicit specification of how streamlines should be broken into segments, and how each segment should be scaled.
  • The parameter seg is analogous to a Dashing specification for segments of a streamline. The following forms can be used:
  • sequivalent to {s,s/15}
    {s1,s2,…}successive line segments of length s1, s2, …, with every other segment rendered and repeated cyclically
    Large,Medium,Small,Tinyuse large, medium, etc. segment lengths
  • The following settings can be used for npts to control the number of points rendered on each streamline segment:
  • 2use two points, giving a straight streamline segment
    nuse up to n points for each streamline segment
    Alluse all computed points for each streamline segment
    Automaticuse an automatic method based on curve simplification
  • Every streamline segment effectively lies in a curved strip, with the arrowhead for the segment spanning one end of the strip.
  • The following settings can be used for aratio to control the aspect ratio of the streamline strip:
  • rabsolute aspect ratio relative to the longest line segment
    Scaled[r]relative aspect ratio relative to each line segment
    Automaticautomatic method based on the number points
  • After the length of segments is determined by seg, they can be rescaled by applying the function sfun. The following settings can be used:
  • Nonedo no rescaling
    funca function of x, y, vx, vy, Norm[{vx,vy}]
    Automaticautomatically determine rescaling

Examples

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Basic Examples  (3)

Specify the length of streamline segments to use:

Wolfram Language code: Table[StreamPlot[{Sin[x], Cos[y]}, {x, -Pi, Pi}, {y, -Pi, Pi}, StreamScale -> s], {s, {Tiny, Large}}]

Specify the number of points used per segment:

Wolfram Language code: Table[StreamPlot[{y, -Sin[x]}, {x, 0, 2π}, {y, -2, 2}, StreamScale -> {Large, n, Automatic}], {n, {3, 6}}]

Specify the size of the arrows used:

Wolfram Language code: Table[StreamPlot[{Sin[x], Cos[y]}, {x, -Pi, Pi}, {y, -Pi, Pi}, StreamPoints -> 10, StreamScale -> {Automatic, Automatic, a}], {a, {.02, .04}}]
Wolfram Language code: Table[StreamPlot[{Sin[x], Cos[y]}, {x, -Pi, Pi}, {y, -Pi, Pi}, StreamPoints -> 10, StreamScale -> {Full, Automatic, a}], {a, {.02, .04}}]

Scope  (3)

Use curves for the streamlines:

Wolfram Language code: StreamPlot[{Sin[x], Cos[y]}, {x, -Pi, Pi}, {y, -Pi, Pi}, StreamScale -> None]

Use a single segment for each streamline:

Wolfram Language code: StreamPlot[{Sin[x], Cos[y]}, {x, -Pi, Pi}, {y, -Pi, Pi}, StreamScale -> Full]

Use larger arrowheads:

Wolfram Language code: StreamPlot[{Sin[x], Cos[y]}, {x, -Pi, Pi}, {y, -Pi, Pi}, StreamScale -> {Full, All, .05}]

When the number of points per segment is set to 2, scaled arrows are used:

Wolfram Language code: StreamPlot[{y, x - x ^ 2}, {x, -1, 2}, {y, -1.5, 1.5}, StreamScale -> {Automatic, 2, Automatic}]

Scale the length of the arrows by the coordinate:

Wolfram Language code: StreamPlot[{y, x - x ^ 2}, {x, -1, 2}, {y, -1.5, 1.5}, StreamScale -> {Automatic, 2, Automatic, #2&}]

Properties & Relations  (1)

Show all line strips:

Wolfram Language code: h[x_, y_] := {3 * x * y * Cos[Norm[{x, y}]] + x * y * Norm[{x, y}] * Sin[Norm[{x, y}]], (2 * y ^ 2 - x ^ 2) * Cos[Norm[{x, y}]] - x * x * Norm[{x, y}] * Sin[Norm[{x, y}]]} StreamPlot[h[x, y], {x, -3Pi, 3Pi}, {y, -3Pi, 3Pi}, StreamStyle -> "ControlPoints"]

Neat Examples  (1)

Magnetic dipole field:

Wolfram Language code: h[x_, y_] := {3 * x * y * Cos[Norm[{x, y}]] + x * y * Norm[{x, y}] * Sin[Norm[{x, y}]], (2 * y ^ 2 - x ^ 2) * Cos[Norm[{x, y}]] - x * x * Norm[{x, y}] * Sin[Norm[{x, y}]]}
Wolfram Language code: Plot3D[Norm@h[x, y], {x, -3Pi, 3Pi}, {y, -3Pi, 3Pi}]
Wolfram Language code: StreamPlot[h[x, y], {x, -3Pi, 3Pi}, {y, -3Pi, 3Pi}]
Wolfram Research (2008), StreamScale, Wolfram Language function, https://reference.wolfram.com/language/ref/StreamScale.html.

Text

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

CMS

Wolfram Language. 2008. "StreamScale." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/StreamScale.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_streamscale, author="Wolfram Research", title="{StreamScale}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/StreamScale.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_streamscale, organization={Wolfram Research}, title={StreamScale}, year={2008}, url={https://reference.wolfram.com/language/ref/StreamScale.html}, note=[Accessed: 14-November-2026]}