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ComplexVectorPlot

✖
ComplexVectorPlot[f,{z,zmin,zmax}]

generates a vector plot of the vector field {Re[f],Im[f]} over the complex rectangle with corners zmin and zmax.

✖
ComplexVectorPlot[{f1,f2,…},{z,zmin,zmax}]

plots several vector fields.

Details and Options

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Plot the vector field for with color indicating the vector magnitude:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-6cxjl
Out[1]=1

Include a legend for the vector magnitudes:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-sgxlon
Out[1]=1

Use a drop-shaped marker to represent the vectors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-62np7l
Out[1]=1

Scope  (19)Survey of the scope of standard use cases

Sampling  (7)

Plot a vector field with vectors placed with specified densities:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-bnkdo9
Out[1]=1

Sample the vector field on a regular grid of points:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-jnswso
Out[1]=1

Sample the vector field on an irregular mesh:

In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-gm12d0
Out[2]=2

Specify how many vector points to use in each direction:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-6tjb00
Out[1]=1

Plot the vectors that go through a set of seed points:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-bpn1i8
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-howfal
Out[2]=2

Plot vectors over a specified region:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-lvahe5
Out[1]=1

Plot the fields for a function and its conjugate:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-zc12x
Out[1]=1

Use Evaluate to evaluate the vector field symbolically before numeric assignment:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-dzznsr
Out[1]=1

Presentation  (12)

Plot a vector field with automatically scaled arrows:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-bs9khg
Out[1]=1

Plot a vector field with arrows of specified size:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-3obw1y
Out[1]=1

Draw the arrows starting from the sample points:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-y0g4bu
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-2zlizz
Out[2]=2

Draw the arrows without the arrowheads:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-fzve6t
Out[1]=1

Use drop-like shapes instead of arrows:

In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-1zp5de
Out[2]=2

Change the overall shape of the markers:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-oc0qdy
Out[1]=1

Change the default color function:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-v6aid7
Out[1]=1

Include a legend:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-2kyz35
Out[1]=1

Vary the arrow sizes instead of the colors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-cvzhyi
Out[1]=1

Set the style for multiple vector fields:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-n89e4w
Out[1]=1

Apply vector style:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-pblujj
Out[1]=1

Set the style for multiple vector fields:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-om0hcz
Out[1]=1

Use a theme with simple ticks and grid lines:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-fboha9
Out[1]=1

Options  (65)Common values & functionality for each option

Background  (1)

Use a colored background:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-bkxb9f
Out[1]=1

ClippingStyle  (4)

By default, extremely short and extremely long vectors are displayed:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-dxfsnw
Out[1]=1

Use ClippingStyleNone to remove extreme vectors from the plot:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-f7s8c3
Out[1]=1

Style the clipped vectors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-edm9pg
Out[1]=1

Style the short and long clipped vectors differently:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-b6iwnl
Out[1]=1

EvaluationMonitor  (2)

Show where the vector field function is sampled:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-d8kukt
Out[1]=1

Count the number of times the vector field function is evaluated:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-c385n4
Out[1]=1

PlotLegends  (5)

Include a legend for the vector norms:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-js95u9
Out[1]=1

Use the expressions in the legend for multiple vector functions:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-ba8k3h
Out[1]=1

Specify the legend labels for multiple functions:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-n2fvi5
Out[1]=1

Control the placement of the legend:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-cvx3dl
Out[1]=1

Use a legend with placeholders:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-m36w5m
Out[1]=1

PlotRange  (5)

The full plot range is used by default:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-g6xoyw
Out[1]=1

Specify an explicit limit for both real and imaginary ranges:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-5on0y
Out[1]=1

Specify an explicit real range:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-i4n6y8
Out[1]=1

Specify an explicit imaginary range:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-xat4r
Out[1]=1

Specify different real and imaginary ranges:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-f1lr1g
Out[1]=1

PlotTheme  (2)

Use a theme:

In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-ezofsx
Out[2]=2

Change the vector style:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-ealv4w
Out[1]=1

RegionBoundaryStyle  (5)

Show the region defined by a region function:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-d6s6um
Out[1]=1

The boundaries of full rectangular regions are not shown:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-7wf5ba
Out[1]=1

Use None to not show the boundary:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-d87zny
Out[1]=1

Omit the interior filling as well:

In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-gr12m6
Out[2]=2

Specify a style for the boundary:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-dd19je
Out[1]=1

Specify a style for full rectangular regions:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-ozzhd4
Out[1]=1

RegionFillingStyle  (5)

Show the region defined by a region function:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-b1r4jl
Out[1]=1

The interiors of full rectangular regions are not shown:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-cxnsd5
Out[1]=1

Use None to not show the interior filling:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-clzxe7
Out[1]=1

Omit the boundary curve as well:

In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-f27m9u
Out[2]=2

Specify a style for the interior filling:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-uquau7
Out[1]=1

Specify a style for full rectangular region:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-f0shd2
Out[1]=1

RegionFunction  (2)

Restrict the plotting region based on :

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-beqsd2
Out[1]=1

Restrict the plotting region based on :

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-d47ora
Out[1]=1

VectorAspectRatio  (2)

The default ratio of the width to the length of the vector marker is 1/4:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-6j8ah
Out[1]=1

Modify the ratio of the width to the length of the vector marker:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-bg45yi
Out[1]=1

VectorColorFunction  (5)

Vectors are colored according to their norms by default:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-b7adpr
Out[1]=1

Choose the color scheme for coloring vectors by their norms:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-cdiw5o
Out[1]=1

Use any named color gradient from ColorData:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-dsi8pl
Out[1]=1

Color the vectors according to the real part of its location:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-bw7lma
Out[1]=1

Color the vectors according to the real part of the function:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-lf15n
Out[1]=1

VectorColorFunctionScaling  (2)

By default, scaled values are used:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-c7h4ae
Out[1]=1

Use VectorColorFunctionScalingFalse to get unscaled values:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-drzoi2
Out[1]=1

VectorMarkers  (4)

Vectors are drawn as arrows by default:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-d31ee2
Out[1]=1

Use a named appearance to draw the vectors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-kk973g
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-et2q04
Out[2]=2

Use different markers for different vector fields:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-i7fp68
Out[1]=1

By default, markers are centered on vector points:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-dfllwr
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-lfxai2
Out[2]=2

Start the vectors at the points:

In[3]:=3
✖
https://wolfram.com/xid/0n4i0sam2ea-opwap5
Out[3]=3

End the vectors at the points:

In[4]:=4
✖
https://wolfram.com/xid/0n4i0sam2ea-iweszu
Out[4]=4

VectorPoints  (5)

Use automatically determined vector points:

In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-bkxnrk
Out[2]=2

Use symbolic names to specify the set of field vectors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-dhad3u
Out[1]=1

Create a hexagonal grid of field vectors with the same number of arrows in the real and imaginary directions:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-lp1zg
Out[1]=1

Create a hexagonal grid of field vectors with a different number of arrows in the real and imaginary directions:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-e0q7cn
Out[1]=1

Specify a list of points for showing field vectors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-fkgaai
Out[1]=1

VectorRange  (6)

By default, vector ranges are determined automatically:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-fdojbp
Out[1]=1

Plot vectors with magnitudes between 0.2 and 2:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-m4l3r
Out[1]=1

Plot vectors with magnitudes between 0.2 and 2 with scaled arrow lengths:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-gthzzm
Out[1]=1

Style the clipped vectors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-y3wfh
Out[1]=1

Plot scaled vectors with all lengths:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-g9h1vr
Out[1]=1

Increase the lengths of the smaller vectors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-fljz8c
Out[1]=1

VectorScaling  (2)

By default, VectorScaling is None:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-ml02wa
Out[1]=1

Use automatic scaling to scale the length of vectors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-84w8x5
Out[1]=1

VectorSizes  (2)

Vector markers have automatically scaled lengths to prevent any vectors from being too small and to keep them from overlapping:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-c77jdr
Out[1]=1

Specify a minimum and maximum scaled vector size:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-c6wdj4
Out[1]=1

VectorStyle  (6)

Set the style for the displayed vectors:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-hnrejz
Out[1]=1

Set the style for multiple functions:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-fqpqa1
Out[1]=1

Use Arrowheads to specify an explicit style of the arrowheads:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-bjd7u
Out[1]=1

Specify both arrow tail and head:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-f4aho
Out[1]=1

Graphics primitives without Arrowheads are scaled based on the vector scale:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-dmphsg
Out[1]=1

Change the scaling using the VectorScaling option:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-i0vjuu
Out[1]=1

Applications  (7)Sample problems that can be solved with this function

For a complex function f, plot {Re[f],Im[f]}:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-de7yae
Out[1]=1

The vector length increases with Abs[f] and the orientation is determined by Arg[f]:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-c2tmq2
Out[1]=1

Identify poles and zeros. Poles are visible at and :

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-lm37cf
Out[1]=1

The zeros at and are more readily visible if the vectors are scaled:

In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-bftb2b
Out[2]=2

Vectors in the field rotate twice along the unit circle surrounding the zero of the function at the origin, which implies that has a double zero at the origin:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-gqfooa
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-lftmd9
In[3]:=3
✖
https://wolfram.com/xid/0n4i0sam2ea-dz4b1
Out[3]=3

The function has a pole of order 2 at since has a double zero:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-fb86wg
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-g66tey
Out[2]=2

Specify a direction field and several solutions for the complex initial value problem , :

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-fhs1yu
Out[1]=1

The Pólya field of an analytic function is both divergence and curl free:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-t15cu
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-7ibeo
Out[2]=2
Out[2]=2
Out[2]=2

Examine partial sums of an infinite series:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-f2wpwi
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-f0vzlx
Out[2]=2

Properties & Relations  (15)Properties of the function, and connections to other functions

ComplexVectorPlot is a special case of VectorPlot:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-cb87oq
Out[1]=1

ComplexStreamPlot plots complex numbers as streamlines:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-7studa
Out[1]=1

ComplexStreamPlot is a special case of StreamPlot:

In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-c53rr6
Out[2]=2

Use VectorDisplacementPlot to visualize the effect of a complex function on a specified region:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-kx8huh
Out[1]=1

Use VectorPlot3D and StreamPlot3D to visualize 3D vector fields:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-h3ykri
Out[1]=1

ComplexContourPlot plots curves over the complexes:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-pesif0
Out[1]=1

ComplexRegionPlot plots regions over the complexes:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-ko83ut
Out[1]=1

ComplexPlot shows the argument and magnitude of a function using color:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-e28611
Out[1]=1

Use ComplexPlot3D to use the axis for the magnitude:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-vgce1e
Out[1]=1

Use ComplexArrayPlot for arrays of complex numbers:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-p6xumo
Out[1]=1

Use ReImPlot and AbsArgPlot to plot complex values over the real numbers:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-0vi62l
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-mqa938
Out[2]=2

Use ComplexListPlot to show the location of complex numbers in the plane:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-wyd4bn
Out[1]=1

Use ListVectorPlot for plotting data:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-czc8d0
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-bzenb8
Out[2]=2

Use ListStreamPlot to plot streams instead of vectors:

In[3]:=3
✖
https://wolfram.com/xid/0n4i0sam2ea-efbl3z
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-gljrl7
Out[1]=1

Use StreamDensityPlot to use streams instead of vectors:

In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-kxyms1
Out[2]=2

Use ListVectorDensityPlot to generate a density plot of a scalar field based on data:

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-2fsjy
In[2]:=2
✖
https://wolfram.com/xid/0n4i0sam2ea-b5me24
Out[2]=2

Use ListStreamDensityPlot to plot streams instead of vectors:

In[3]:=3
✖
https://wolfram.com/xid/0n4i0sam2ea-eootc
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0n4i0sam2ea-c9d537
Out[1]=1
Wolfram Research (2020), ComplexVectorPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.
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Wolfram Research (2020), ComplexVectorPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.

Text

Wolfram Research (2020), ComplexVectorPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.

✖
Wolfram Research (2020), ComplexVectorPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.

CMS

Wolfram Language. 2020. "ComplexVectorPlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.

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Wolfram Language. 2020. "ComplexVectorPlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComplexVectorPlot.html.

APA

Wolfram Language. (2020). ComplexVectorPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComplexVectorPlot.html

✖
Wolfram Language. (2020). ComplexVectorPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComplexVectorPlot.html

BibTeX

@misc{reference.wolfram_2025_complexvectorplot, author="Wolfram Research", title="{ComplexVectorPlot}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexVectorPlot.html}", note=[Accessed: 04-April-2025 ]}

✖
@misc{reference.wolfram_2025_complexvectorplot, author="Wolfram Research", title="{ComplexVectorPlot}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexVectorPlot.html}", note=[Accessed: 04-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_complexvectorplot, organization={Wolfram Research}, title={ComplexVectorPlot}, year={2020}, url={https://reference.wolfram.com/language/ref/ComplexVectorPlot.html}, note=[Accessed: 04-April-2025 ]}

✖
@online{reference.wolfram_2025_complexvectorplot, organization={Wolfram Research}, title={ComplexVectorPlot}, year={2020}, url={https://reference.wolfram.com/language/ref/ComplexVectorPlot.html}, note=[Accessed: 04-April-2025 ]}