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

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Basic Examples  (3)

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

Include a legend for the vector magnitudes:

Use a drop-shaped marker to represent the vectors:

Scope  (19)

Sampling  (7)

Plot a vector field with vectors placed with specified densities:

Sample the vector field on a regular grid of points:

Sample the vector field on an irregular mesh:

Specify how many vector points to use in each direction:

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

Plot vectors over a specified region:

Plot the fields for a function and its conjugate:

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

Presentation  (12)

Plot a vector field with automatically scaled arrows:

Plot a vector field with arrows of specified size:

Draw the arrows starting from the sample points:

Draw the arrows without the arrowheads:

Use drop-like shapes instead of arrows:

Change the overall shape of the markers:

Change the default color function:

Include a legend:

Vary the arrow sizes instead of the colors:

Set the style for multiple vector fields:

Apply vector style:

Set the style for multiple vector fields:

Use a theme with simple ticks and grid lines:

Options  (68)

AspectRatio  (2)

By default, the aspect ratio is 1:

Set the aspect ratio:

Background  (1)

Use a colored background:

ClippingStyle  (4)

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

Use ClippingStyleNone to remove extreme vectors from the plot:

Style the clipped vectors:

Style the short and long clipped vectors differently:

EvaluationMonitor  (2)

Show where the vector field function is sampled:

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

FrameLabel  (1)

Label the frame:

PlotLegends  (5)

Include a legend for the vector norms:

Use the expressions in the legend for multiple vector functions:

Specify the legend labels for multiple functions:

Control the placement of the legend:

Use a legend with placeholders:

PlotRange  (5)

The full plot range is used by default:

Specify an explicit limit for both real and imaginary ranges:

Specify an explicit real range:

Specify an explicit imaginary range:

Specify different real and imaginary ranges:

PlotTheme  (2)

Use a theme:

Change the vector style:

RegionBoundaryStyle  (5)

Show the region defined by a region function:

The boundaries of full rectangular regions are not shown:

Use None to not show the boundary:

Omit the interior filling as well:

Specify a style for the boundary:

Specify a style for full rectangular regions:

RegionFillingStyle  (5)

Show the region defined by a region function:

The interior of full rectangular regions are not shown:

Use None to not show the interior filling:

Omit the boundary curve as well:

Specify a style for the interior filling:

Specify a style for full rectangular region:

RegionFunction  (2)

Restrict the plotting region based on :

Restrict the plotting region based on :

VectorAspectRatio  (2)

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

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

VectorColorFunction  (5)

Vectors are colored according to their norms by default:

Choose the color scheme for coloring vectors by their norms:

Use any named color gradient from ColorData:

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

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

VectorColorFunctionScaling  (2)

By default, scaled values are used:

Use VectorColorFunctionScalingFalse to get unscaled values:

VectorMarkers  (4)

Vectors are drawn as arrows by default:

Use a named appearance to draw the vectors:

Use different markers for different vector fields:

By default, markers are centered on vector points:

Start the vectors at the points:

End the vectors at the points:

VectorPoints  (5)

Use automatically determined vector points:

Use symbolic names to specify the set of field vectors:

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

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

Specify a list of points for showing field vectors:

VectorRange  (6)

By default, vector ranges are determined automatically:

Plot vectors with magnitudes between 0.2 and 2:

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

Style the clipped vectors:

Plot scaled vectors with all lengths:

Increase the lengths of the smaller vectors:

VectorScaling  (2)

By default, VectorScaling is None:

Use automatic scaling to scale the length of vectors:

VectorSizes  (2)

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

Specify a minimum and maximum scaled vector size:

VectorStyle  (6)

Set the style for the displayed vectors:

Set the style for multiple functions:

Use Arrowheads to specify an explicit style of the arrowheads:

Specify both arrow tail and head:

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

Change the scaling using the VectorScaling option:

Applications  (7)

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

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

Identify poles and zeros. Poles are visible at and :

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

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:

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

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

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

Examine partial sums of an infinite series:

Properties & Relations  (9)

ComplexVectorPlot is a special case of VectorPlot:

ComplexStreamPlot plots complex numbers as streamlines:

ComplexContourPlot plots curves over the complexes:

ComplexRegionPlot plots regions over the complexes:

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

Use ComplexPlot3D to use the axis for the magnitude:

Use ComplexArrayPlot for arrays of complex numbers:

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

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

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.

BibTeX

@misc{reference.wolfram_2020_complexvectorplot, author="Wolfram Research", title="{ComplexVectorPlot}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexVectorPlot.html}", note=[Accessed: 18-April-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_complexvectorplot, organization={Wolfram Research}, title={ComplexVectorPlot}, year={2020}, url={https://reference.wolfram.com/language/ref/ComplexVectorPlot.html}, note=[Accessed: 18-April-2021 ]}

CMS

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