AbsArgPlot [f,{x,xmin,xmax}]
generates a plot of Abs [f] colored by Arg [f] as a function of x∈ from xmin to xmax.
AbsArgPlot [{f1,f2,…},{x,xmin,xmax}]
plots several functions.
AbsArgPlot [{…,w[fi],…},…]
plots fi with features defined by the symbolic wrapper w.
AbsArgPlot […,{x}∈reg]
takes the variable x to be in the geometric region reg.
AbsArgPlot
AbsArgPlot [f,{x,xmin,xmax}]
generates a plot of Abs [f] colored by Arg [f] as a function of x∈ from xmin to xmax.
AbsArgPlot [{f1,f2,…},{x,xmin,xmax}]
plots several functions.
AbsArgPlot [{…,w[fi],…},…]
plots fi with features defined by the symbolic wrapper w.
AbsArgPlot […,{x}∈reg]
takes the variable x to be in the geometric region reg.
Details and Options
- AbsArgPlot evaluates f at different values of x to create smooth curves of the form {x,Abs [f[x]]} colored by {x,Arg [f[x]]}.
- Gaps are left at any x where the fi evaluate to non-numeric values.
- The region reg can be any RegionQ object in 1D.
- AbsArgPlot treats the variable x as local, effectively using Block .
- AbsArgPlot has the attribute HoldAll and evaluates f only after assigning specific numerical values to x.
- In some cases, it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to x.
- Wrappers apply to both Re [f] and Im [f].
- The following wrappers w can be used for the fi:
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- Wrappers w can be applied at multiple levels:
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w[fi] wrap the fiw[{f1,…}] wrap a collection of fiw1[w2[…]] use nested wrappers
- Callout , Labeled and Placed can use the following positions pos:
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Automatic automatically placed labelsx near the curve at a position x{pos,epos} epos in label placed at relative position pos of the curve
- AbsArgPlot has the same options as Graphics , with the following additions and changes: [List of all options]
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- Possible settings for ClippingStyle are:
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Automatic use a dotted line for the clipped portionNone omit the clipped portion of the curvestyle use style for the clipped portion
- With the default settings Exclusions->Automatic and ExclusionsStyle->None , AbsArgPlot breaks curves at discontinuities and singularities it detects. Exclusions->None joins across discontinuities and singularities.
- Exclusions->{x1,x2,…} is equivalent to Exclusions->{x==x1,x==x2,…}.
- PlotLabels->"Expressions" uses the fi as the label text.
- AbsArgPlot initially evaluates f at a number of equally spaced sample points specified by PlotPoints . Then it uses an adaptive algorithm to choose additional sample points, subdividing a given interval at most MaxRecursion times.
- Since only a finite number of sample points are used, it is possible for AbsArgPlot to miss features of f. Increasing the settings for PlotPoints and MaxRecursion will often catch such features.
- Themes that affect curves include:
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"ThinLines" thin plot lines"MediumLines" medium plot lines"ThickLines" thick plot lines
- The arguments supplied to functions in MeshFunctions and RegionFunction are x, y. Functions in ColorFunction are by default supplied with scaled versions of these arguments.
- ScalingFunctions->"scale" scales the coordinate; ScalingFunctions {"scalex","scaley"} scales both the and coordinates.
- Possible highlighting effects for Highlighted and PlotHighlighting include:
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style highlight the indicated curve"Ball" highlight and label the indicated point in a curve"Dropline" highlight and label the indicated point in a curve with droplines to the axes"XSlice" highlight and label all points along a vertical slice"YSlice" highlight and label all points along a horizontal slice
- Highlight position specifications pos include:
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x, {x} effect at {x,y} with y chosen automatically{x,y} effect at {x,y}{pos1,pos2,…} multiple positions posi
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ImageMargins 0. the margins to leave around the graphicPreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic
List of all options
Examples
open all close allBasic Examples (6)
Plot the modulus of a complex function of a real variable colored by its argument:
Plot several functions:
Label each curve:
Include a legend:
Fill below a curve:
Compare Plot and AbsArgPlot :
Scope (18)
Sampling (8)
More points are sampled where the function changes quickly:
The plot range is selected automatically:
The curve is split when there are discontinuities in the function:
Use Exclusions ->None to draw connected curves:
Use PlotPoints and MaxRecursion to control adaptive sampling:
The domain can be specified by a region:
Specify a domain using a MeshRegion :
Plot over an infinite domain with automatic ticks:
Labeling and Legending (5)
Presentation (5)
Provide explicit styling to different curves:
Add labels and a legend:
Create filled plots:
Use a plot theme:
Use ScalingFunctions to scale the axes:
Options (113)
AspectRatio (4)
By default, AbsArgPlot uses a fixed ratio of the height to the width of the plot:
Make the height the same as the width with AspectRatio 1:
AspectRatio Automatic determines the ratio from the plot ranges:
AspectRatio Full adjusts the height and width to tightly fit inside other constructs:
Axes (4)
By default, Axes is drawn for AbsArgPlot :
Use Frame instead of axes:
Use AxesOrigin to specify where the axes intersect:
Turn each axis on individually:
AxesLabel (3)
No axes labels are drawn by default:
Place a label on the axis:
Use specific labels for each axis:
AxesOrigin (2)
The position of the axes is determined automatically:
Specify an explicit origin for the axes:
AxesStyle (4)
Change the style for the axes:
Specify the style of each axis:
Use different styles for the ticks and the axes:
Use different styles for the labels and the axes:
ClippingStyle (2)
Omit clipped regions of the plot:
Show clipped regions with black lines:
ColorFunction (4)
Color by the scaled argument:
Use a named color gradient:
ColorFunction has higher priority than PlotStyle :
Highlight part of the plot:
ColorFunctionScaling (1)
No argument scaling on the left; automatic scaling on the right:
Exclusions (3)
ExclusionStyle (1)
Use gray lines to connect portions of the curve and black points to indicate exclusions:
Filling (4)
Use symbolic or explicit values:
Filling uses transparent colors if more than one curve is specified:
Fill between curve 1 and the axis:
Fill between curves 1 and 2:
FillingStyle (2)
Use different fill colors:
Fill between two curves with red below the second curve and blue above:
Frame (3)
Draw a frame around the plot:
Draw a frame on the left and right edges:
Draw a frame on the top and bottom edges:
FrameLabel (2)
Frame labels are placed on the bottom and left frame edges by default:
Place labels on each of the edges in the frame:
FrameStyle (2)
Specify the style of the frame:
Specify the style for each frame edge:
FrameTicks (8)
FrameTicks are placed automatically by default:
Use a frame with no ticks:
Use frame ticks on the axes but not the axes:
Place frame ticks at specific positions:
Draw frame ticks at the specified positions with specific labels:
Specify the lengths for frame ticks as a fraction on graphics size:
Use different sizes in the positive and negative directions for each frame tick:
Specify a style for each frame tick:
Construct a function that places frame ticks at the midpoint and extremes of the frame edge:
FrameTicksStyle (3)
By default, the frame ticks and frame tick labels use the same styles as the frame:
Specify an overall style for the ticks, including the labels:
Use a different style for the different frame edges:
ImageSize (7)
Use named sizes such as Tiny , Small , Medium and Large :
Specify the width of the plot:
Specify the height of the plot:
Allow the width and height to be up to a certain size:
Specify the width and height for a graphic, padding with space if necessary:
Setting AspectRatio Full will fill the available space:
Use maximum sizes for the width and height:
Use ImageSize Full to fill the available space in an object:
Specify the image size as a fraction of the available space:
MaxRecursion (1)
Each level of MaxRecursion adaptively subdivides the initial mesh into a finer mesh:
Mesh (3)
Show the initial and final sampling meshes:
Use 10 mesh points evenly spaced in the direction:
Use an explicit list of values for the mesh in the direction:
MeshFunctions (2)
Use a mesh evenly spaced in the and directions:
Show 10 mesh levels in the direction (black) and 6 in the direction (red):
MeshShading (2)
Remove segments of the curve:
MeshShading has higher priority than PlotStyle for styling:
MeshStyle (2)
Use a black mesh in the direction:
Use a black mesh in the direction and a red mesh in the direction:
PerformanceGoal (2)
Generate a higher-quality plot:
Emphasize performance, possibly at the cost of quality:
PlotHighlighting (8)
Plots have interactive coordinate callouts with the default setting PlotHighlighting Automatic :
Use PlotHighlighting None to disable the highlighting for the entire plot:
Move the mouse over the curve to highlight it with a ball and label:
Move the mouse over the curve to highlight it with a label and droplines to the axes:
Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:
Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:
Use a component that shows the points on the curve closest to the position of the mouse cursor:
Specify the style for the points:
Use a component that shows the coordinates on the curve closest to the mouse cursor:
Use Callout options to change the appearance of the label:
Combine components to create a custom effect:
PlotLabel (1)
Add an overall label to the plot:
PlotLabels (6)
Specify text to label curves:
Modify the appearance of the labels:
Place the labels differently for each curve:
PlotLabels ->"Expressions" uses functions as curve labels:
Use callouts to identify the curves:
Use None to not add a label:
PlotLegends (2)
Create a legend for the argument color:
Create multiple legends:
PlotPoints (1)
Use more initial points to get smoother curves:
PlotRange (1)
The plot range is selected automatically:
Focus on a specified range of values:
PlotStyle (2)
PlotTheme (1)
Use a theme:
RegionFunction (1)
Show the curve where :
ScalingFunctions (6)
By default, plots have linear scales in each direction:
Use a logarithm to scale the modulus but leave the argument (color) unscaled:
Use different scales in the and directions:
Domains that contain infinite values are scaled automatically:
Use "Reverse" scale in an infinite domain:
Use Interval to focus on a region of interest in an infinite domain:
Ticks (9)
Ticks are placed automatically on each axis:
Draw axes but no tick marks:
Use ticks on the axis but not the axis:
Place tick marks at specific positions:
Draw tick marks at the specified positions with the specified labels:
Use specific ticks on one axis and automatic ticks on the other:
Specify the lengths for ticks as a fraction on graphics size:
Use different sizes in the positive and negative directions for each tick:
Specify a style for each tick:
Construct a function that places ticks at the midpoint and extremes of the axis:
TicksStyle (4)
By default, the ticks and tick labels use the same style as the axis:
Specify an overall ticks style, including the tick labels:
Specify ticks style for each of the axes:
Use a different style for the tick labels and tick marks:
Applications (3)
Plot Fourier transforms:
Plot the solution of a complex differential equation with initial conditions:
The colors are rescaled since the argument never exceeds 1 in magnitude:
Graph special functions:
Properties & Relations (8)
AbsArgPlot is a special case of Plot :
ComplexPlot shows the argument and magnitude of a function using color:
Use ComplexPlot3D to use the axis for the magnitude:
Use ReImPlot to plot real and imaginary components over the real numbers:
Use ComplexListPlot to show the location of complex numbers in the plane:
ComplexContourPlot plots curves over the complexes:
ComplexRegionPlot plots regions over the complexes:
ComplexStreamPlot and ComplexVectorPlot treat complex numbers as directions:
Possible Issues (2)
An apparent lack of color change does not mean that the argument value does not change:
Mesh points that coincide with argument exclusions may be missing:
Related Guides
Text
Wolfram Research (2019), AbsArgPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/AbsArgPlot.html (updated 2023).
CMS
Wolfram Language. 2019. "AbsArgPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/AbsArgPlot.html.
APA
Wolfram Language. (2019). AbsArgPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AbsArgPlot.html
BibTeX
@misc{reference.wolfram_2025_absargplot, author="Wolfram Research", title="{AbsArgPlot}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/AbsArgPlot.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_absargplot, organization={Wolfram Research}, title={AbsArgPlot}, year={2023}, url={https://reference.wolfram.com/language/ref/AbsArgPlot.html}, note=[Accessed: 17-November-2025]}