generates a plot of Abs[f] colored by Arg[f] as a function of x from xmin to xmax.


plots several functions.


plots fi with features defined by the symbolic wrapper w.


takes the variable x to be in the geometric region reg.

Details and Options


open allclose all

Basic 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  (16)

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  (3)

The Automatic legend shows the range of Arg values:

Explicitly label the individual curves:

Identify curves with wrappers:

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  (105)

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 AspectRatio1:

AspectRatioAutomatic determines the ratio from the plot ranges:

AspectRatioFull 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)

Use automatic methods for computing exclusions:

Exclusions are automatically computed for both Abs and Arg:

Indicate that no exclusions should be computed:

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 AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull 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:

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)

PlotStyle can be used to style curves:

The coloring of the argument takes precedence over colors specified with PlotStyle:

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:

Wolfram Research (2019), AbsArgPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/AbsArgPlot.html (updated 2021).


Wolfram Research (2019), AbsArgPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/AbsArgPlot.html (updated 2021).


Wolfram Language. 2019. "AbsArgPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/AbsArgPlot.html.


Wolfram Language. (2019). AbsArgPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AbsArgPlot.html


@misc{reference.wolfram_2022_absargplot, author="Wolfram Research", title="{AbsArgPlot}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/AbsArgPlot.html}", note=[Accessed: 21-March-2023 ]}


@online{reference.wolfram_2022_absargplot, organization={Wolfram Research}, title={AbsArgPlot}, year={2021}, url={https://reference.wolfram.com/language/ref/AbsArgPlot.html}, note=[Accessed: 21-March-2023 ]}