LineIntegralConvolutionPlot
✖
LineIntegralConvolutionPlot
generates a line integral convolution plot of image convolved with the vector field {vx,vy} as a function of x and y.
generates a line integral convolution plot of white noise with the vector field {vx,vy}.
Details and Options


- LineIntegralConvolutionPlot creates a rasterized version of image, then does a line integral convolution of each pixel according to the field defined by the vector function {vx,vy}.
- LineIntegralConvolutionPlot has the same options as Graphics, with the following additions and changes: [List of all options]
-
AspectRatio 1 ratio of height to width BoxRatios Automatic effective 3D box ratios for simulated lighting ColorFunction Automatic how to color background densities ColorFunctionScaling True whether to scale arguments to ColorFunction EvaluationMonitor None expression to evaluate at every function evaluation Frame True whether to draw a frame around the plot FrameTicks Automatic frame tick marks LightingAngle None effective angle for simulated lighting LineIntegralConvolutionScale Automatic length of convolution along streamlines Method Automatic methods to use for the plot PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotLegends None legends for color gradients PlotRange {Full,Full} range of x, y values to include PlotRangePadding Automatic how much to pad the range of values PlotTheme $PlotTheme overall theme for the plot RasterSize Automatic the pixel width of the rasterized image WorkingPrecision MachinePrecision precision to use in internal computations - If image is not specified, or is not already rasterized, a raster is created with a size specified by the RasterSize option.
- With a setting other than LightingAngle->None, simulated lighting is used, with the height at each point being taken to be determined from the norm of the vector field.
- The arguments supplied to ColorFunction are x, y, vx, vy, Norm[{vx,vy}].
-
AlignmentPoint Center the default point in the graphic to align with AspectRatio 1 ratio of height to width Axes False whether to draw axes AxesLabel None axes labels AxesOrigin Automatic where axes should cross AxesStyle {} style specifications for the axes Background None background color for the plot BaselinePosition Automatic how to align with a surrounding text baseline BaseStyle {} base style specifications for the graphic BoxRatios Automatic effective 3D box ratios for simulated lighting ColorFunction Automatic how to color background densities ColorFunctionScaling True whether to scale arguments to ColorFunction ContentSelectable Automatic whether to allow contents to be selected CoordinatesToolOptions Automatic detailed behavior of the coordinates tool Epilog {} primitives rendered after the main plot EvaluationMonitor None expression to evaluate at every function evaluation FormatType TraditionalForm the default format type for text Frame True whether to draw a frame around the plot FrameLabel None frame labels FrameStyle {} style specifications for the frame FrameTicks Automatic frame tick marks FrameTicksStyle {} style specifications for frame ticks GridLines None grid lines to draw GridLinesStyle {} style specifications for grid lines ImageMargins 0. the margins to leave around the graphic ImagePadding All what extra padding to allow for labels etc. ImageSize Automatic the absolute size at which to render the graphic LabelStyle {} style specifications for labels LightingAngle None effective angle for simulated lighting LineIntegralConvolutionScale Automatic length of convolution along streamlines Method Automatic methods to use for the plot PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotLabel None an overall label for the plot PlotLegends None legends for color gradients PlotRange {Full,Full} range of x, y values to include PlotRangeClipping False whether to clip at the plot range PlotRangePadding Automatic how much to pad the range of values PlotRegion Automatic the final display region to be filled PlotTheme $PlotTheme overall theme for the plot PreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic Prolog {} primitives rendered before the main plot RasterSize Automatic the pixel width of the rasterized image RotateLabel True whether to rotate y labels on the frame Ticks Automatic axes ticks TicksStyle {} style specifications for axes ticks WorkingPrecision MachinePrecision precision to use in internal computations
List of all options



Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Scope (12)Survey of the scope of standard use cases
Sampling (5)
Transform an image by a line integral convolution:

https://wolfram.com/xid/0elv7nm1q5f5jhe-hpxopv


https://wolfram.com/xid/0elv7nm1q5f5jhe-k9obid

Use an image directly as input:

https://wolfram.com/xid/0elv7nm1q5f5jhe-d74pf0

Use an image created from a sparse matrix:

https://wolfram.com/xid/0elv7nm1q5f5jhe-bjkvxf


https://wolfram.com/xid/0elv7nm1q5f5jhe-6ahcw

Use a white noise background image with different levels of color quantization:

https://wolfram.com/xid/0elv7nm1q5f5jhe-dfdi3i

Plot a field image, increasing the line integral convolution length:

https://wolfram.com/xid/0elv7nm1q5f5jhe-nsrv8

Presentation (7)
Plot a field image and overlaid streamlines:

https://wolfram.com/xid/0elv7nm1q5f5jhe-dhe4x3

Plot a field image and overlaid field vectors:

https://wolfram.com/xid/0elv7nm1q5f5jhe-duy68f

Plot a field image and overlaid vectors at random positions:

https://wolfram.com/xid/0elv7nm1q5f5jhe-f2esdd


https://wolfram.com/xid/0elv7nm1q5f5jhe-j5nkyn

Specify a color function that blends two colors by the coordinate:

https://wolfram.com/xid/0elv7nm1q5f5jhe-bfj87l

Fix the lighting angle at 0 (right of the plot), and vary the altitude from 0 to :

https://wolfram.com/xid/0elv7nm1q5f5jhe-7qytx

Use a theme with detailed ticks and a legend:

https://wolfram.com/xid/0elv7nm1q5f5jhe-0i0ovc

Options (46)Common values & functionality for each option
Background (1)
ColorFunction (5)
Color the field magnitude using Hue:

https://wolfram.com/xid/0elv7nm1q5f5jhe-kjr6zw

Use any named color gradient from ColorData:

https://wolfram.com/xid/0elv7nm1q5f5jhe-bj9dhi

Use ColorData for predefined color gradients:

https://wolfram.com/xid/0elv7nm1q5f5jhe-hurujc

Specify a color function that blends two colors by the coordinate:

https://wolfram.com/xid/0elv7nm1q5f5jhe-c3yjqc

Use ColorFunctionScaling->False to get unscaled values:

https://wolfram.com/xid/0elv7nm1q5f5jhe-i4ddd4

ColorFunctionScaling (4)
By default, scaled values are used:

https://wolfram.com/xid/0elv7nm1q5f5jhe-cv1gcl

Use ColorFunctionScaling->False to get unscaled values:

https://wolfram.com/xid/0elv7nm1q5f5jhe-jm11f7

Use unscaled coordinates in the direction and scaled coordinates in the
direction:

https://wolfram.com/xid/0elv7nm1q5f5jhe-oma29

Explicitly specify the scaling for each color function argument:

https://wolfram.com/xid/0elv7nm1q5f5jhe-9tvz

EvaluationMonitor (1)
Frame (1)
FrameTicks (8)
Place frame tick marks and labels automatically:

https://wolfram.com/xid/0elv7nm1q5f5jhe-gogwt4


https://wolfram.com/xid/0elv7nm1q5f5jhe-cwls9w

Place frame ticks and labels on all the edges:

https://wolfram.com/xid/0elv7nm1q5f5jhe-5h550

Place frame ticks on the right and top edges:

https://wolfram.com/xid/0elv7nm1q5f5jhe-cbr0w7

Place frame tick marks at the specified positions:

https://wolfram.com/xid/0elv7nm1q5f5jhe-heaczx

Draw frame ticks at the specified positions with the specific labels:

https://wolfram.com/xid/0elv7nm1q5f5jhe-e8sz98

Specify the style of each frame tick:

https://wolfram.com/xid/0elv7nm1q5f5jhe-fr9e8z

Specify overall frame ticks style, including frame tick labels, using FrameTicksStyle:

https://wolfram.com/xid/0elv7nm1q5f5jhe-kgss0k

LightingAngle (2)
LineIntegralConvolutionScale (2)
PerformanceGoal (2)
PlotLegends (2)
Use a legend to show the vector field gradient colors:

https://wolfram.com/xid/0elv7nm1q5f5jhe-p1oi3n

Legends automatically pick up settings of ColorFunction:

https://wolfram.com/xid/0elv7nm1q5f5jhe-1wez0h

PlotRange (7)
The full plot range is used by default:

https://wolfram.com/xid/0elv7nm1q5f5jhe-e5htpa

Specify an explicit limit for both and
ranges:

https://wolfram.com/xid/0elv7nm1q5f5jhe-iujowz


https://wolfram.com/xid/0elv7nm1q5f5jhe-nvj2f1

Specify an explicit minimum range:

https://wolfram.com/xid/0elv7nm1q5f5jhe-6mhl8


https://wolfram.com/xid/0elv7nm1q5f5jhe-f1b74a

Specify an explicit maximum range:

https://wolfram.com/xid/0elv7nm1q5f5jhe-dv35v5


https://wolfram.com/xid/0elv7nm1q5f5jhe-eji1ea

PlotRangePadding (6)
Padding is computed automatically by default:

https://wolfram.com/xid/0elv7nm1q5f5jhe-d2h2aw

Specify no padding for all ,
, and
ranges:

https://wolfram.com/xid/0elv7nm1q5f5jhe-0h4yz

Specify an explicit padding for all ,
, and
ranges:

https://wolfram.com/xid/0elv7nm1q5f5jhe-cl0fye

Add 10% padding to all ,
, and
ranges:

https://wolfram.com/xid/0elv7nm1q5f5jhe-djbx3

Specify different padding for and
ranges:

https://wolfram.com/xid/0elv7nm1q5f5jhe-eirhh1

Specify padding for the range:

https://wolfram.com/xid/0elv7nm1q5f5jhe-n1k40

PlotTheme (2)
Applications (5)Sample problems that can be solved with this function
Use a line integral convolution plot as a background for an interactive demo:

https://wolfram.com/xid/0elv7nm1q5f5jhe-02ris8

Display characteristics of several different types of linear planar systems:

https://wolfram.com/xid/0elv7nm1q5f5jhe-bzo06m

https://wolfram.com/xid/0elv7nm1q5f5jhe-eowl6y

Show the local direction of the gradient of a function along with its level curves:

https://wolfram.com/xid/0elv7nm1q5f5jhe-jm2o0h

Use the image as a background for investigating different unconstrained optimization methods:

https://wolfram.com/xid/0elv7nm1q5f5jhe-ppb809

Apply to a texture from ExampleData:

https://wolfram.com/xid/0elv7nm1q5f5jhe-gx9a2v


https://wolfram.com/xid/0elv7nm1q5f5jhe-dzqdv


https://wolfram.com/xid/0elv7nm1q5f5jhe-qstke

Properties & Relations (4)Properties of the function, and connections to other functions
Use ListLineIntegralConvolutionPlot to plot data:

https://wolfram.com/xid/0elv7nm1q5f5jhe-d476t5

https://wolfram.com/xid/0elv7nm1q5f5jhe-k30stq

Other alternatives for visualizing vector field functions:

https://wolfram.com/xid/0elv7nm1q5f5jhe-jpz8rp

Other alternatives for visualizing vector field data:

https://wolfram.com/xid/0elv7nm1q5f5jhe-siw3r

https://wolfram.com/xid/0elv7nm1q5f5jhe-qgw60

Use VectorPlot3D and StreamPlot3D to visualize 3D vector fields:

https://wolfram.com/xid/0elv7nm1q5f5jhe-hxuyz7

Neat Examples (1)Surprising or curious use cases
Algorithmic texture generation:

https://wolfram.com/xid/0elv7nm1q5f5jhe-jt6221


https://wolfram.com/xid/0elv7nm1q5f5jhe-eamgd3


https://wolfram.com/xid/0elv7nm1q5f5jhe-prn9lo


https://wolfram.com/xid/0elv7nm1q5f5jhe-bsokpv


https://wolfram.com/xid/0elv7nm1q5f5jhe-wqy9f

Wolfram Research (2008), LineIntegralConvolutionPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/LineIntegralConvolutionPlot.html (updated 2014).
Text
Wolfram Research (2008), LineIntegralConvolutionPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/LineIntegralConvolutionPlot.html (updated 2014).
Wolfram Research (2008), LineIntegralConvolutionPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/LineIntegralConvolutionPlot.html (updated 2014).
CMS
Wolfram Language. 2008. "LineIntegralConvolutionPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/LineIntegralConvolutionPlot.html.
Wolfram Language. 2008. "LineIntegralConvolutionPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/LineIntegralConvolutionPlot.html.
APA
Wolfram Language. (2008). LineIntegralConvolutionPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LineIntegralConvolutionPlot.html
Wolfram Language. (2008). LineIntegralConvolutionPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LineIntegralConvolutionPlot.html
BibTeX
@misc{reference.wolfram_2025_lineintegralconvolutionplot, author="Wolfram Research", title="{LineIntegralConvolutionPlot}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/LineIntegralConvolutionPlot.html}", note=[Accessed: 15-April-2025
]}
BibLaTeX
@online{reference.wolfram_2025_lineintegralconvolutionplot, organization={Wolfram Research}, title={LineIntegralConvolutionPlot}, year={2014}, url={https://reference.wolfram.com/language/ref/LineIntegralConvolutionPlot.html}, note=[Accessed: 15-April-2025
]}