--- title: "ListVectorPlot" language: "en" type: "Symbol" summary: "ListVectorPlot[varr] generates a vector plot from an array varr of vectors. ListVectorPlot[{{{x1, y1}, {vx1, vy1}}, ...}] generates a vector plot from vectors {vxi, vyi} given at specified points {xi, yi}. ListVectorPlot[{data1, data2, ...}] plots data for several vector fields." keywords: - list vector plot - plot vector field - visualize vector field - arrow plot - phase portrait - quiver - quiver plot canonical_url: "https://reference.wolfram.com/language/ref/ListVectorPlot.html" source: "Wolfram Language Documentation" related_guides: - title: "Vector Visualization" link: "https://reference.wolfram.com/language/guide/VectorVisualization.en.md" - title: "Data Visualization" link: "https://reference.wolfram.com/language/guide/DataVisualization.en.md" - title: "Vector Analysis" link: "https://reference.wolfram.com/language/guide/VectorAnalysis.en.md" related_functions: - title: "ListStreamPlot" link: "https://reference.wolfram.com/language/ref/ListStreamPlot.en.md" - title: "ListVectorPlot3D" link: "https://reference.wolfram.com/language/ref/ListVectorPlot3D.en.md" - title: "ListStreamPlot3D" link: "https://reference.wolfram.com/language/ref/ListStreamPlot3D.en.md" - title: "ListStreamDensityPlot" link: "https://reference.wolfram.com/language/ref/ListStreamDensityPlot.en.md" - title: "VectorPlot" link: "https://reference.wolfram.com/language/ref/VectorPlot.en.md" - title: "ListSliceVectorPlot3D" link: "https://reference.wolfram.com/language/ref/ListSliceVectorPlot3D.en.md" - title: "GeoVectorPlot" link: "https://reference.wolfram.com/language/ref/GeoVectorPlot.en.md" - title: "ComplexVectorPlot" link: "https://reference.wolfram.com/language/ref/ComplexVectorPlot.en.md" --- # ListVectorPlot ListVectorPlot[varr] generates a vector plot from an array varr of vectors. ListVectorPlot[{{{x1, y1}, {vx1, vy1}}, …}] generates a vector plot from vectors {vxi, vyi} given at specified points {xi, yi}. ListVectorPlot[{data1, data2, …}] plots data for several vector fields. ## Details and Options * ``ListVectorPlot`` is also known as field plot and direction plot. * ``ListVectorPlot`` displays a vector field $\left\{v_x,v_y\right\}$ by drawing arrows normalized to a fixed length. The arrows are colored by default according to the magnitude $s=\left\| \left\{v_x,v_y\right\}\right\|$ of the vector field. * The plot visualizes the set $\left\{\left.\left\{v_x,v_y\right\}\right|\{x,y\}\in \text{reg}\right\}$, where $\text{reg}$ is the region for which $\left\{v_x,v_y\right\}$ is defined. [image] * ``ListVectorPlot`` interpolates the data into field functions $\left\{v_x(x,y),v_y(x,y)\right\}$. * For regular data, the vector field $\left\{v_x,v_y\right\}$ has value ``varr[[i, j]]`` at $\{x,y\}=\{i,j\}$. * For irregular data, the vector field $\left\{v_x,v_y\right\}$ has value ``{vxi, vyi}`` at $\{x,y\}=\left\{\text{\textit{$x$}}_{\text{\textit{$i$}}},\text{\textit{$y$}}_{\text{\textit{$i$}}}\right\}$. [image] * ``ListVectorPlot[varr]`` arranges successive rows of ``varr`` up the page and successive columns across. * ``ListVectorPlot`` by default interpolates the data given and plots vectors for the vector field at a specified grid of positions. * ``ListVectorPlot`` has the same options as ``Graphics``, with the following additions and changes: [] | | | | | --------------------------- | ----------------- | ---------------------------------------------------- | | AspectRatio | 1 | ratio of height to width | | ClippingStyle | Automatic | how to display arrows outside the vector range | | DataRange | Automatic | the range of x and y values to assume for data | | Frame | True | whether to draw a frame around the plot | | FrameTicks | Automatic | frame tick marks | | Method | Automatic | methods to use for the plot | | PerformanceGoal | \$PerformanceGoal | aspects of performance to try to optimize | | PlotLayout | Automatic | how to position fields | | PlotLegends | None | legends for vector fields | | 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 | | RegionFunction | (True&) | determine what region to include | | RegionBoundaryStyle | Automatic | how to style plot region boundaries | | RegionFillingStyle | Automatic | how to style plot region interiors | | ScalingFunctions | None | how to scale individual coordinates | | VectorAspectRatio | Automatic | width to length ratio for arrows | | VectorColorFunction | Automatic | how to color arrows | | VectorColorFunctionScaling | True | whether to scale the argument to VectorColorFunction | | VectorMarkers | Automatic | shape to use for arrows | | VectorPoints | Automatic | the number or placement of arrows | | VectorRange | Automatic | range of vector lengths to show | | VectorScaling | None | how to scale the sizes of arrows | | VectorSizes | Automatic | sizes of displayed arrows | | VectorStyle | Automatic | how to draw vectors | * The individual arrows are scaled to fit inside bounding circles around each point. [image] * With the setting ``VectorPoints -> All``, ``ListVectorPlot`` instead shows vectors associated with the particular vector field data points given. * ``VectorScaling`` scales the magnitudes of the vectors into the range of arrow sizes ``smin`` to ``smax`` given by ``VectorSizes``. * ``VectorScaling -> Automatic`` will scale the arrow lengths depending on the vector magnitudes: [image] * Possible settings for ``PlotLayout`` that show a single group of vectors in multiple plot panels include: | | | | ------------------------------------- | --------------------------------------------------- | | "Column" | use separate group of vectors in a column of panels | | "Row" | use separate group of vectors in a row of panels | | {"Column", k}, {"Row", k} | use k columns or rows | | {"Column", UpTo[k]}, {"Row", UpTo[k]} | use at most k columns or rows | [image] * The arrow markers given by ``VectorMarkers`` are drawn inside a box whose width and length are in the proportion $w/l$ specified by ``VectorAspectRatio``. * Common markers include: | | | | | ------- | --------- | ------------------------------------------- | | [image] | "Segment" | line segment aligned in the field direction | | [image] | "PinDart" | pin dart aligned along the field | | [image] | "Dart" | dart-shaped marker | | [image] | "Drop" | drop-shaped marker | * ``VectorColorFunction -> None`` will draw the arrows with the style specified by ``VectorStyle``. * The arguments supplied to functions in ``RegionFunction`` and ``VectorColorFunction`` are ``x``, ``y``, ``vx``, ``vy``, ``Norm[{vx, vy}]``. * Possible settings for ``ScalingFunctions`` are: {Subscript[``s``, ``x``], Subscript[``s``, ``y``]} scale ``x`` and ``y`` axes * Common built-in scaling functions ``s`` include: | | | | | ----------- | ------- | --------------------------------------------------- | | "Log" | [image] | log scale with automatic tick labeling | | "Log10" | [image] | base-10 log scale with powers of 10 for ticks | | "SignedLog" | [image] | log-like scale that includes 0 and negative numbers | | "Reverse" | [image] | reverse the coordinate direction | | "Infinite" | [image] | infinite scale | ### List of all options | | | | | -------------------------- | ----------------- | ---------------------------------------------------------------------------------- | | 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 | | ClippingStyle | Automatic | how to display arrows outside the vector range | | ContentSelectable | Automatic | whether to allow contents to be selected | | CoordinatesToolOptions | Automatic | detailed behavior of the coordinates tool | | DataRange | Automatic | the range of x and y values to assume for data | | Epilog | {} | primitives rendered after the main plot | | 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 | | 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 | | PlotLayout | Automatic | how to position fields | | PlotLegends | None | legends for vector fields | | 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 | | RegionBoundaryStyle | Automatic | how to style plot region boundaries | | RegionFillingStyle | Automatic | how to style plot region interiors | | RegionFunction | (True&) | determine what region to include | | RotateLabel | True | whether to rotate y labels on the frame | | ScalingFunctions | None | how to scale individual coordinates | | Ticks | Automatic | axes ticks | | TicksStyle | {} | style specifications for axes ticks | | VectorAspectRatio | Automatic | width to length ratio for arrows | | VectorColorFunction | Automatic | how to color arrows | | VectorColorFunctionScaling | True | whether to scale the argument to VectorColorFunction | | VectorMarkers | Automatic | shape to use for arrows | | VectorPoints | Automatic | the number or placement of arrows | | VectorRange | Automatic | range of vector lengths to show | | VectorScaling | None | how to scale the sizes of arrows | | VectorSizes | Automatic | sizes of displayed arrows | | VectorStyle | Automatic | how to draw vectors | --- ## Examples (133) ### Basic Examples (4) Plot the vector field interpolated from a specified set of vectors: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]] Out[1]= [image] ``` --- Include a legend showing the vector magnitudes: ```wl In[1]:= data = Table[{{x, y}, {y, -x}}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, PlotLegends -> Automatic] Out[2]= [image] ``` --- Use a drop-shaped marker to represent the vectors: ```wl In[1]:= ListVectorPlot[Table[{x + y, y - x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], VectorMarkers -> "Drop"] Out[1]= [image] ``` --- Use a multi-panel layout to show multiple vector fields at the same time: ```wl In[1]:= ListVectorPlot[{IconizedObject[«data1»], IconizedObject[«data2»]}, PlotLayout -> "Row"] Out[1]= [image] ``` ### Scope (16) #### Sampling (6) Plot vectors for a regular collection of vectors, and give a data range for the domain: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], DataRange -> {{-3, 3}, {-3, 3}}] Out[1]= [image] ``` --- Plot an irregular collection of vectors: ```wl In[1]:= data = Table[{{x, y} = RandomReal[{-3, 3}, {2}], {y, -x}}, {200}]; In[2]:= ListVectorPlot[data] Out[2]= [image] ``` Show all of the specified field vectors: ```wl In[3]:= ListVectorPlot[data, VectorPoints -> All] Out[3]= [image] ``` Explicitly set the number of vectors in each direction: ```wl In[4]:= ListVectorPlot[data, VectorPoints -> {4, 7}] Out[4]= [image] ``` --- Specify a list of points for showing field vectors: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], DataRange -> {{-3, 3}, {-3, 3}}, VectorSizes -> Large, VectorPoints -> RandomReal[{-3, 3}, {300, 2}]] Out[1]= [image] ``` --- Plot a vector field with vectors placed with specified densities: ```wl In[1]:= data = Table[{y, -x}, {x, -2, 2, 0.2}, {y, -2, 2, 0.2}]; In[2]:= Table[ListVectorPlot[data, PlotLabel -> p, VectorPoints -> p], {p, {5, Coarse, Automatic, Fine}}] Out[2]= {[image], [image], [image], [image]} ``` --- Plot the vectors that go through a set of seed points: ```wl In[1]:= points = {{-1, -1}, {-1, 1}, {0, 0}, {1, -1}, {1, 1}}; data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -2, 2, 0.2}, {y, -2, 2, 0.2}]; In[2]:= ListVectorPlot[data, DataRange -> {{-2, 2}, {-2, 2}}, VectorPoints -> points, Epilog -> {Red, PointSize[Medium], Point[points]}] Out[2]= [image] ``` --- Plot vectors over a specified region: ```wl In[1]:= ListVectorPlot[Table[{{x, y} = RandomReal[{-3, 3}, {2}], {y, -x}}, {200}], RegionFunction -> Function[{x, y, vx, vy, n}, x y < 0]] Out[1]= [image] ``` #### Presentation (10) Plot a vector field with arrows scaled according to their magnitudes: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], VectorScaling -> Automatic] Out[1]= [image] ``` --- Use a single color for the arrows: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], VectorColorFunction -> None] Out[1]= [image] ``` --- Plot a vector field with arrows of specified size: ```wl In[1]:= data = Table[{x, -y}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= Table[ListVectorPlot[data, VectorColorFunction -> "BrightBands", PlotLabel -> s, VectorSizes -> s], {s, {Small, Medium, Large, 0.5}}] Out[2]= {[image], [image], [image], [image]} ``` --- Plot a vector field with arrows colored according to the magnitude of the field: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], VectorColorFunction -> "Rainbow"] Out[1]= [image] ``` --- Set the style for multiple vector fields: ```wl In[1]:= data1 = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; data2 = Table[{-(1 + x - y ^ 2), -1 - x ^ 2 + y}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[{data1, data2}, VectorPoints -> 8, VectorMarkers -> {"Drop", "Dart"}] Out[2]= [image] ``` --- Apply vector style: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorPoints -> 8, VectorStyle -> Arrowheads[{{0.03, Automatic, Graphics[Circle[]]}}]] Out[2]= [image] ``` --- Use a named appearance to draw the vectors: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorMarkers -> "Drop"] Out[2]= [image] ``` Style the vectors as well: ```wl In[3]:= ListVectorPlot[data, VectorMarkers -> "Drop", VectorColorFunction -> None, VectorStyle -> Red] Out[3]= [image] ``` --- Use a theme with more detail: ```wl In[1]:= data1 = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; data2 = Table[{-(1 + x - y ^ 2), -1 - x ^ 2 + y}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[{data1, data2}, PlotTheme -> "Detailed"] Out[2]= [image] ``` Combine the theme with a specific style for the vectors: ```wl In[3]:= ListVectorPlot[{data1, data2}, PlotTheme -> "Detailed", VectorMarkers -> "Dart"] Out[3]= [image] ``` --- Show multiple vector fields in separate panels: ```wl In[1]:= ListVectorPlot[{IconizedObject[«field1»], IconizedObject[«field1»]}, PlotLayout -> "Row"] Out[1]= [image] ``` Use a column instead of a row: ```wl In[2]:= ListVectorPlot[{IconizedObject[«field1»], IconizedObject[«field1»]}, PlotLayout -> "Column"] Out[2]= [image] ``` --- Use a log scale in the ``y`` direction: ```wl In[1]:= ListVectorPlot[Table[{y, x + y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], ScalingFunctions -> {None, "Log"}] Out[1]= [image] ``` ### Options (95) #### AspectRatio (3) By default, ``ListVectorPlot`` uses the same width and height: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»]] Out[1]= [image] ``` --- Use numerical value to specify the height to width ratio: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], AspectRatio -> 1 / GoldenRatio] Out[1]= [image] ``` --- ``AspectRatio -> Automatic`` determines the ratio from the plot ranges: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], AspectRatio -> Automatic] Out[1]= [image] ``` #### Axes (4) By default, ``ListVectorPlot`` uses a frame instead of axes: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»]] Out[1]= [image] ``` --- Use axes instead of a frame: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True] Out[1]= [image] ``` --- Use ``AxesOrigin`` to specify where the axes intersect: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True, AxesOrigin -> {1, 1}] Out[1]= [image] ``` --- Turn each axis on individually: ```wl In[1]:= {ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> {True, False}], ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> {False, True}]} Out[1]= {[image], [image]} ``` #### AxesLabel (3) No axes labels are drawn by default: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True] Out[1]= [image] ``` --- Place a label on the $y$ axis: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True, AxesLabel -> y] Out[1]= [image] ``` --- Specify axes labels: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True, AxesLabel -> {x, y}] Out[1]= [image] ``` #### AxesOrigin (2) The position of the axes is determined automatically: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True] Out[1]= [image] ``` --- Specify an explicit origin for the axes: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True, AxesOrigin -> {1, 1}] Out[1]= [image] ``` #### AxesStyle (4) Change the style for the axes: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True, AxesStyle -> Red] Out[1]= [image] ``` --- Specify the style of each axis: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True, AxesStyle -> {Red, Blue}] Out[1]= [image] ``` --- Use different styles for the ticks and the axes: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True, AxesStyle -> Green, TicksStyle -> Black] Out[1]= [image] ``` --- Use different styles for the labels and the axes: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], Frame -> False, Axes -> True, AxesStyle -> Green, LabelStyle -> Black] Out[1]= [image] ``` #### Background (1) Use colored backgrounds: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], Background -> LightGray] Out[1]= [image] ``` #### DataRange (1) By default, the data range is taken to be the index range of the data array: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.3}]; Dimensions[data] Out[1]= {31, 21, 2} In[2]:= ListVectorPlot[data] Out[2]= [image] ``` Specify the data range for the domain: ```wl In[3]:= ListVectorPlot[data, DataRange -> {{-3, 3}, {-3, 3}}] Out[3]= [image] ``` #### EvaluationMonitor (1) Count the number of times the vector field function is evaluated: ```wl In[1]:= Block[{k = 0}, ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], EvaluationMonitor :> k++];k] Out[1]= 250 ``` #### ImageSize (5) Use named sizes such as ``Tiny``, ``Small``, ``Medium`` and ``Large`` : ```wl In[1]:= {ListVectorPlot[IconizedObject[«field»], ImageSize -> Tiny], ListVectorPlot[IconizedObject[«field»], ImageSize -> Small]} Out[1]= {[image], [image]} ``` --- Specify the width of the plot: ```wl In[1]:= {ListVectorPlot[IconizedObject[«field»], ImageSize -> 150], ListVectorPlot[IconizedObject[«field»], AspectRatio -> 1.5, ImageSize -> 150]} Out[1]= {[image], [image]} ``` Specify the height of the plot: ```wl In[2]:= {ListVectorPlot[IconizedObject[«field»], ImageSize -> {Automatic, 150}], ListVectorPlot[IconizedObject[«field»], AspectRatio -> 2, ImageSize -> {Automatic, 150}]} Out[2]= {[image], [image]} ``` --- Allow the width and height to be up to a certain size: ```wl In[1]:= {ListVectorPlot[IconizedObject[«field»], ImageSize -> UpTo[200]], ListVectorPlot[IconizedObject[«field»], AspectRatio -> 2, ImageSize -> UpTo[200]]} Out[1]= {[image], [image]} ``` --- Specify the width and height for a graphic, padding with space if necessary: ```wl In[1]:= ListVectorPlot[IconizedObject[«field»], ImageSize -> {300, 200}, Background -> LightBlue] Out[1]= [image] ``` Setting ``AspectRatio -> Full`` will fill the available space: ```wl In[2]:= ListVectorPlot[IconizedObject[«field»], AspectRatio -> Full, ImageSize -> {300, 200}, Background -> LightBlue] Out[2]= [image] ``` --- Use maximum sizes for the width and height: ```wl In[1]:= {ListVectorPlot[IconizedObject[«field»], ImageSize -> {UpTo[150], UpTo[100]}], ListVectorPlot[IconizedObject[«field»], AspectRatio -> 2, ImageSize -> {UpTo[150], UpTo[100]}]} Out[1]= {[image], [image]} ``` #### PerformanceGoal (2) Generate a higher-quality plot: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], PerformanceGoal -> "Quality"] Out[1]= [image] ``` --- Emphasize performance, possibly at the cost of quality: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], PerformanceGoal -> "Speed"] Out[1]= [image] ``` #### PlotLayout (3) Place each field in a separate panel using shared axes: ```wl In[1]:= ListVectorPlot[{IconizedObject[«x + y»], IconizedObject[«-x + y»]}, ImageSize -> Medium, PlotLayout -> "Column"] Out[1]= [image] ``` Use a row instead of a column: ```wl In[2]:= ListVectorPlot[{IconizedObject[«x + y»], IconizedObject[«-x + y»]}, ImageSize -> Medium, PlotLayout -> "Row"] Out[2]= [image] ``` --- Use multiple columns or rows: ```wl In[1]:= ListVectorPlot[{IconizedObject[«x + y»], IconizedObject[«-x»], IconizedObject[«y»], IconizedObject[«-x + y»]}, ImageSize -> Medium, PlotLayout -> {"Column", 2}] Out[1]= [image] ``` --- Prefer full columns or rows: ```wl In[1]:= ListVectorPlot[{IconizedObject[«x + y»], IconizedObject[«-x»], IconizedObject[«y»], IconizedObject[«x»], IconizedObject[«-x + y»], IconizedObject[«0»]}, ImageSize -> Medium, PlotLayout -> {"Column", UpTo[4]}] Out[1]= [image] In[2]:= ListVectorPlot[{IconizedObject[«x + y»], IconizedObject[«-x»], IconizedObject[«y»], IconizedObject[«x»], IconizedObject[«-x + y»], IconizedObject[«0»]}, ImageSize -> Medium, PlotLayout -> {"Column", 4}] Out[2]= [image] ``` #### PlotLegends (2) No legends are included by default: ```wl In[1]:= ListVectorPlot[Table[{y, Exp[-x]}, {x, -3, 3, 0.3}, {y, -3, 3, 0.3}]] Out[1]= [image] ``` --- Include a legend to show the color range of vector norms: ```wl In[1]:= ListVectorPlot[Table[{y, Exp[-x]}, {x, -3, 3, 0.3}, {y, -3, 3, 0.3}], PlotLegends -> Automatic] Out[1]= [image] ``` Add legends with placeholder text: ```wl In[2]:= data1 = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; data2 = Table[{x, y}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[3]:= ListVectorPlot[{data1, data2}, VectorColorFunction -> None, PlotLegends -> Automatic] Out[3]= [image] ``` Specify labels for the legend: ```wl In[4]:= ListVectorPlot[{data1, data2}, PlotLegends -> {"one", "two"}, VectorColorFunction -> None] Out[4]= [image] ``` Place the legend below the plot: ```wl In[5]:= ListVectorPlot[{data1, data2}, VectorColorFunction -> None, PlotLegends -> Placed[{"one", "two"}, Below]] Out[5]= [image] ``` Control the appearance of the legend: ```wl In[6]:= ListVectorPlot[{data1, data2}, VectorColorFunction -> None, PlotLegends -> SwatchLegend[{"one", "two"}, LegendMarkerSize -> {40, 10}]] Out[6]= [image] ``` #### PlotRange (7) The full plot range is used by default: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], PlotRange -> Full] Out[1]= [image] ``` --- Specify an explicit limit for both $x$ and $y$ ranges: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], DataRange -> {{-3, 3}, {-3, 3}}, PlotRange -> 2] Out[1]= [image] ``` --- Specify an explicit $x$ range: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], DataRange -> {{-3, 3}, {-3, 3}}, PlotRange -> {{-1, 2}, Automatic}] Out[1]= [image] ``` --- Specify an explicit $x$ minimum range: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], DataRange -> {{-3, 3}, {-3, 3}}, PlotRange -> {{0, Full}, Automatic}] Out[1]= [image] ``` --- Specify an explicit $y$ range: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], DataRange -> {{-3, 3}, {-3, 3}}, PlotRange -> {Full, {0, 2}}] Out[1]= [image] ``` --- Specify an explicit $y$ maximum range: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], DataRange -> {{-3, 3}, {-3, 3}}, PlotRange -> {Full, {Full, 5}}] Out[1]= [image] ``` --- Specify different $x$ and $y$ ranges: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], DataRange -> {{-3, 3}, {-3, 3}}, PlotRange -> {{-2, 1.5}, {-1, 2}}] Out[1]= [image] ``` #### PlotTheme (1) Use a theme with gridlines, dark background and bold colors: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, PlotTheme -> "Marketing"] Out[2]= [image] ``` Change the ``VectorColorFunction`` : ```wl In[3]:= ListVectorPlot[data, PlotTheme -> "Marketing", VectorColorFunction -> Hue] Out[3]= [image] ``` #### RegionBoundaryStyle (5) Show the region defined by a region function: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionFunction -> Function[{x, y}, x + y > 0], DataRange -> {{-1, 1}, {-1, 1}}] Out[1]= [image] ``` --- The boundaries of full rectangular regions are not shown: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}]] Out[1]= [image] ``` --- Use ``None`` to not show the boundary: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionFunction -> Function[{x, y}, x^2 + y^2 < 1], DataRange -> {{-1, 1}, {-1, 1}}, RegionBoundaryStyle -> None] Out[1]= [image] ``` Omit the interior filling as well: ```wl In[2]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionFunction -> Function[{x, y}, x^2 + y^2 < 1], DataRange -> {{-1, 1}, {-1, 1}}, RegionBoundaryStyle -> None, RegionFillingStyle -> None] Out[2]= [image] ``` --- Specify a style for the boundary: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionFunction -> Function[{x, y}, x^2 + y^2 < 1], DataRange -> {{-1, 1}, {-1, 1}}, RegionBoundaryStyle -> Red] Out[1]= [image] ``` --- Specify a style for full rectangular regions: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionBoundaryStyle -> Red] Out[1]= [image] ``` #### RegionFillingStyle (5) Show the region defined by a region function: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionFunction -> Function[{x, y}, x + y > 0], DataRange -> {{-1, 1}, {-1, 1}}] Out[1]= [image] ``` --- The interior of full rectangular regions are not shown: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}]] Out[1]= [image] ``` --- Use ``None`` to not show the interior filling: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionFunction -> Function[{x, y}, x^2 + y^2 < 1], DataRange -> {{-1, 1}, {-1, 1}}, RegionFillingStyle -> None] Out[1]= [image] ``` Omit the boundary curve as well: ```wl In[2]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionFunction -> Function[{x, y}, x^2 + y^2 < 1], DataRange -> {{-1, 1}, {-1, 1}}, RegionBoundaryStyle -> None, RegionFillingStyle -> None] Out[2]= [image] ``` --- Specify a style for the interior filling: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionFunction -> Function[{x, y}, x^2 + y^2 < 1], DataRange -> {{-1, 1}, {-1, 1}}, RegionFillingStyle -> Gray] Out[1]= [image] ``` --- Specify a style for full rectangular region: ```wl In[1]:= ListVectorPlot[Table[{x, y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], RegionFillingStyle -> Gray] Out[1]= [image] ``` #### RegionFunction (3) Plot vectors only over certain quadrants: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, DataRange -> {{-3, 3}, {-3, 3}}, RegionFunction -> Function[{x, y, vx, vy, n}, x y < 0]] Out[2]= [image] ``` --- Plot vectors only over regions where the field magnitude is above a given threshold: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, DataRange -> {{-3, 3}, {-3, 3}}, RegionFunction -> Function[{x, y, vx, vy, n}, n > 6]] Out[2]= [image] ``` --- Use any logical combination of conditions: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, DataRange -> {{-3, 3}, {-3, 3}}, RegionFunction -> Function[{x, y, vx, vy, n}, 4 < n < 9 || 0 < n < 2]] Out[2]= [image] ``` #### ScalingFunctions (3) By default, linear scales are used: ```wl In[1]:= ListVectorPlot[Table[{y, x - y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}]] Out[1]= [image] ``` --- Use a log scale in the ``y`` direction: ```wl In[1]:= ListVectorPlot[Table[{y, x - y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], ScalingFunctions -> {None, "Log"}] Out[1]= [image] ``` --- Reverse the direction of the ``y`` direction: ```wl In[1]:= ListVectorPlot[Table[{y, x - y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}], ScalingFunctions -> {None, "Reverse"}] Out[1]= [image] ``` #### VectorColorFunction (4) Color the vectors according to their norms: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorColorFunction -> Hue] Out[2]= [image] ``` --- Use any named color gradient from ``ColorData``: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorColorFunction -> "Rainbow"] Out[2]= [image] ``` --- Color the vectors according to their $x$ values: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorColorFunction -> Function[{x, y, vx, vy, n}, ColorData["ThermometerColors"][x]]] Out[2]= [image] ``` --- Use ``VectorColorFunctionScaling -> False`` to get unscaled values: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorColorFunction -> Function[{x, y, vx, vy, n}, ColorData[22][Round[n]]], VectorColorFunctionScaling -> False] Out[2]= [image] ``` #### VectorColorFunctionScaling (4) By default, scaled values are used: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], VectorColorFunction -> Hue] Out[1]= [image] ``` --- Use ``VectorColorFunctionScaling -> False`` to get unscaled values: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorColorFunction -> Function[{x, y, vx, vy, n}, ColorData[22][Round[n]]], VectorColorFunctionScaling -> False] Out[2]= [image] ``` --- Use unscaled coordinates in the $x$ direction and scaled coordinates in the $y$ direction: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorColorFunction -> Function[{x, y, vx, vy, n}, Hue[x, y, 1]], VectorColorFunctionScaling -> {False, True}, DataRange -> {{0, 1}, {0, 1}}] Out[2]= [image] ``` --- Explicitly specify the scaling for each color function argument: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorColorFunction -> Function[{x, y, vx, vy, n}, Hue[n, y, 1]], VectorColorFunctionScaling -> {True, True, True, True, False}] Out[2]= [image] ``` #### VectorMarkers (9) Vectors are drawn as arrows by default: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data] Out[2]= [image] ``` --- Use a named appearance to draw the vectors: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, VectorMarkers -> "Drop"] Out[2]= [image] ``` --- Use different markers for different vector fields: ```wl In[1]:= data1 = Table[{{x, y}, {y, -x}}, {x, -5, 5}, {y, -5, 5}]; data2 = Table[{{x, y}, {x, y}}, {x, -5, 5}, {y, -5, 5}]; In[2]:= ListVectorPlot[{data1, data2}, VectorMarkers -> {"Drop", "Dart"}] Out[2]= [image] ``` --- By default, markers are centered on vector points: ```wl In[1]:= data = Table[{{x, y}, {y, -x}}, {x, -5, 5}, {y, -5, 5}]; In[2]:= pts = Tuples[Range[-5, 5], 2]; In[3]:= ListVectorPlot[data, VectorMarkers -> "Arrow", VectorPoints -> pts, Epilog -> {Red, Point[pts]}] Out[3]= [image] ``` Start the vectors at the points: ```wl In[4]:= ListVectorPlot[data, VectorMarkers -> Placed["Arrow", "Start"], VectorPoints -> pts, Epilog -> {Red, Point[pts]}] Out[4]= [image] ``` End the vectors at the points: ```wl In[5]:= ListVectorPlot[data, VectorMarkers -> Placed["Arrow", "End"], VectorPoints -> pts, Epilog -> {Red, Point[pts]}] Out[5]= [image] ``` --- Arrow vector markers: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= Table[ListVectorPlot[data, VectorPoints -> 8, PlotLabel -> s, VectorMarkers -> s], {s, {"Arrow", "DotArrow", "ArrowArrow"}}] Out[2]= {[image], [image], [image]} ``` --- Circular vector markers: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= Table[ListVectorPlot[data, VectorPoints -> 10, PlotLabel -> s, VectorStyle -> s], {s, {"Circle", "Disk", "CircleArrow"}}] Out[2]= {[image], [image], [image]} ``` --- Dart vector markers: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= Table[ListVectorPlot[data, VectorPoints -> 8, PlotLabel -> s, VectorStyle -> s], {s, {"Dart", "PinDart", "DoubleDart"}}] Out[2]= [image] ``` --- Vector markers with dots: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= Table[ListVectorPlot[data, VectorPoints -> 8, PlotLabel -> s, VectorStyle -> s], {s, {"BarDot", "Dot", "DotArrow", "DotDot"}}] Out[2]= {[image], [image], [image], [image]} ``` --- Pointer vector markers: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= Table[ListVectorPlot[data, VectorPoints -> 8, PlotLabel -> s, VectorStyle -> s], {s, {"Drop", "Pointer", "BackwardPointer", "Toothpick"}}] Out[2]= [image] ``` #### VectorPoints (8) Use automatically determined vector points: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -1, 1, 0.2}, {y, -1, 1, 0.2}], VectorPoints -> Automatic] Out[1]= [image] ``` --- Show all of the specified field vectors: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -1, 1, 0.2}, {y, -1, 1, 0.2}], VectorPoints -> All] Out[1]= [image] ``` --- Use symbolic names to specify the set of field vectors: ```wl In[1]:= data = Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= Table[ListVectorPlot[data, PlotLabel -> k, VectorPoints -> k], {k, {Fine, Coarse}}] Out[2]= {[image], [image]} ``` --- Create a regular grid of field vectors with the same number of arrows for $x$ and $y$ : ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], VectorPoints -> 5] Out[1]= [image] ``` --- Create a regular grid of field vectors with a different number of arrows for $x$ and $y$ : ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], VectorPoints -> {4, 7}] Out[1]= [image] ``` --- Specify a list of points for showing field vectors: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[data, DataRange -> {{-3, 3}, {-3, 3}}, VectorPoints -> RandomReal[{-3, 3}, {300, 2}], VectorSizes -> Large] Out[2]= [image] ``` --- Use a different number of field vectors on a hexagonal grid: ```wl In[1]:= data = Table[{y ^ 2, x ^ 2 - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= Table[ListVectorPlot[data, PlotLabel -> n, VectorPoints -> n, VectorSizes -> Medium], {n, 5, 20, 5}] Out[2]= {[image], [image], [image], [image]} ``` --- The location for vectors is given in the middle of the drawn vector: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -2, 2, 0.2}, {y, -2, 2, 0.2}]; points = {{-1, -1}, {-1, 1}, {0, 0}, {1, -1}, {1, 1}}; In[2]:= ListVectorPlot[data, DataRange -> {{-2, 2}, {-2, 2}}, VectorPoints -> points, VectorSizes -> 1, Epilog -> {Red, PointSize[Medium], Point[points]}] Out[2]= [image] ``` #### VectorRange (4) The clipping of vectors with very small or very large magnitudes is done automatically: ```wl In[1]:= ListVectorPlot[Table[({x, y}/Norm[{x, y}]^3), {x, -3, 3, 0.35}, {y, -3, 3, 0.35}], VectorRange -> Automatic] Out[1]= [image] ``` --- Specify the range of vector norms: ```wl In[1]:= ListVectorPlot[Table[({x, y}/Norm[{x, y}]^3), {x, -3, 3, 0.35}, {y, -3, 3, 0.35}], VectorRange -> {0.1, 2}] Out[1]= [image] ``` --- Suppress the clipped vectors: ```wl In[1]:= ListVectorPlot[Table[({x, y}/Norm[{x, y}]^3), {x, -3, 3, 0.35}, {y, -3, 3, 0.35}], VectorRange -> {0.1, 2}, ClippingStyle -> None] Out[1]= [image] ``` --- Show all the vectors: ```wl In[1]:= ListVectorPlot[Table[({x, y}/Norm[{x, y}]^3), {x, -3, 3, 0.35}, {y, -3, 3, 0.35}], VectorRange -> All] Out[1]= [image] ``` #### VectorScaling (2) Use automatically determined vector scales: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.5}, {y, -3, 3, 0.5}], VectorScaling -> Automatic] Out[1]= [image] ``` --- With the vector scaling function set to ``None``, all vectors have the same size: ```wl In[1]:= ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.5}, {y, -3, 3, 0.5}], VectorScaling -> None] Out[1]= [image] ``` #### VectorSizes (2) The size of the displayed vector is determined automatically: ```wl In[1]:= ListVectorPlot[Table[{y - x(1 - x^2 - y^2)^2, -x - y(1 - x^2 - y^2)^2}, {x, -3, 3, 0.1}, {y, -3, 3, 0.1}], VectorScaling -> Automatic, VectorSizes -> Automatic] Out[1]= [image] ``` --- Specify the range of arrow lengths: ```wl In[1]:= ListVectorPlot[Table[{y - x(1 - x^2 - y^2)^2, -x - y(1 - x^2 - y^2)^2}, {x, -3, 3, 0.1}, {y, -3, 3, 0.1}], VectorScaling -> Automatic, VectorSizes -> {0, 1}] Out[1]= [image] ``` #### VectorStyle (7) ``VectorColorFunction`` has precedence over ``VectorStyle`` for colors: ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], VectorStyle -> Red] Out[1]= [image] ``` --- Use ``VectorColorFunction`` -> ``None`` to style the displayed vectors with ``VectorStyle`` : ```wl In[1]:= ListVectorPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}], VectorStyle -> Red, VectorColorFunction -> None] Out[1]= [image] ``` --- Set the style for multiple vector fields: ```wl In[1]:= data1 = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; data2 = Table[{-(1 + x - y ^ 2), -1 - x ^ 2 + y}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorPlot[{data1, data2}, VectorPoints -> 8, VectorStyle -> {Red, Blue}, VectorColorFunction -> None] Out[2]= [image] ``` --- Use ``Arrowheads`` to specify an explicit style of the arrowheads: ```wl In[1]:= data = Table[{x, y}, {x, -1, 1, 0.2}, {y, -1, 1, 0.2}]; In[2]:= ListVectorPlot[data, VectorPoints -> 8, PlotRange -> All, VectorStyle -> Arrowheads[{{0.03, Automatic, Graphics[Circle[]]}}]] Out[2]= [image] ``` --- Specify both arrow tail and head: ```wl In[1]:= data = Table[{x, y}, {x, -1, 1, 0.2}, {y, -1, 1, 0.2}]; In[2]:= ListVectorPlot[data, VectorPoints -> 8, PlotRange -> All, VectorStyle -> Arrowheads[{{0.03, Automatic, Graphics[Rectangle[{-0.5, -0.5}, {0.5, 0.5}]]}, {0.03, Automatic, Graphics[Circle[]]}}]] Out[2]= [image] ``` --- Graphics primitives without ``Arrowheads`` are scaled based on the ``VectorSizes`` : ```wl In[1]:= data = Table[{x, y}, {x, -1, 1, 0.2}, {y, -1, 1, 0.2}]; In[2]:= ListVectorPlot[data, VectorPoints -> 8, PlotRange -> All, VectorStyle -> Graphics[Circle[]], VectorSizes -> {0.5, 0.9}] Out[2]= [image] ``` --- Change the scaling using the ``VectorSizes`` option: ```wl In[1]:= data = Table[{x, y}, {x, -1, 1, 0.2}, {y, -1, 1, 0.2}]; In[2]:= ListVectorPlot[data, VectorPoints -> 8, PlotRange -> All, VectorStyle -> Graphics[Circle[]], VectorSizes -> {0.2, 0.4}] Out[2]= [image] ``` ### Applications (3) Hamiltonian vector field of $\sin (x y)$ : ```wl In[1]:= data = Table[Evaluate@{D[Sin[x y], {y}], -D[Sin[x y], {x}]}, {x, 0, 2Pi}, {y, 0, 2Pi}]; In[2]:= ListVectorPlot[data] Out[2]= [image] ``` --- Visualize the first horizontal and vertical Gaussian derivatives of an image: ```wl In[1]:= image = ColorConvert[Rasterize[π, ImageSize -> 40, RasterSize -> 40], "Grayscale"] Out[1]= [image] In[2]:= {dx, dy} = Table[ImageAdjust@GaussianFilter[image, {6, 2}, δ], {δ, {{1, 0}, {0, 1}}}] Out[2]= {[image], [image]} ``` Combine the vertical and horizontal Gaussian derivatives: ```wl In[3]:= data = Reverse /@ Transpose[2ImageData /@ {dx, dy} - 1, {3, 2, 1}]; In[4]:= ListVectorPlot[data, VectorPoints -> 30] Out[4]= [image] ``` --- Characterize linear planar systems interactively: ```wl In[1]:= Manipulate[Row[{Text["m"] == MatrixForm[m], ListVectorPlot[Table[Evaluate[m.{x, y}], {x, -1, 1}, {y, -1, 1}], VectorSizes -> 1, VectorColorFunction -> "Rainbow", ImageSize -> Small]}], {{m, (| | | | - | - | | 1 | 0 | | 0 | 2 |)}, {(| | | | - | - | | 1 | 0 | | 0 | 2 |) -> "Nodal source", (| | | | - | - | | 1 | 1 | | 0 | 1 |) -> "Degenerate source", (| | | | -- | - | | 0 | 1 | | -1 | 1 |) -> "Spiral source", (| | | | -- | -- | | -1 | 0 | | 0 | -2 |) -> "Nodal sink", (| | | | -- | -- | | -1 | 1 | | 0 | -1 |) -> "Degenerate sink", (| | | | -- | -- | | 0 | 1 | | -1 | -1 |) -> "Spiral sink", (| | | | -- | - | | 0 | 1 | | -1 | 0 |) -> "Center", (| | | | - | -- | | 1 | 0 | | 0 | -2 |) -> "Saddle"}}] Out[1]= DynamicModule[«8»] ``` ### Properties & Relations (15) Use ``VectorPlot`` to plot functions: ```wl In[1]:= VectorPlot[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3}, {y, -3, 3}] Out[1]= [image] ``` Use ``StreamPlot`` to plot streams instead of vectors: ```wl In[2]:= StreamPlot[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3}, {y, -3, 3}] Out[2]= [image] ``` --- Use ``ListStreamPlot`` to plot data with streamlines instead of vectors : ```wl In[1]:= ListStreamPlot[Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]] Out[1]= [image] ``` --- Use ``VectorDensityPlot`` to add a density plot of a scalar field: ```wl In[1]:= VectorDensityPlot[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3}, {y, -3, 3}] Out[1]= [image] ``` Use ``StreamDensityPlot`` to use streams instead of vectors: ```wl In[2]:= StreamDensityPlot[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3}, {y, -3, 3}] Out[2]= [image] ``` --- Use ``ListVectorDensityPlot`` for plotting data with a density plot of the scalar field: ```wl In[1]:= data = Table[{{x, y} = RandomReal[{-1.5, 1.5}, {2}], {{y, x - x ^ 3}, Abs[x + y]}}, {300}]; In[2]:= ListVectorDensityPlot[data] Out[2]= [image] ``` Use ``ListStreamDensityPlot`` to plot streams instead of vectors: ```wl In[3]:= ListStreamDensityPlot[data] Out[3]= [image] ``` --- Use ``ListLineIntegralConvolutionPlot`` to plot the line integral convolution of vector field data: ```wl In[1]:= data = Table[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, -3, 3, .2}, {y, -3, 3, .2}]; In[2]:= ListLineIntegralConvolutionPlot[data] Out[2]= [image] ``` --- Use ``VectorDisplacementPlot`` to visualize the effect of a displacement vector field on a specified region: ```wl In[1]:= VectorDisplacementPlot[{-1 - x ^ 2 + y, 1 + x - y ^ 2}, {x, y}∈Annulus[], VectorPoints -> Automatic] Out[1]= [image] ``` --- Use ``ListVectorDisplacementPlot`` to visualize the effect of displacement field data on a region: ```wl In[1]:= data = Table[{{x, y}, {x + y, 1 + x - y}}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; In[2]:= ListVectorDisplacementPlot[data, Polygon[{{3, 3}, {0, 1}, {-3, 3}, {-3, -3}, {0, -1}, {3, -3}}], VectorPoints -> Automatic] Out[2]= [image] ``` --- Use ``VectorPlot3D`` and ``StreamPlot3D`` to visualize 3D vector fields: ```wl In[1]:= {VectorPlot3D[{z, x, x + y}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}], StreamPlot3D[{z, x, x + y}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}]} Out[1]= {[image], [image]} ``` --- Use ``ListVectorPlot3D`` and ``ListStreamPlot3D`` to visualize 3D vector field data: ```wl In[1]:= data = Table[{z, -x, y}, {x, -1, 1, .1}, {y, -1, 1, .1}, {z, -1, 1, .1}]; In[2]:= {ListVectorPlot3D[data], ListStreamPlot3D[data]} Out[2]= {[image], [image]} ``` --- Plot vectors on surfaces with ``SliceVectorPlot3D`` : ```wl In[1]:= SliceVectorPlot3D[{-y, x, z}, Sphere[], {x, -1, 1}, {y, -1, 1}, {z, -1, 1}] Out[1]= [image] ``` --- Plot data vectors on surfaces with ``ListSliceVectorPlot3D`` : ```wl In[1]:= ListSliceVectorPlot3D[Table[{-y, x, z}, {x, -1, 1, .1}, {y, -1, 1, .1}, {z, -1, 1, .1}], Sphere[], DataRange -> {{-1, 1}, {-1, 1}, {-1, 1}}] Out[1]= [image] ``` --- Plot complex functions as a vector field with ``ComplexVectorPlot`` : ```wl In[1]:= ComplexVectorPlot[z + 1 / z, {z, 2}] Out[1]= [image] ``` Plot streams instead of vectors with ``ComplexStreamPlot`` : ```wl In[2]:= ComplexStreamPlot[z^2 + 1, {z, 2}] Out[2]= [image] ``` --- Use ``VectorDisplacementPlot3D`` to visualize the effect of a displacement vector field on a specified 3D region: ```wl In[1]:= VectorDisplacementPlot3D[{-y, x, x + z}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, VectorPoints -> "Boundary"] Out[1]= [image] ``` --- Use ``ListVectorDisplacementPlot3D`` to visualize the effect of a 3D displacement vector field based on data: ```wl In[1]:= data = Table[{{x, y, z}, {-y, x, x + z}}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]; In[2]:= ListVectorDisplacementPlot3D[data, VectorPoints -> "Boundary"] Out[2]= [image] ``` --- Use ``GeoVectorPlot`` to plot vectors on a map: ```wl In[1]:= GeoVectorPlot[GeoVector[GeoPosition[CompressedData["«6488»"]] -> {{0.5706379232485146, Quantity[354.01686143622794, "AngularDegrees"]}, {0.48751317221734114, Quantity[327.18610724051325, "AngularDegrees"]}, {0.42407845478418604, Quantity[199.859344783 ... 904, "AngularDegrees"]}, {0.9366099079317551, Quantity[357.70482317743733, "AngularDegrees"]}, {0.8256817194791912, Quantity[242.07227508889662, "AngularDegrees"]}, {0.2661401145642981, Quantity[152.90003252279325, "AngularDegrees"]}}]] Out[1]= [image] ``` Use ``GeoStreamPlot`` to use streams instead of vectors: ```wl In[2]:= GeoStreamPlot[GeoVector[GeoPosition[CompressedData["«6488»"]] -> {{0.5706379232485146, Quantity[354.01686143622794, "AngularDegrees"]}, {0.48751317221734114, Quantity[327.18610724051325, "AngularDegrees"]}, {0.42407845478418604, Quantity[199.859344783 ... 904, "AngularDegrees"]}, {0.9366099079317551, Quantity[357.70482317743733, "AngularDegrees"]}, {0.8256817194791912, Quantity[242.07227508889662, "AngularDegrees"]}, {0.2661401145642981, Quantity[152.90003252279325, "AngularDegrees"]}}]] Out[2]= [image] ``` ## See Also * [`ListStreamPlot`](https://reference.wolfram.com/language/ref/ListStreamPlot.en.md) * [`ListVectorPlot3D`](https://reference.wolfram.com/language/ref/ListVectorPlot3D.en.md) * [`ListStreamPlot3D`](https://reference.wolfram.com/language/ref/ListStreamPlot3D.en.md) * [`ListStreamDensityPlot`](https://reference.wolfram.com/language/ref/ListStreamDensityPlot.en.md) * [`VectorPlot`](https://reference.wolfram.com/language/ref/VectorPlot.en.md) * [`ListSliceVectorPlot3D`](https://reference.wolfram.com/language/ref/ListSliceVectorPlot3D.en.md) * [`GeoVectorPlot`](https://reference.wolfram.com/language/ref/GeoVectorPlot.en.md) * [`ComplexVectorPlot`](https://reference.wolfram.com/language/ref/ComplexVectorPlot.en.md) ## Related Guides * [Vector Visualization](https://reference.wolfram.com/language/guide/VectorVisualization.en.md) * [Data Visualization](https://reference.wolfram.com/language/guide/DataVisualization.en.md) * [Vector Analysis](https://reference.wolfram.com/language/guide/VectorAnalysis.en.md) ## History * [Introduced in 2008 (7.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn70.en.md) \| [Updated in 2012 (9.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn90.en.md) ▪ [2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md) ▪ [2018 (11.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn113.en.md) ▪ [2020 (12.1)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn121.en.md) ▪ [2021 (13.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn130.en.md) ▪ [2022 (13.1)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn131.en.md)