--- title: "ListLinePlot3D" language: "en" type: "Symbol" summary: "ListLinePlot3D[{{x1, y1, z1}, {x2, y2, z2}, ..., {xn, yn, zn}}] plots a curve through the 3D points {xi, yi, zi}. ListLinePlot3D[{{z11, z12, ..., z 1 n}, ..., {z m 1, z m 2, ..., zmn}}] plots each row {z i 1, z i 2, ..., z in} as a curve in the x direction, with successive curves stacked in the y direction. ListLinePlot3D[{data1, data2, ...}] plots curves through multiple sets of {x, y, z} points." keywords: - 3D curve plot - line plot 3D - ridgeline plot - 3D path plot - 3D stacked plot - 3D line graph - 3D line plot - 3D area plot - 3D area graph - ridge graph - slice graph - ridge contour - layer graph - strata graph - partition plot - spectral plot canonical_url: "https://reference.wolfram.com/language/ref/ListLinePlot3D.html" source: "Wolfram Language Documentation" related_guides: - title: "Data Visualization" link: "https://reference.wolfram.com/language/guide/DataVisualization.en.md" - title: "Tabular Visualization" link: "https://reference.wolfram.com/language/guide/TabularVisualization.en.md" related_functions: - title: "ListLinePlot" link: "https://reference.wolfram.com/language/ref/ListLinePlot.en.md" - title: "ListPointPlot3D" link: "https://reference.wolfram.com/language/ref/ListPointPlot3D.en.md" - title: "ListPlot3D" link: "https://reference.wolfram.com/language/ref/ListPlot3D.en.md" - title: "ParametricPlot3D" link: "https://reference.wolfram.com/language/ref/ParametricPlot3D.en.md" - title: "ListPlot" link: "https://reference.wolfram.com/language/ref/ListPlot.en.md" - title: "DiscretePlot3D" link: "https://reference.wolfram.com/language/ref/DiscretePlot3D.en.md" - title: "StackedListPlot" link: "https://reference.wolfram.com/language/ref/StackedListPlot.en.md" --- # ListLinePlot3D ListLinePlot3D[{{x1, y1, z1}, {x2, y2, z2}, …, {xn, yn, zn}}] plots a curve through the 3D points {xi, yi, zi}. ListLinePlot3D[{{z11, z12, …, z1n}, …, {zm1, zm2, …, zmn}}] plots each row {zi1, zi2, …, zin} as a curve in the $x$ direction, with successive curves stacked in the $y$ direction. ListLinePlot3D[{data1, data2, …}] plots curves through multiple sets of {x, y, z} points. ## Details and Options * ``ListLinePlot3D`` is also known as 3D line graph, or 3D area graph when the area under the curve is filled. When showing each row of the data as a separate curve, ``ListLinePlot3D`` is also known as a ridgeline plot. * ``ListLinePlot3D`` allows you to draw curves in 3D through a given set of points. [image] * Data values ``xi``, ``yi`` and ``zi`` can be given in the following forms: | | | | ---------------------- | ----------------------------- | | xi | a real-valued number | | Quantity[xi, unit] | a quantity with a unit | | Around[xi, ei] | value xi with uncertainty ei | | Interval[{xmin, xmax}] | values between xmin and xmax | * Values ``xi``, ``yi`` and ``zi`` that are not of the preceding form are taken to be missing and are not shown. * The ``datai`` have the following forms and interpretations: <\|"Subscript[k, 1]"->{Subscript[x, 1],Subscript[y, 1],Subscript[z, 1]},"Subscript[k, 2]"->{Subscript[x, 2],Subscript[y, 2],Subscript[z, 2]},\[Ellipsis]\|> values {{Subscript[x, 1],Subscript[y, 1],Subscript[z, 1]},{Subscript[x, 2],Subscript[y, 2],Subscript[z, 2]},\[Ellipsis]} {{Subscript[x, 1],Subscript[y, 1],Subscript[z, 1]}->"Subscript[lbl, 1]",{Subscript[x, 2],Subscript[y, 2],Subscript[z, 2]}->"Subscript[lbl, 2]",\[Ellipsis]}, data->{"Subscript[lbl, 1]","Subscript[lbl, 2]",\[Ellipsis]} values {{Subscript[x, 1],Subscript[y, 1],Subscript[z, 1]},{Subscript[x, 2],Subscript[y, 2],Subscript[z, 2]},\[Ellipsis]} with labels {Subscript[lbl, 1],Subscript[lbl, 2],\[Ellipsis]} SparseArray values as a normal array QuantityArray magnitudes WeightedData unweighted values * ``ListLinePlot3D[Tabular[…] -> cspec]`` extracts and plots values from the tabular object using the column specification ``cspec``. * The following forms of column specifications ``cspec`` are allowed for plotting tabular data: | | | | ------------------------------------------------- | -------------------------------------------------------- | | {colx, coly, colz} | plot values from columns colx, coly and colz | | {{colx1, coly1, colz1}, {colx2, coly2, colz2}, …} | plot values from multiple sets of columns | | {{colz1}, {colz2}, …} | plot each column colz1, colz2, … as sequences of heights | * The following wrappers ``w`` can be used for the ``datai``: | | | | -------------------------- | ---------------------------------------------------- | | Annotation[datai, label] | provide an annotation for the data | | Button[datai, action] | define an action to execute when the data is clicked | | Callout[datai, label] | label the data with a callout | | Callout[datai, label, pos] | place the callout at relative position pos | | EventHandler[datai, …] | define a general event handler for the data | | Hyperlink[datai, uri] | make the data a hyperlink | | Labeled[datai, label] | label the data | | Labeled[datai, label, pos] | place the label at relative position pos | | Legended[datai, label] | identify the data in a legend | | PopupWindow[datai, cont] | attach a popup window to the data | | StatusArea[datai, label] | display in the status area on mouseover | | Style[datai, styles] | show the data using the specified styles | | Tooltip[datai, label] | attach a tooltip to the data | | Tooltip[datai] | use data values as tooltips | * Wrappers ``w`` can be applied at multiple levels: | | | | ----------------------- | ---------------------------------- | | {{…, w[zi, j], …}} | wrap the value zi, j in array data | | {…, w[{xi, yi, zi}], …} | wrap the point {xi, yi, zi} | | w[datai] | wrap the data | | w[{data1, …}] | wrap a collection of datai | | w1[w2[…]] | use nested wrappers | * ``ListLinePlot3D`` takes the same options as ``Graphics3D`` with the following additions and changes: [] | | | | | :-------------------- | :---------------------------- | :--------------------------------------------------- | | Axes | True | whether to draw axes | | BoxRatios | {1, 1, 0.4} | bounding 3D box ratios | | ColorFunction | Automatic | how to determine the color of points | | ColorFunctionScaling | True | whether to scale arguments to ColorFunction | | DataRange | Automatic | the range of x and y values to assume for data | | Filling | None | how to fill in stems for each point | | FillingStyle | Automatic | style to use for filling | | IntervalMarkers | Automatic | how to render uncertainty | | IntervalMarkersStyle | Automatic | style for uncertainty elements | | Joined | True | whether to join the points | | LabelingFunction | Automatic | how to label points | | LabelingSize | Automatic | size to use for callout and label | | Mesh | None | how many mesh points to draw on each line | | MeshFunctions | {#1&} | how to determine the placement of mesh points | | MeshShading | None | how to shade regions between mesh points | | MeshStyle | Automatic | the style for mesh points | | PerformanceGoal | \$PerformanceGoal | aspects of performance to try to optimize | | PlotLabels | None | labels to use for curves | | PlotLegends | None | legends for points | | PlotMarkers | None | markers to use for points | | PlotRange | {Full, Full, Automatic} | the range of z or other values to include | | PlotRangePadding | Automatic | how much to pad the range of values | | PlotStyle | Automatic | styles of points | | PlotTheme | \$PlotTheme | overall theme for the plot | | RegionFunction | (True&) | how to determine whether a point should be included | | RegionBoundaryStyle | $$\fbox{$\text{Automatic}$}$$ | style to use for a region | | ScalingFunctions | None | how to scale individual coordinates | * ``ListLinePlot3D[{{z11, z12, …}, …}]`` by default takes the ``x`` and ``y`` coordinate values for each data point to be successive integers starting at 1. * The setting ``DataRange -> {{xmin, xmax}, {ymin, ymax}}`` specifies other ranges of coordinate values to use. * With the default setting ``DataRange -> Automatic``, ``ListLinePlot3D[{{z11, z12, z13}, …, {zn 1, zn 2, zn 3}}]`` will assume that the data being given is ``{{x1, y1, z1}, …}``, rather than an $n$×3 array of heights. * ``ListLinePlot3D[data, DataRange -> All]`` always takes ``data`` to represent an array of heights. * Possible settings for ``PlotMarkers`` include: | | | | --------------------------- | -------------------------------------------- | | None | omit markers when drawing surfaces | | "Point" | use 2D points as markers | | "Sphere" | use 3D spheres as markers | | {"Point", s}, {"Sphere", s} | specify the size s of the markers | | {spec1, spec2, …} | use specification speci for expression expri | * The marker size ``s`` can be a symbolic value such as ``Tiny``, ``Small``, ``Medium`` and ``Large`` or a scaled fraction of the width of the graphic. * Possible settings for ``IntervalMarkers`` include: | | | | | ------- | ------- | ------------------------------ | | [image] | "Bars" | draw bars to represent errors | | [image] | "Tubes" | draw tubes to represent errors | * Possible settings for ``ScalingFunctions`` include: | | | | ------------ | --------------------- | | sz | scale the z axis | | {sx, sy} | scale x and y axes | | {sx, sy, sz} | scale x, y and z axes | * Each scaling function ``si`` is either a string ``"scale"`` or ``{g, g^-1}``, where ``g^-1`` is the inverse of ``g``. * The arguments supplied to functions in ``MeshFunctions`` and ``RegionFunction`` are $x$, $y$ and $z$. Functions in ``ColorFunction`` are by default supplied with scaled versions of these arguments. ### List of all options | | | | | -------------------- | ----------------------------- | ---------------------------------------------------------------------------------- | | AlignmentPoint | Center | the default point in the graphic to align with | | AspectRatio | Automatic | ratio of height to width | | Axes | True | whether to draw axes | | AxesEdge | Automatic | on which edges to put axes | | AxesLabel | None | axes labels | | AxesOrigin | Automatic | where axes should cross | | AxesStyle | {} | graphics directives to specify the style for 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 | | Boxed | True | whether to draw the bounding box | | BoxRatios | {1, 1, 0.4} | bounding 3D box ratios | | BoxStyle | {} | style specifications for the box | | ClipPlanes | None | clipping planes | | ClipPlanesStyle | Automatic | style specifications for clipping planes | | ColorFunction | Automatic | how to determine the color of points | | ColorFunctionScaling | True | whether to scale arguments to ColorFunction | | ContentSelectable | Automatic | whether to allow contents to be selected | | ControllerLinking | False | when to link to external rotation controllers | | ControllerPath | Automatic | what external controllers to try to use | | DataRange | Automatic | the range of x and y values to assume for data | | Epilog | {} | 2D graphics primitives to be rendered after the main plot | | FaceGrids | None | grid lines to draw on the bounding box | | FaceGridsStyle | {} | style specifications for face grids | | Filling | None | how to fill in stems for each point | | FillingStyle | Automatic | style to use for filling | | FormatType | TraditionalForm | default format type for text | | ImageMargins | 0. | the margins to leave around the graphic | | ImagePadding | All | what extra padding to allow for labels, etc. | | ImageSize | Automatic | absolute size at which to render the graphic | | IntervalMarkers | Automatic | how to render uncertainty | | IntervalMarkersStyle | Automatic | style for uncertainty elements | | Joined | True | whether to join the points | | LabelingFunction | Automatic | how to label points | | LabelingSize | Automatic | size to use for callout and label | | LabelStyle | {} | style specifications for labels | | Lighting | Automatic | simulated light sources to use | | Mesh | None | how many mesh points to draw on each line | | MeshFunctions | {#1&} | how to determine the placement of mesh points | | MeshShading | None | how to shade regions between mesh points | | MeshStyle | Automatic | the style for mesh points | | Method | Automatic | details of 3D graphics methods to use | | PerformanceGoal | \$PerformanceGoal | aspects of performance to try to optimize | | PlotLabel | None | a label for the plot | | PlotLabels | None | labels to use for curves | «2 rows removed» | PlotRange | {Full, Full, Automatic} | the range of z or other values to include | | PlotRangePadding | Automatic | how much to pad the range of values | | PlotRegion | Automatic | final display region to be filled | | PlotStyle | Automatic | styles of points | | PlotTheme | \$PlotTheme | overall theme for the plot | | PreserveImageOptions | Automatic | whether to preserve image options when displaying new versions of the same graphic | | Prolog | {} | 2D graphics primitives to be rendered before the main plot | | RegionBoundaryStyle | $$\fbox{$\text{Automatic}$}$$ | style to use for a region | | RegionFunction | (True&) | how to determine whether a point should be included | | RotationAction | "Fit" | how to render after interactive rotation | | ScalingFunctions | None | how to scale individual coordinates | | SphericalRegion | Automatic | whether to make the circumscribing sphere fit in the final display area | | Ticks | Automatic | specification for ticks | | TicksStyle | {} | style specification for ticks | | TouchscreenAutoZoom | False | whether to zoom to fullscreen when activated on a touchscreen | | ViewAngle | Automatic | angle of the field of view | | ViewCenter | Automatic | point to display at the center | | ViewMatrix | Automatic | explicit transformation matrix | | ViewPoint | {1.3, -2.4, 2.} | viewing position | | ViewProjection | Automatic | projection method for rendering objects distant from the viewer | | ViewRange | All | range of viewing distances to include | | ViewVector | Automatic | position and direction of a simulated camera | | ViewVertical | {0, 0, 1} | direction to make vertical | --- ## Examples (138) ### Basic Examples (5) Plot a path through a set of points: ```wl In[1]:= ListLinePlot3D[{{0, 0, 0}, {1, 0, 1}, {1, 1, 2}, {2, 2, 2}, {2, 4, 3}, {3, 6, 4}}] Out[1]= [image] ``` --- Fill the area under the curve: ```wl In[1]:= ListLinePlot3D[{{0, 0, 0}, {1, 0, 1}, {1, 1, 2}, {2, 2, 2}, {2, 4, 3}, {3, 6, 4}}, Filling -> Bottom] Out[1]= [image] ``` --- Plot multiple filled paths at successive locations along the axis: ```wl In[1]:= ListLinePlot3D[{{2.1, 2.9, 2.8, 1.9, 1.1, 1.2, 2.1}, {2.2, 2.7, 1.1, 2.2, 2.7, 1.1, 2.2}, {2.3, 1.7, 2.3, 1.7, 2.3, 1.7, 2.3}, {2.4, 1.0, 2.6, 2.4, 1.0, 2.6, 2.4}}] Out[1]= [image] ``` --- Plot multiple filled paths at successive locations along the axis: ```wl In[1]:= ListLinePlot3D[IconizedObject[«data»], Filling -> Axis] Out[1]= [image] ``` --- Plot multiple curves through space: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2Pi, Pi / 15}]] Out[1]= [image] ``` ### Scope (36) #### General Data (7) For regular data consisting of $z$ values, the $x$ and $y$ data ranges are taken to be integer values: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»]] Out[1]= [image] ``` --- Provide explicit $x$ and $y$ data ranges by using ``DataRange`` : ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], DataRange -> {{0, 1}, {0, 1}}] Out[1]= [image] ``` --- For irregular data consisting of $\{x,y,z\}$ triples, the $x$ and $y$ data ranges are inferred from the data: ```wl In[1]:= ListLinePlot3D[Table[{i, Cos[i], Sin[i]}, {i, 0, 20, .1}]] Out[1]= [image] ``` --- Plot multiple sets of irregular data: ```wl In[1]:= data1 = Table[{i, Cos[i], Sin[i]}, {i, 0, 20, .1}]; data2 = Table[{i, Cos[i + Pi / 2], Sin[i + Pi / 2]}, {i, 0, 20, .1}]; In[2]:= ListLinePlot3D[{data1, data2}] Out[2]= [image] ``` --- Areas around where the data is nonreal are excluded: ```wl In[1]:= ListLinePlot3D[Table[Sqrt[2 - i ^ 2 - j ^ 2], {i, -2, 2, .1}, {j, -2, 2, .1}]] Out[1]= [image] ``` --- ``PlotRange`` is selected automatically: ```wl In[1]:= ListLinePlot3D[Table[1 / (x ^ 2 + y ^ 2), {x, -2, 2, 8 / 51}, {y, -2, 2, 8 / 51}]] Out[1]= [image] ``` Use ``PlotRange`` to focus in on areas of interest: ```wl In[2]:= {ListLinePlot3D[Table[x ^ 4 + y ^ 4 - x ^ 2 - y ^ 2 + 1, {x, -2, 2, 0.15}, {y, -2, 2, 0.15}]], ListLinePlot3D[Table[x ^ 4 + y ^ 4 - x ^ 2 - y ^ 2 + 1, {x, -2, 2, 0.15}, {y, -2, 2, 0.15}], PlotRange -> {0, 2}]} Out[2]= {[image], [image]} ``` --- Use ``RegionFunction`` to restrict lines to a region given by inequalities: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], RegionFunction -> (#1 ^ 2 + #2 ^ 2 < 7&), DataRange -> {{-Pi, Pi}, {-Pi, Pi}}] Out[1]= [image] ``` #### Tabular Data (1) Get tabular data: ```wl In[1]:= tabdata = Tabular[IconizedObject[«waves»], {"n=1", "n=2", "n=3", "n=4", "n=5", "n=6"}] Out[1]= Tabular[Association["RawSchema" -> Association["ColumnProperties" -> Association["n=1" -> Association["ElementType" -> "Real64"], "n=2" -> Association["ElementType" -> "Real64"], "n=3" -> Association["ElementType" -> "Real64"], ... 64814730119271, 1.1050599544663169, 0.9675390689570036, 0.94379447076751, 1.0441995714318935, 1.1859235307290874, 1.2808436971118813, 1.2974606473182722, 1.2580447225693001}, {}, None}, "ElementType" -> "Real64"]]}}]]]] ``` Plot separate curves for separate columns: ```wl In[2]:= ListLinePlot3D[tabdata -> {{"n=1"}, {"n=2"}, {"n=3" }, {"n=4"}, {"n=5"}, {"n=6"}}] Out[2]= [image] ``` Get temperature data for a few years, split by city: ```wl In[1]:= temps = PivotToColumns[Tabular[IconizedObject[«Temperature data»], {"IndexDate", "Date", "City", "Temperature"}], "City" -> "Temperature"] Out[1]= Tabular[Association["RawSchema" -> Association["ColumnProperties" -> Association["IndexDate" -> Association["ElementType" -> "Integer64"], "Date" -> Association["ElementType" -> TypeSpecifier["Date"]["Integer64", "Month", "G ... ypeSpecifier["Quantity"]["Real64", "DegreesFahrenheit"]]], TabularColumn[Association["Data" -> {49, {{CompressedData["«303»"], {}, None}}, None}, "ElementType" -> TypeSpecifier["Quantity"]["Real64", "DegreesFahrenheit"]]]}}]]]] ``` Plot the temperatures as separate curves over time: ```wl In[15]:= ListLinePlot3D[temps -> {{"Austin"}, {"Atlanta"}, {"Denver"}, {"Miami"}, {"New York City"}}] Out[15]= [image] ``` #### Special Data (6) Use ``Quantity`` to include units with the data: ```wl In[1]:= ListLinePlot3D[Quantity[RandomReal[1, {6, 3}], "Meters"], AxesLabel -> Automatic] Out[1]= [image] ``` --- Plot data in a ``QuantityArray`` : ```wl In[1]:= temps = QuantityArray[StructuredArray`StructuredData[{6, 28}, {CompressedData["«733»"], "DegreesFahrenheit", {{2}, {1}}}]]; In[2]:= cities = {Entity["City", {"Austin", "Texas", "UnitedStates"}], Entity["City", {"Atlanta", "Georgia", "UnitedStates"}], Entity["City", {"Chicago", "Illinois", "UnitedStates"}], Entity["City", {"Denver", "Colorado", "UnitedStates"}], Entity["City", {"Miami", "Florida", "UnitedStates"}], Entity["City", {"NewYork", "NewYork", "UnitedStates"}]}; In[3]:= ListLinePlot3D[temps, AxesLabel -> Automatic, PlotLegends -> cities] Out[3]= [image] ``` Specify the units used with ``TargetUnits`` : ```wl In[4]:= ListLinePlot3D[temps, TargetUnits -> {None, None, "DegreesCelsius"}, AxesLabel -> Automatic, PlotLegends -> cities] Out[4]= [image] ``` --- Plot data with uncertainty: ```wl In[1]:= zvar = Table[Around[Sin[x] Cos[y], 0.25], {x, -4, 4}, {y, -4, 4}]; In[2]:= ListLinePlot3D[zvar] Out[2]= [image] ``` --- Plot data from time series with automatic date ticks: ```wl In[1]:= cities = {Entity["City", {"Austin", "Texas", "UnitedStates"}], Entity["City", {"Atlanta", "Georgia", "UnitedStates"}], Entity["City", {"Chicago", "Illinois", "UnitedStates"}], Entity["City", {"Denver", "Colorado", "UnitedStates"}], Entity["City", {"Miami", "Florida", "UnitedStates"}], Entity["City", {"NewYork", "NewYork", "UnitedStates"}]}; In[2]:= data = AirTemperatureData[cities, {DateObject[{2021, 2, 1}, "Day", "Gregorian", -5.], DateObject[{2021, 2, 28}, "Day", "Gregorian", -5.], "Day"}]; In[3]:= ListLinePlot3D[data, PlotLegends -> cities] Out[3]= [image] ``` --- Specify strings to use as labels: ```wl In[1]:= ListLinePlot3D[RandomReal[1, {6, 3}] -> RandomWord[6], LabelingFunction -> Callout] Out[1]= [image] ``` --- Plot data in a ``SparseArray`` : ```wl In[1]:= ListLinePlot3D[SparseArray[{{i_, i_} -> -2, {i_, j_} /; Abs[i - j] == 1 -> 1}, {5, 5}]] Out[1]= [image] ``` #### Data Wrappers (6) Use a wrapper to style a specific curve: ```wl In[1]:= ListLinePlot3D[{Style[IconizedObject[«curve A»], Green], IconizedObject[«curve B»]}] Out[1]= [image] ``` --- Apply a style to all the curves: ```wl In[1]:= ListLinePlot3D[Style[{IconizedObject[«curve A»], IconizedObject[«curve B»]}, Blue]] Out[1]= [image] ``` --- Use the value of each point as a tooltip: ```wl In[1]:= ListLinePlot3D[Tooltip[RandomReal[1, {10, 3}]], PlotMarkers -> Automatic] Out[1]= [image] ``` Use a specific label for all the points: ```wl In[2]:= ListLinePlot3D[Tooltip[RandomReal[1, {10, 3}], "hello"]] Out[2]= [image] ``` --- Label points with automatically positioned text: ```wl In[1]:= ListLinePlot3D[Sort[Table[Labeled[RandomReal[1, 3], i], {i, 15}]], PlotMarkers -> Automatic] Out[1]= [image] ``` --- Use ``PopupWindow`` to provide additional drilldown information: ```wl In[1]:= ListLinePlot3D[{{1, 1, 1}, PopupWindow[{2, 2, 2}, DateListPlot[FinancialData["IBM", "Jan. 1, 2004"]]], {3, 3, 3}}, PlotMarkers -> {"Sphere", .05}] Out[1]= [image] ``` --- ``Button`` can be used to trigger any action: ```wl In[1]:= ListLinePlot3D[{{1, 1, 1}, Button[{2, 2, 2}, Speak[2]], {3, 3, 3}}, PlotMarkers -> {"Sphere", 0.05}] Out[1]= [image] ``` #### Labeling and Legending (6) Label points with automatically positioned text: ```wl In[1]:= ListLinePlot3D[{Table[Labeled[i, i], {i, 10}], Table[Labeled[i, i], {i, 10}]}] Out[1]= [image] ``` --- Specify that labels should be above or below the curve: ```wl In[1]:= ListLinePlot3D[{Table[Labeled[i, i, Above], {i, 10}], Table[Labeled[i, i, Below], {i, 10}]}] Out[1]= [image] ``` --- Specify label names with ``LabelingFunction`` : ```wl In[1]:= ListLinePlot3D[Sort[RandomReal[1, {10, 3}]], LabelingFunction -> (#1[[1]] &)] Out[1]= [image] ``` --- Include legends for each point collection: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotLegends -> Automatic] Out[1]= [image] ``` --- Specify the maximum size of labels: ```wl In[1]:= data = Sort[Table[Labeled[{RandomReal[i], RandomReal[i], RandomReal[i]}, RandomWord[]], {i, 10}]]; In[2]:= ListLinePlot3D[data, LabelingSize -> 30] Out[2]= [image] ``` Use the full label: ```wl In[3]:= ListLinePlot3D[data, LabelingSize -> Full] Out[3]= [image] ``` --- For dense sets of points, some labels may be turned into tooltips by default: ```wl In[1]:= data = Table[Labeled[{Cos[i], Sin[i], Sin[7i]}, i], {i, 0, 2Pi, 0.1}]; In[2]:= ListLinePlot3D[data, ImageSize -> 200] Out[2]= [image] In[3]:= ListLinePlot3D[data, ImageSize -> 400] Out[3]= [image] ``` #### Presentation (10) ```wl Out[1]= Presentation ``` --- Provide an explicit ``PlotStyle`` for the lines: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotStyle -> {Red, Green, Blue, Orange, Magenta}] Out[1]= [image] ``` --- Provide separate styles for different sets: ```wl In[1]:= data1 = Table[Sqrt[1 - x ^ 2 - y ^ 2], {x, -1, 1, 0.05}, {y, -1, 1, 0.1}]; In[2]:= data2 = Table[-Sqrt[1 - x ^ 2 - y ^ 2], {x, -1, 1, 0.05}, {y, -1, 1, 0.1}]; In[3]:= ListLinePlot3D[{data1, data2}, PlotStyle -> {Red, Blue}, BoxRatios -> Automatic, DataRange -> {{-1, 1}, {-1, 1}}] Out[3]= [image] ``` --- Add labels: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], AxesLabel -> {j, i}, PlotLabel -> Sin[i + j ^ 2], PlotStyle -> Purple] Out[1]= [image] ``` --- Color lines by height: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], ColorFunction -> Function[{x, y, z}, Hue[z]]] Out[1]= [image] ``` --- Provide an interactive ``Tooltip`` for the whole plot: ```wl In[1]:= ListLinePlot3D[Tooltip[IconizedObject[«waves»], TraditionalForm@Sin[i + j ^ 2]], PlotStyle -> Darker[Green]] Out[1]= [image] ``` --- Fill below the points: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], Filling -> Bottom, FillingStyle -> Directive[Opacity[0.3], Blue], PlotStyle -> Red] Out[1]= [image] ``` --- Use a theme with simple ticks in a bright color scheme: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotTheme -> "Business"] Out[1]= [image] ``` --- Use a highly styled theme: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotTheme -> "Marketing"] Out[1]= [image] ``` --- Use a logarithmic scale on the $z$ axis: ```wl In[1]:= ListLinePlot3D[EntityValue[EntityClass["Country", "GroupOf7"], Dated["Population", All], "EntityAssociation"], PlotLegends -> "Expressions", ScalingFunctions -> {None, None, "Log"}] Out[1]= [image] ``` --- Specify scaling functions for each axis: ```wl In[1]:= curve = Table[t ^ 2{Cos[t], Sin[t], Sqrt[t]}, {t, 0, 100, 0.25}]; In[2]:= ListLinePlot3D[curve, BoxRatios -> 1, ScalingFunctions -> {"Reverse", "Infinite", "Log"}] Out[2]= [image] ``` ### Options (79) #### Axes (3) By default, axes are drawn: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»]] Out[1]= [image] ``` --- Use ``Axes -> False`` to turn off axes: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], Axes -> False] Out[1]= [image] ``` --- Turn each axis on individually: ```wl In[1]:= {ListLinePlot3D[IconizedObject[«waves»], Axes -> {True, False, False}], ListLinePlot3D[IconizedObject[«waves»], Axes -> {False, True, False}], ListLinePlot3D[IconizedObject[«waves»], Axes -> {False, False, True}]} Out[1]= {[image], [image], [image]} ``` #### AxesLabel (4) No axes labels are drawn by default: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»]] Out[1]= [image] ``` --- Place a label on the $z$ axis: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], AxesLabel -> "zlabel"] Out[1]= [image] ``` --- Specify axes labels: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], AxesLabel -> {"Label1", "Label2", "Label3"}] Out[1]= [image] ``` --- Use units as labels: ```wl In[1]:= ListLinePlot3D[QuantityArray[Table[PDF[NormalDistribution[m, Sqrt[Abs[3 - m]]]][x], {m, -2, 2}, {x, -5, 5, 0.5}], "Meters"], AxesLabel -> Automatic] Out[1]= [image] ``` #### AxesOrigin (2) The position of the axes is determined automatically: ```wl In[1]:= ListLinePlot3D[Table[PDF[NormalDistribution[m, Sqrt[Abs[3 - m]]]][x], {m, -2, 2}, {x, -5, 5, 0.5}]] Out[1]= [image] ``` --- Specify an explicit origin for the axes: ```wl In[1]:= ListLinePlot3D[Table[PDF[NormalDistribution[m, Sqrt[Abs[3 - m]]]][x], {m, -2, 2}, {x, -5, 5, 0.5}], AxesOrigin -> {10, 0, 0}] Out[1]= [image] ``` #### AxesStyle (4) Change the style for the axes: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], AxesStyle -> Red] Out[1]= [image] ``` --- Specify the style of each axis: ```wl In[1]:= ListLinePlot3D[Table[PDF[NormalDistribution[m, 0.4]][x], {m, 1, 5}, {x, 0, 5, 0.2}], AxesStyle -> {Directive[Thick, RGBColor[0.6, 0.4, 0.2]], Directive[Thick, RGBColor[0, 0, 1]], Directive[Thick, RGBColor[1, 0.5, 0]]}] Out[1]= [image] ``` --- Use different styles for the ticks and the axes: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], AxesStyle -> Green, TicksStyle -> Black] Out[1]= [image] ``` --- Use different styles for the labels and the axes: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], AxesStyle -> Green, LabelStyle -> Black] Out[1]= [image] ``` #### BoxRatios (2) ``Automatic`` uses the natural scale from ``PlotRange`` : ```wl In[1]:= {ListLinePlot3D[IconizedObject[«waves»]], ListLinePlot3D[IconizedObject[«waves»], BoxRatios -> Automatic]} Out[1]= {[image], [image]} ``` --- Use ``BoxRatios`` to emphasize some particular feature, in this case, a saddle surface: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], BoxRatios -> {1, 1, 2}] Out[1]= [image] ``` #### ColorFunction (7) Use a named gradient from ``ColorData`` to color curves by their height: ```wl In[1]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> "Rainbow"] Out[1]= [image] ``` --- Color curves by scaled $x$ values: ```wl In[1]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> Function[{x, y, z}, Hue[x]]] Out[1]= [image] ``` --- Color curves by scaled $x$ values: ```wl In[1]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> Function[{x, y, z}, Hue[y]]] Out[1]= [image] ``` --- Color curves by scaled $x$ values: ```wl In[1]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> Function[{x, y, z}, Hue[z]]] Out[1]= [image] ``` --- Colors from ``ColorFunction`` are used with the filled regions as well as the curve: ```wl In[1]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> "Rainbow", Filling -> Axis] Out[1]= [image] ``` --- Colors from ``ColorFunction`` have higher priority than from ``PlotStyle`` : ```wl In[1]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> "Rainbow", PlotStyle -> Red] Out[1]= [image] ``` --- Colors from ``ColorFunction`` combine with non-color styles from ``PlotStyle`` : ```wl In[1]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> "Rainbow", PlotStyle -> Directive[Thick, Dashed, Opacity[0.5]]] Out[1]= [image] ``` #### ColorFunctionScaling (2) Use unscaled coordinates: ```wl In[1]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> Function[{x, y, z}, Hue@Rescale[Arg[Sin[x + I y]], {-Pi, Pi}]], ColorFunctionScaling -> False] Out[1]= [image] ``` --- Unscaled coordinates are dependent on ``DataRange`` : ```wl In[1]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> Function[{x, y, z}, RGBColor[x, y, 0]], ColorFunctionScaling -> False] Out[1]= [image] In[2]:= ListLinePlot3D[IconizedObject[«curves»], ColorFunction -> Function[{x, y, z}, RGBColor[x, y, 0]], ColorFunctionScaling -> False, DataRange -> {{0, 1}, {0, 1}}] Out[2]= [image] ``` #### DataRange (4) Arrays of height values are displayed against the number of elements in each direction: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»]] Out[1]= [image] ``` --- Rescale to the sampling space: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], DataRange -> {{0, 1}, {0, 1}}] Out[1]= [image] ``` --- Triples are interpreted as $x$, $y$, $z$ coordinates: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»]] Out[1]= [image] ``` --- Force interpretation as arrays of height values: ```wl In[1]:= data = Table[Sin[i + j], {j, 0, 2Pi, 0.1}, {i, -1, 1}]; In[2]:= ListLinePlot3D[data, DataRange -> All] Out[2]= [image] ``` The dataset is normally interpreted as a list of $x$, $y$, $z$ triples: ```wl In[3]:= ListLinePlot3D[data] Out[3]= [image] ``` #### Filling (3) Fill to the bottom, using "stems": ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], Filling -> Bottom, PlotRange -> All] Out[1]= [image] ``` --- Filling occurs along the region cut by the ``RegionFunction`` : ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], Filling -> Bottom, RegionFunction -> (#1 ^ 2 + #2 ^ 2 < 5&), DataRange -> {{-Pi, Pi}, {-Pi, Pi}}] Out[1]= [image] ``` --- Fill surface 1 to the bottom with blue and surface 2 to the top with red: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotRange -> All, Filling -> {1 -> {Bottom, Blue}, 2 -> {Top, Red}}] Out[1]= [image] ``` #### FillingStyle (2) Fill to the bottom with a variety of styles: ```wl In[1]:= {ListLinePlot3D[IconizedObject[«heights»], Filling -> Bottom, FillingStyle -> Directive[Opacity[0.2], Gray]], ListLinePlot3D[IconizedObject[«heights»], Filling -> Bottom, FillingStyle -> Opacity[0.75]]} Out[1]= {[image], [image]} ``` --- Fill to the plane $z=0$ from above only: ```wl In[1]:= ListLinePlot3D[IconizedObject[«heights»], Filling -> 0, FillingStyle -> Blue] Out[1]= [image] ``` #### ImageSize (7) Use named sizes such as ``Tiny``, ``Small``, ``Medium`` and ``Large`` : ```wl In[1]:= {ListLinePlot3D[IconizedObject[«waves»], ImageSize -> Tiny], ListLinePlot3D[IconizedObject[«waves»], ImageSize -> Small]} Out[1]= {[image], [image]} ``` --- Specify the width of the plot: ```wl In[1]:= {ListLinePlot3D[IconizedObject[«waves»], ImageSize -> 150], ListLinePlot3D[IconizedObject[«waves»], BoxRatios -> {1, 1, 2}, ImageSize -> 150]} Out[1]= {[image], [image]} ``` Specify the height of the plot: ```wl In[2]:= {ListLinePlot3D[IconizedObject[«waves»], ImageSize -> {Automatic, 150}], ListLinePlot3D[IconizedObject[«waves»], BoxRatios -> {1, 1, 2}, ImageSize -> {Automatic, 150}]} Out[2]= {[image], [image]} ``` --- Allow the width and height to be up to a certain size: ```wl In[1]:= {ListLinePlot3D[IconizedObject[«waves»], ImageSize -> UpTo[200]], ListLinePlot3D[IconizedObject[«waves»], BoxRatios -> {1, 1, 2}, ImageSize -> UpTo[200]]} Out[1]= {[image], [image]} ``` --- Specify the width and height for a graphic, padding with space if necessary: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], ImageSize -> {200, 250}, Background -> LightBlue] Out[1]= [image] ``` --- Use maximum sizes for the width and height: ```wl In[1]:= {ListLinePlot3D[IconizedObject[«waves»], ImageSize -> {UpTo[150], UpTo[100]}], ListLinePlot3D[IconizedObject[«waves»], BoxRatios -> {1, 1, 2}, ImageSize -> {UpTo[150], UpTo[100]}]} Out[1]= {[image], [image]} ``` --- Use ``ImageSize -> Full`` to fill the available space in an object: ```wl In[1]:= Framed[Pane[ListLinePlot3D[IconizedObject[«waves»], ImageSize -> Full, Background -> LightBlue], {200, 100}]] Out[1]= [image] ``` --- Specify the image size as a fraction of the available space: ```wl In[1]:= Framed[Pane[ListLinePlot3D[IconizedObject[«waves»], AspectRatio -> Full, ImageSize -> {Scaled[0.5], Scaled[0.5]}, Background -> LightBlue], {200, 200}]] Out[1]= [image] ``` #### IntervalMarkers (2) Interval markers are bars by default: ```wl In[1]:= zvar = Table[Around[Sin[x] Cos[y], 0.25], {x, -4, 4}, {y, -4, 4}]; In[2]:= ListLinePlot3D[zvar] Out[2]= [image] ``` --- Use named ``IntervalMarkers`` : ```wl In[1]:= xyzvar = Table[{Cos[t], Sin[t], Around[Sin[t] Cos[t], 1]}, {t, 0, 2Pi, 0.2}]; In[2]:= ListLinePlot3D[xyzvar, IntervalMarkers -> "Tubes"] Out[2]= [image] ``` #### IntervalMarkersStyle (2) Interval markers are black by default: ```wl In[1]:= zvar = Table[Around[Sin[x] Cos[y], 0.25], {x, -4, 4}, {y, -4, 4}]; In[2]:= ListLinePlot3D[zvar] Out[2]= [image] ``` --- Specify the style for the bars: ```wl In[1]:= xyzvar = Table[{Cos[t], Sin[t], Around[Sin[t] Cos[t], 1]}, {t, 0, 2Pi, 0.2}]; In[2]:= ListLinePlot3D[xyzvar, IntervalMarkersStyle -> Red] Out[2]= [image] ``` #### Joined (3) Datasets are joined by default: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»]] Out[1]= [image] ``` --- Join the first dataset with a line, but use points for the second dataset: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], Joined -> {True, False, False, False, False}] Out[1]= [image] ``` --- Join the dataset with a line and show the original points: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], Joined -> True, Mesh -> All, PlotStyle -> Thin] Out[1]= [image] ``` #### PlotLegends (5) No legend is used by default: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»]] Out[1]= [image] ``` --- Generate a legend using labels: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotStyle -> {Red, Blue}, PlotLegends -> {"One", "Two"}] Out[1]= [image] ``` --- Generate a legend using placeholders: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotLegends -> Automatic] Out[1]= [image] ``` --- Use ``Placed`` to specify legend placement: ```wl In[1]:= {ListLinePlot3D[IconizedObject[«waves»], PlotLegends -> Placed[Range[5], Above]], ListLinePlot3D[IconizedObject[«waves»], PlotLegends -> Placed[Range[5], Below]]} Out[1]= {[image], [image]} ``` --- Build a custom legend with ``BarLegend`` : ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], ColorFunction -> (ColorData["Rainbow"][#1]&), PlotLegends -> Placed[BarLegend[{"Rainbow", {-1, 1}}], Below]] Out[1]= [image] ``` #### PlotMarkers (4) ``ListLinePlot`` normally shows just the curves: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotMarkers -> None] Out[1]= [image] ``` --- Include the data points in the plot: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotMarkers -> Automatic, PlotStyle -> Thin] Out[1]= [image] ``` --- Change the size of the default plot markers: ```wl In[1]:= {ListLinePlot3D[IconizedObject[«waves»], PlotMarkers -> {Automatic, Medium}], ListLinePlot3D[IconizedObject[«waves»], PlotMarkers -> {Automatic, Large}]} Out[1]= {[image], [image]} ``` --- Use spheres as markers: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotMarkers -> "Sphere"] Out[1]= [image] ``` Specify how large the spheres should be: ```wl In[2]:= ListLinePlot3D[IconizedObject[«waves»], PlotMarkers -> {"Sphere", Medium}] Out[2]= [image] ``` #### PlotRange (3) Automatically compute the $z$ range: ```wl In[1]:= ListLinePlot3D[IconizedObject[«array»]] Out[1]= [image] ``` --- Use all points to compute the range: ```wl In[1]:= ListLinePlot3D[IconizedObject[«array»], PlotRange -> All] Out[1]= [image] ``` --- Use an explicit $z$ range to emphasize features: ```wl In[1]:= ListLinePlot3D[Table[y ^ 2 - x ^ 2, {x, -4, 4, 0.1}, {y, -4, 4, 0.1}], PlotRange -> {-2, 2}] Out[1]= [image] ``` #### PlotStyle (1) Plot two point sets with different styles: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotStyle -> {Pink, Green}] Out[1]= [image] ``` #### PlotTheme (2) Use a theme with simple ticks in a bold color scheme: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotTheme -> "Marketing"] Out[1]= [image] ``` --- Change the color for the curves: ```wl In[1]:= ListLinePlot3D[IconizedObject[«waves»], PlotTheme -> "Marketing", PlotStyle -> Red] Out[1]= [image] ``` #### RegionBoundaryStyle (3) Show the region being plotted: ```wl In[1]:= ListLinePlot3D[Table[Exp[-(i ^ 2 + j ^ 2)], {i, -2, 2, 0.1}, {j, -2, 2, 0.1}], RegionFunction -> Function[{x, y, z}, x < 0 || y > 0], DataRange -> {{-2, 2}, {-2, 2}}] Out[1]= [image] ``` --- Use ``None`` to not draw the region: ```wl In[1]:= ListLinePlot3D[Table[Exp[-(i ^ 2 + j ^ 2)], {i, -2, 2, 0.1}, {j, -2, 2, 0.1}], RegionFunction -> Function[{x, y, z}, x < 0 || y > 0], DataRange -> {{-2, 2}, {-2, 2}}, RegionBoundaryStyle -> None] Out[1]= [image] ``` --- Use a custom ``RegionBoundaryStyle`` : ```wl In[1]:= ListLinePlot3D[Table[Exp[-(i ^ 2 + j ^ 2)], {i, -2, 2, 0.1}, {j, -2, 2, 0.1}], RegionFunction -> Function[{x, y, z}, x < 0 || y > 0], DataRange -> {{-2, 2}, {-2, 2}}, PlotStyle -> PointSize[Small], RegionBoundaryStyle -> Directive[Yellow, Opacity[.2]]] Out[1]= [image] ``` #### ScalingFunctions (5) By default, plots have linear scales in each direction: ```wl In[1]:= ListLinePlot3D[IconizedObject[«data»], PlotRange -> All] Out[1]= [image] ``` --- Use a log scale in the $z$ direction: ```wl In[1]:= ListLinePlot3D[IconizedObject[«data»], ScalingFunctions -> "Log"] Out[1]= [image] ``` --- Use a linear scale in the $z$ direction that shows smaller numbers at the top: ```wl In[1]:= ListLinePlot3D[IconizedObject[«data»], ScalingFunctions -> "Reverse", PlotRange -> All] Out[1]= [image] ``` --- Use different scales in the $x$, $y$ and $z$ directions: ```wl In[1]:= ListLinePlot3D[IconizedObject[«data»], ScalingFunctions -> {"Log", "Log", "Reverse"}] Out[1]= [image] ``` --- Use a scale defined by a function and its inverse: ```wl In[1]:= ListLinePlot3D[IconizedObject[«data»], ScalingFunctions -> {None, None, {-Log[#]&, Exp[-#]&}}] Out[1]= [image] ``` #### Ticks (6) Ticks are placed automatically in each plot: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2 Pi, Pi / 25}]] Out[1]= [image] ``` --- Use ``Ticks -> None`` to not draw any tick marks: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2 Pi, Pi / 25}], Ticks -> None] Out[1]= [image] ``` --- Place tick marks at specific positions: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2 Pi, Pi / 25}], Ticks -> {{-1, 1, 2}, {-1, 1, 2}, {-1, 0, 1}}] Out[1]= [image] ``` --- Draw tick marks at the specified positions with the specified labels: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2 Pi, Pi / 25}], Ticks -> {{{-1, -a}, {1, a}, {2, b}}, {{-1, -a}, {1, a}, {2, b}}, {{-1, -a}, {0, zero}, {1, a}}}] Out[1]= [image] ``` --- Specify tick marks with scaled lengths: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2 Pi, Pi / 25}], Ticks -> {{{-1, -a, .10}, {1, a, .1}, {2, b, .075}}, {{-1, -a, .05}, {1, a, .06}, {2, b, .07}}, {{-1, -a, Automatic}, {0, zero, .14}, {1, a, .6}}}] Out[1]= [image] ``` --- Customize each tick with position, length, labeling and styling: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2 Pi, Pi / 25}], Ticks -> {{{-1, -a, .10, Directive[Thick, Red]}, {1, a, .1, Directive[Thick, Red]}, {2, b, .075, Directive[Thick, Red]}}, {{-1, -a, .05, Directive[Red]}, {1, a, .06, Directive[Red]}, {2, b, .07, Directive[Red]}}, {{-1, -a, Automatic, Directive[Thick, Blue]}, {0, zero, .14, Directive[Dashed, Thick, Blue]}, {1, a, .13, Directive[Thick, Blue]}}}] Out[1]= [image] ``` #### TicksStyle (3) By default, the ticks and tick labels use the same styles as the axis: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2 Pi, Pi / 25}], AxesStyle -> Directive[Red, Thick]] Out[1]= [image] ``` --- Specify the overall tick style, including the tick labels: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2 Pi, Pi / 25}], TicksStyle -> Red] Out[1]= [image] ``` --- Specify the tick style for each of the axes: ```wl In[1]:= ListLinePlot3D[Table[{r Sin[t], r Cos[t], Cos[r t]}, {r, 4}, {t, 0, 2 Pi, Pi / 25}], TicksStyle -> {Red, Directive[Blue, Thick], Directive[Brown, 14]}] Out[1]= [image] ``` ### Applications (6) #### Random Walks (3) Visualize a random walk in 3D: ```wl In[1]:= ListLinePlot3D[Accumulate[RandomReal[{-1, 1}, {100, 3}]], BoxRatios -> Automatic] Out[1]= [image] ``` View multiple random walks: ```wl In[2]:= ListLinePlot3D[Table[Accumulate[RandomReal[{-1, 1}, {100, 3}]], 5], BoxRatios -> Automatic] Out[2]= [image] ``` --- Visualize a random walk on a lattice: ```wl In[1]:= ListLinePlot3D[Accumulate[RandomChoice[IconizedObject[«moves»], 100]], BoxRatios -> Automatic] Out[1]= [image] ``` View multiple random walks: ```wl In[2]:= ListLinePlot3D[Table[Accumulate[RandomChoice[IconizedObject[«moves»], 100]], 5], BoxRatios -> Automatic] Out[2]= [image] ``` --- Make a random walk where successive steps change direction by between 0° and 20° in any Euler angle: ```wl In[1]:= ListLinePlot3D[AnglePath3D[RandomReal[{0°, 20°}, {1000, 3}]], BoxRatios -> Automatic] Out[1]= [image] ``` Plot multiple walks: ```wl In[2]:= ListLinePlot3D[Table[AnglePath3D[RandomReal[{0°, 20°}, {250, 3}]], 10], BoxRatios -> Automatic] Out[2]= [image] ``` #### Optimization Paths (1) Show the steps used by an optimization method to arrive at a minimum: ```wl In[1]:= fn = y Sin[x] + x Cos[y] + 5Sqrt[x ^ 2 + y ^ 2]; In[2]:= surf = Plot3D[fn, {x, -10, 10}, {y, -10, 10}, Mesh -> None, PlotStyle -> Opacity[0.7, White]] Out[2]= [image] ``` Use ``StepMonitor`` to follow the progress of ``FindMinimum`` from different starting points: ```wl In[3]:= path = Quiet[Table[First[Last[Reap[FindMinimum[fn, {{x, RandomReal[{-10, 10}]}, {y, RandomReal[{-10, 10}]}}, StepMonitor :> Sow[{x, y, fn}, "A"]], "A"]]], 15]]; ``` Plot the sequences of steps on the actual surface: ```wl In[4]:= Show[surf, ListLinePlot3D[path]] Out[4]= [image] ``` #### Time Series (1) Plot the performance of several companies as separate curves: ```wl In[1]:= companies = {\[FreeformPrompt]["AAPL"], \[FreeformPrompt]["Amazon"], \[FreeformPrompt]["IBM"], \[FreeformPrompt]["MSFT"]}; In[2]:= data = EntityValue[companies, EntityProperty["Financial", "CumulativeFractionalChange", {"Date" -> Interval[{DateObject[{2021, 1, 1}, "Day", "Gregorian", -5.], DateObject[{2021, 3, 14}, "Day", "Gregorian", -5.]}]}]]; In[3]:= ListLinePlot3D[data, Filling -> Axis, PlotLegends -> companies] Out[3]= [image] ``` #### Spatial Data (1) Find the position of the International Space Station for the next few hours: ```wl In[1]:= iss = GeoPositionXYZ[Entity["Satellite", "25544"][Dated["Position", #]& /@ DateRange[Now, Now + Quantity[6, "Hours"], Quantity[1, "Minutes"]]]]["XYZ"]; ``` Show the path around a simple model of the Earth: ```wl In[2]:= Show[ListLinePlot3D[iss, PlotTheme -> "NoAxes"], Graphics3D[{Gray, Sphere[{0, 0, 0}, 6.37 * 10 ^ 6]}], BoxRatios -> 1, PlotRange -> All] Out[2]= [image] ``` ### Properties & Relations (12) Use ``ListPlot`` and ``ListLinePlot`` to plot heights in 2D: ```wl In[1]:= {ListPlot[{1, 3, 4, 2, 7, 5}], ListLinePlot[{1, 3, 4, 2, 7, 5}]} Out[1]= {[image], [image]} ``` Plot points: ```wl In[2]:= {ListPlot[{{1, 5}, {2, 2}, {3, 9}, {4, 3}, {4, 7}, {5, 7}, {7, 1}, {8, 4}}], ListLinePlot[{{1, 5}, {2, 2}, {3, 9}, {4, 3}, {4, 7}, {5, 7}, {7, 1}, {8, 4}}]} Out[2]= {[image], [image]} ``` --- Use ``ListPointPlot3D`` to show three-dimensional data plots: ```wl In[1]:= ListPointPlot3D[Table[Sin[j ^ 2 + i], {i, 0, Pi, 0.1}, {j, 0, Pi, 0.1}]] Out[1]= [image] ``` --- Use ``ListPlot3D`` to create surfaces from data: ```wl In[1]:= ListPlot3D[Table[Sin[j ^ 2 + i], {i, 0, Pi, 0.1}, {j, 0, Pi, 0.1}]] Out[1]= [image] ``` --- Use ``Plot3D`` to visualize functions: ```wl In[1]:= Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}] Out[1]= [image] ``` --- Use ``ParametricPlot3D`` to plot a curve from functions: ```wl In[1]:= ParametricPlot3D[{Cos[t], Sin[t], Sin[5t]}, {t, 0, 2Pi}] Out[1]= [image] ``` --- Use ``ListLogPlot``, ``ListLogLogPlot`` and ``ListLogLinearPlot`` for logarithmic data plots: ```wl In[1]:= ListLogPlot[Table[Binomial[25, k], {k, 0, 25}], Joined -> True] Out[1]= [image] ``` --- Use ``ListPolarPlot`` for polar plots: ```wl In[1]:= ListPolarPlot[Table[{x, Sqrt[x]}, {x, 0, 2Pi, 0.1}], Joined -> True] Out[1]= [image] ``` --- Use ``DateListPlot`` to show data over time: ```wl In[1]:= DateListPlot[{34, 51, 11, 5, 39, 47, 28, 42, 66, 13, 24, 31}, {2006, 1}, Joined -> True] Out[1]= [image] ``` --- Use ``ListContourPlot`` to create contours from continuous data: ```wl In[1]:= ListContourPlot[Table[Sin[j ^ 2 + i], {i, 0, Pi, 0.1}, {j, 0, Pi, 0.1}]] Out[1]= [image] ``` --- Use ``ListDensityPlot`` to create densities from continuous data: ```wl In[1]:= ListDensityPlot[Table[Sin[j ^ 2 + i], {i, 0, Pi, 0.1}, {j, 0, Pi, 0.1}]] Out[1]= [image] ``` --- Use ``ArrayPlot`` and ``MatrixPlot`` for arrays of discrete values: ```wl In[1]:= ArrayPlot[Table[GCD[i, j], {i, 1, 20}, {j, 1, 20}]] Out[1]= [image] ``` --- Use ``ParametricPlot`` for parametric curves: ```wl In[1]:= {ParametricPlot[{Cos[θ], Sin[θ]}, {θ, 0, 2Pi}], ListLinePlot[Table[{Cos[θ], Sin[θ]}, {θ, 0, 2Pi, 0.1}], AspectRatio -> 1]} Out[1]= {[image], [image]} ``` ## See Also * [`ListLinePlot`](https://reference.wolfram.com/language/ref/ListLinePlot.en.md) * [`ListPointPlot3D`](https://reference.wolfram.com/language/ref/ListPointPlot3D.en.md) * [`ListPlot3D`](https://reference.wolfram.com/language/ref/ListPlot3D.en.md) * [`ParametricPlot3D`](https://reference.wolfram.com/language/ref/ParametricPlot3D.en.md) * [`ListPlot`](https://reference.wolfram.com/language/ref/ListPlot.en.md) * [`DiscretePlot3D`](https://reference.wolfram.com/language/ref/DiscretePlot3D.en.md) * [`StackedListPlot`](https://reference.wolfram.com/language/ref/StackedListPlot.en.md) ## Related Guides * [Data Visualization](https://reference.wolfram.com/language/guide/DataVisualization.en.md) * [Tabular Visualization](https://reference.wolfram.com/language/guide/TabularVisualization.en.md) ## History * [Introduced in 2021 (12.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn123.en.md) \| [Updated in 2025 (14.2)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn142.en.md)