--- title: "LogLogPlot" language: "en" type: "Symbol" summary: "LogLogPlot[f, {x, xmin, xmax}] generates a log-log plot of f as a function of x from xmin to xmax. LogLogPlot[{f1, f2, ...}, {x, xmin, xmax}] plots several functions fi. LogLogPlot[{..., w[fi], ...}, ...] plots fi with features defined by the symbolic wrapper w. LogLogPlot[..., {x} \\[Element] reg] takes the variable x to be in the geometric region reg." keywords: - double-logarithmic plot - double logarithmic plot - loglog - log-log scale plot - Bode plot - frequency plot - spectrum plot - complexity plot - loglog canonical_url: "https://reference.wolfram.com/language/ref/LogLogPlot.html" source: "Wolfram Language Documentation" related_guides: - title: "Function Visualization" link: "https://reference.wolfram.com/language/guide/FunctionVisualization.en.md" related_functions: - title: "ListLogLogPlot" link: "https://reference.wolfram.com/language/ref/ListLogLogPlot.en.md" - title: "LogPlot" link: "https://reference.wolfram.com/language/ref/LogPlot.en.md" - title: "LogLinearPlot" link: "https://reference.wolfram.com/language/ref/LogLinearPlot.en.md" - title: "Plot" link: "https://reference.wolfram.com/language/ref/Plot.en.md" - title: "ParametricPlot" link: "https://reference.wolfram.com/language/ref/ParametricPlot.en.md" related_tutorials: - title: "Some Special Plots" link: "https://reference.wolfram.com/language/tutorial/GraphicsAndSound.en.md#31896" --- # LogLogPlot LogLogPlot[f, {x, xmin, xmax}] generates a log-log plot of f as a function of x from xmin to xmax. LogLogPlot[{f1, f2, …}, {x, xmin, xmax}] plots several functions fi. LogLogPlot[{…, w[fi], …}, …] plots fi with features defined by the symbolic wrapper w. LogLogPlot[…, {x}∈reg] takes the variable x to be in the geometric region reg. ## Details and Options * ``LogLogPlot`` makes power-law functions appear as straight lines. It allows very small or very large value changes to be seen over very large domains. * ``LogLogPlot`` effectively generates a curve in which ``Log[f]`` is plotted against ``Log[x]``, but with tick marks indicating the original values of ``f`` and ``x``. It visualizes the set $\{(\log (x),\log (y))|y=f(x)\land x\in \text{reg}\}$. [image] * Gaps are left at any ``x`` where the ``fi`` evaluate to anything other than positive real numbers or ``Quantity``. * The limits ``xmin`` and ``xmax`` can be real numbers or ``Quantity`` expressions. * The region ``reg`` can be any ``RegionQ`` object in 1D. * ``LogLogPlot`` treats the variable ``x`` as local, effectively using ``Block``. * ``LogLogPlot`` has attribute ``HoldAll`` and evaluates ``f`` only after assigning specific numerical values to ``x``. * In some cases, it may be more efficient to use ``Evaluate`` to evaluate ``f`` symbolically before specific numerical values are assigned to ``x``. * The following wrappers ``w`` can be used for the ``fi``: | | | | ------------------------------------ | ------------------------------------------------------ | | Annotation[fi, label] | provide an annotation for the fi | | Button[fi, action] | evaluate action when the curve for fi is clicked | | Callout[fi, label] | label the function with a callout | | Callout[fi, label, pos] | place the callout at relative position pos | | EventHandler[fi, events] | define a general event handler for fi | | Highlighted[fi, effect] | dynamically highlight fi with an effect | | Highlighted[fi, Placed[effect, pos]] | statically highlight fi with an effect at position pos | | Hyperlink[fi, uri] | make the function a hyperlink | | Labeled[fi, label] | label the function | | Labeled[fi, label, pos] | place the label at relative position pos | | Legended[fi, label] | identify the function in a legend | | PopupWindow[fi, cont] | attach a popup window to the function | | StatusArea[fi, label] | display in the status area on mouseover | | Style[fi, styles] | show the function using the specified styles | | Tooltip[fi, label] | attach a tooltip to the function | | Tooltip[fi] | use functions as tooltips | * Wrappers ``w`` can be applied at multiple levels: | | | | ---------- | ----------------------- | | w[fi] | wrap the fi | | w[{f1, …}] | wrap a collection of fi | | w1[w2[…]] | use nested wrappers | * ``Callout``, ``Labeled``, and ``Placed`` can use the following positions ``pos``: | | | | --------------------------- | ---------------------------------------------------------- | | Automatic | automatically placed labels | | Above, Below, Before, After | positions around the curve | | x | near the curve at a position x | | Scaled[s] | scaled position s along the curve | | {s, Above}, {s, Below}, … | relative position at position s along the curve | | {pos, epos} | epos in label placed at relative position pos of the curve | * ``LogLogPlot`` has the same options as ``Graphics``, with the following additions and changes: [] | | | | | :-------------------- | :------------------ | :------------------------------------------------------- | | AspectRatio | 1 / GoldenRatio | ratio of height to width | | Axes | True | whether to draw axes | | ClippingStyle | None | what to draw where curves are clipped | | ColorFunction | Automatic | how to determine the coloring of curves | | ColorFunctionScaling | True | whether to scale arguments to ColorFunction | | EvaluationMonitor | None | expression to evaluate at every function evaluation | | Exclusions | Automatic | points in x to exclude | | ExclusionsStyle | None | what to draw at excluded points | | Filling | None | filling to insert under each curve | | FillingStyle | Automatic | style to use for filling | | LabelingSize | Automatic | maximum size of callouts and labels | | MaxRecursion | Automatic | the maximum number of recursive subdivisions allowed | | Mesh | None | how many mesh points to draw on each curve | | 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 | the method to use for refining curves | | PerformanceGoal | \$PerformanceGoal | aspects of performance to try to optimize | | PlotHighlighting | Automatic | highlighting effect for curves | | PlotInteractivity | \$PlotInteractivity | whether to allow interactive elements | | PlotLabel | None | overall label for the plot | | PlotLabels | None | labels to use for curves | | PlotLegends | None | legends for curves | | PlotPoints | Automatic | initial number of sample points | | PlotRange | {Full, Automatic} | the range of y or other values to include | | PlotRangeClipping | True | whether to clip at the plot range | | PlotStyle | Automatic | graphics directives to specify the style for each curve | | PlotTheme | \$PlotTheme | overall theme for the plot | | RegionFunction | (True&) | how to determine whether a point should be included | | ScalingFunctions | None | how to scale individual coordinates | | TargetUnits | Automatic | units to display in the plot | | WorkingPrecision | MachinePrecision | the precision used in internal computations | * Possible settings for ``ClippingStyle`` are: | | | | | ------- | --------- | ----------------------------------------- | | [image] | Automatic | use a dotted line for the clipped portion | | [image] | None | omit the clipped portion of the curve | | [image] | style | use style for the clipped portion | * Possible settings for ``PlotLayout`` that show single curves in multiple plot panels include: | | | | ------------------------------------- | ----------------------------------------- | | "Column" | use separate curves in a column of panels | | "Row" | use separate curves 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 | * With the default settings ``Exclusions -> Automatic`` and ``ExclusionsStyle -> None``, ``LogLogPlot`` breaks curves at discontinuities and singularities it detects. ``Exclusions -> None`` joins across discontinuities and singularities. * ``Exclusions -> {x1, x2, …}`` is equivalent to ``Exclusions -> {x == x1, x == x2, …}``. * ``PlotLegends -> "Expressions"`` uses the ``fi`` as the legend text. * ``ColorData["DefaultPlotColors"]`` gives the default sequence of colors used by ``PlotStyle``. * Possible highlighting effects for ``Highlighted`` and ``PlotHighlighting`` include: | | | | | ------- | ------------------- | ----------------------------------------------------------------------------- | | [image] | style | highlight the indicated curve | | [image] | "Ball" | highlight and label the indicated point in a curve | | [image] | "Dropline" | highlight and label the indicated point in a curve with droplines to the axes | | [image] | "XSlice" | highlight and label all points along a vertical slice | | [image] | "YSlice" | highlight and label all points along a horizontal slice | | [image] | Placed[effect, pos] | statically highlight the given position pos | * Highlight position specifications ``pos`` include: | | | | --------------- | -------------------------------------------- | | x, {x} | effect at {x, y} with y chosen automatically | | {x, y} | effect at {x, y} | | {pos1, pos2, …} | multiple positions posi | * ``LogLogPlot`` initially evaluates ``f`` at a number of equally spaced sample points specified by ``PlotPoints``. Then it uses an adaptive algorithm to choose additional sample points, subdividing a given interval at most ``MaxRecursion`` times. [image] * Since only a finite number of sample points are used, it is possible for ``LogLogPlot`` to miss features of ``f``. Increasing the settings for ``PlotPoints`` and ``MaxRecursion`` will often catch such features. * Themes that affect curves include: | | | | | ------- | ------------- | ----------------- | | [image] | "ThinLines" | thin plot lines | | [image] | "MediumLines" | medium plot lines | | [image] | "ThickLines" | thick plot lines | * The arguments supplied to functions in ``MeshFunctions`` and ``RegionFunction`` are ``x``, ``y``. Functions in ``ColorFunction`` are by default supplied with scaled versions of these arguments. * Possible settings for ``ScalingFunctions`` include: | | | | -------- | ------------------ | | sy | scale the y axis | | {sx, sy} | 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 | * If a scaling function is specified for either direction, it is applied after the normal log scaling. ### List of all options | | | | | ---------------------- | ------------------- | ---------------------------------------------------------------------------------- | | AlignmentPoint | Center | the default point in the graphic to align with | | AspectRatio | 1 / GoldenRatio | ratio of height to width | | Axes | True | 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 | None | what to draw where curves are clipped | | ColorFunction | Automatic | how to determine the coloring of curves | | ColorFunctionScaling | True | whether to scale arguments to ColorFunction | | ContentSelectable | Automatic | whether to allow contents to be selected | | CoordinatesToolOptions | Automatic | detailed behavior of the coordinates tool | | Epilog | {} | primitives rendered after the main plot | | EvaluationMonitor | None | expression to evaluate at every function evaluation | | Exclusions | Automatic | points in x to exclude | | ExclusionsStyle | None | what to draw at excluded points | | Filling | None | filling to insert under each curve | | FillingStyle | Automatic | style to use for filling | | FormatType | TraditionalForm | the default format type for text | | Frame | False | whether to put a frame around the plot | | FrameLabel | None | frame labels | | FrameStyle | {} | style specifications for the frame | | FrameTicks | Automatic | frame ticks | | 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 | | LabelingSize | Automatic | maximum size of callouts and labels | | LabelStyle | {} | style specifications for labels | | MaxRecursion | Automatic | the maximum number of recursive subdivisions allowed | | Mesh | None | how many mesh points to draw on each curve | | 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 | the method to use for refining curves | | PerformanceGoal | \$PerformanceGoal | aspects of performance to try to optimize | | PlotHighlighting | Automatic | highlighting effect for curves | | PlotInteractivity | \$PlotInteractivity | whether to allow interactive elements | | PlotLabel | None | overall label for the plot | | PlotLabels | None | labels to use for curves | | PlotLegends | None | legends for curves | | PlotPoints | Automatic | initial number of sample points | | PlotRange | {Full, Automatic} | the range of y or other values to include | | PlotRangeClipping | True | 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 | | PlotStyle | Automatic | graphics directives to specify the style for each curve | | 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 | | RegionFunction | (True&) | how to determine whether a point should be included | | RotateLabel | True | whether to rotate y labels on the frame | | ScalingFunctions | None | how to scale individual coordinates | | TargetUnits | Automatic | units to display in the plot | | Ticks | Automatic | axes ticks | | TicksStyle | {} | style specifications for axes ticks | | WorkingPrecision | MachinePrecision | the precision used in internal computations | --- ## Examples (134) ### Basic Examples (4) Powers show up as straight lines on a log-log plot: ```wl In[1]:= LogLogPlot[x ^ 2 + x ^ 3, {x, 1, 100}] Out[1]= [image] ``` --- Plot several functions with legends: ```wl In[1]:= LogLogPlot[{x ^ 2, x ^ 3, x ^ 4, x ^ 5}, {x, 1, 10 ^ 4}, PlotLegends -> "Expressions"] Out[1]= [image] ``` --- Label each curve: ```wl In[1]:= LogLogPlot[{Log[x] ^ x, x ^ x}, {x, 0.1, 10}, PlotLabels -> "Expressions"] Out[1]= [image] ``` --- Fill between curves: ```wl In[1]:= LogLogPlot[{10 / (x ^ 2 - 6x + 10), 100 / (x ^ 2 + 100)}, {x, 0.1, 1000}, Filling -> {1 -> {2}}] Out[1]= [image] ``` ### Scope (30) #### Sampling (7) More points are sampled when the function changes quickly: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}] Out[1]= [image] ``` --- The plot range is selected automatically: ```wl In[1]:= LogLogPlot[Abs[1 / (x - 5)], {x, 1, 10}] Out[1]= [image] ``` --- Ranges where the function becomes negative are excluded: ```wl In[1]:= LogLogPlot[1 / ((x - 3)(x - 5)), {x, 1, 10}] Out[1]= [image] ``` --- The curve is split when there are discontinuities in the function: ```wl In[1]:= LogLogPlot[Floor[Sqrt[x]], {x, 1, 100}] Out[1]= [image] ``` --- Use ``PlotPoints`` and ``MaxRecursion`` to control adaptive sampling: ```wl In[1]:= Grid@Table[LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, PlotPoints -> pp, MaxRecursion -> mr], {mr, {0, 1, 2}}, {pp, {5, 10}}] Out[1]= [image] ``` --- Use ``PlotRange`` to focus in on areas of interest: ```wl In[1]:= {LogLogPlot[10 / (x ^ 2 - 5x + 10), {x, 1, 100}], LogLogPlot[10 / (x ^ 2 - 5x + 10), {x, 1, 100}, PlotRange -> {1, 3}]} Out[1]= {[image], [image]} ``` --- Use ``Exclusions`` to remove points or split the resulting curve: ```wl In[1]:= LogLogPlot[Exp[Tan[x]], {x, 1, 10}, Exclusions -> {Cos[x] == 0}] Out[1]= [image] ``` #### Labeling and Legending (11) Label curves with ``Labeled`` : ```wl In[1]:= LogLogPlot[Evaluate@Table[Labeled[Log[n x] ^ x, Log[n x] ^ x], {n, 1, 3}], {x, 0.5, 3}] Out[1]= [image] ``` Place the labels relative to the curves: ```wl In[2]:= Table[LogLogPlot[Labeled[x ^ Sin[x], "label", p], {x, 1, 6}, PlotLabel -> p], {p, {Above, Below, Before, After}}] Out[2]= {[image], [image], [image], [image]} ``` --- Label curves with ``PlotLabels`` : ```wl In[1]:= LogLogPlot[{Log[x] ^ x, x ^ x}, {x, 1, 10}, PlotLabels -> {Log[x] ^ x, x ^ x}] Out[1]= [image] ``` --- Place the label near the curve at an $x$ value: ```wl In[1]:= LogLogPlot[Labeled[x ^ Sin[x], "label", Log[6]], {x, 2, 10}] Out[1]= [image] ``` --- Use a scaled position: ```wl In[1]:= LogLogPlot[Labeled[x ^ Sin[x], "label", Scaled[0.1]], {x, 2, 10}] Out[1]= [image] ``` Specify the text position relative to the point: ```wl In[2]:= LogLogPlot[Labeled[x ^ Sin[x], "label", {Scaled[0.1], Below}], {x, 2, 10}] Out[2]= [image] ``` --- Label curves automatically with ``Callout`` : ```wl In[1]:= LogLogPlot[{Callout[x ^ Sin[x], x ^ Sin[x]], Callout[x, x]}, {x, 1, 20}] Out[1]= [image] ``` --- Place labels at specific locations: ```wl In[1]:= LogLogPlot[Callout[x ^ (Sin[x]), "max", Above], {x, 1, 5}] Out[1]= [image] In[2]:= LogLogPlot[{Callout[x, x, {5, Above}], Callout[x ^ (Sin[x]), x ^ x, {4, Below}]}, {x, 1, 18}] Out[2]= [image] ``` --- Include legends for each curve: ```wl In[1]:= LogLogPlot[{x ^ Sin[x], x ^ Cos[x]}, {x, 1, 2π}, PlotLegends -> {x ^ Sin[x], x ^ Cos[x]}] Out[1]= [image] ``` --- Use ``Legended`` to provide a legend for a specific curve: ```wl In[1]:= LogLogPlot[{x ^ Sin[x], Legended[Mean[{x ^ Sin[x], x ^ Cos[x]}], "average"], x ^ Cos[x]}, {x, 1, 2π}] Out[1]= [image] ``` Use ``Placed`` to change the legend location: ```wl In[2]:= LogLogPlot[{x ^ Sin[x], Legended[Mean[{x ^ Sin[x], x ^ Cos[x]}], Placed["average", Below]], x ^ Cos[x]}, {x, 1, 2π}] Out[2]= [image] ``` --- Curves usually have interactive callouts showing the coordinates when you mouse over them: ```wl In[1]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.1, 4.5}] Out[1]= [image] ``` Including specific wrappers or interactions, such as tooltips, turns off the interactive features: ```wl In[2]:= LogLogPlot[Callout[2^x, "hello", 2], {x, 0.1, 4.5}] Out[2]= [image] ``` --- Choose from multiple interactive highlighting effects: ```wl In[1]:= {LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> "Dropline"], LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> "XSlice"]} Out[1]= {[image], [image]} ``` --- Use ``Highlighted`` to emphasize specific points in a plot: ```wl In[1]:= LogLogPlot[Highlighted[2^x, Placed["Ball", 1]], {x, 0.01, 4.5}, PlotHighlighting -> "Dropline"] Out[1]= [image] ``` #### Presentation (12) Multiple curves are automatically colored to be distinct: ```wl In[1]:= LogLogPlot[{Log[x], x, x ^ 2, E ^ x}, {x, 1, 100}] Out[1]= [image] ``` --- Provide explicit styling to different curves: ```wl In[1]:= LogLogPlot[{Log[x], x, x ^ 2, E ^ x}, {x, 1, 100}, PlotStyle -> {AbsoluteThickness[3], Automatic, Red, Dashed}] Out[1]= [image] ``` --- Add labels: ```wl In[1]:= LogLogPlot[1 / Abs[x - 10], {x, 1, 1000}, AxesLabel -> Automatic, PlotLabel -> 1 / Abs[x - 10]] Out[1]= [image] ``` --- Create legends from the functions: ```wl In[1]:= LogLogPlot[{10 / (x ^ 2 - 6x + 10), 100 / (x ^ 2 + 100)}, {x, 0.1, 1000}, PlotLegends -> "Expressions"] Out[1]= [image] ``` Specify labels for legends: ```wl In[2]:= LogLogPlot[{10 / (x ^ 2 - 6x + 10), 100 / (x ^ 2 + 100)}, {x, 0.1, 1000}, PlotLegends -> {"one", "two"}] Out[2]= [image] ``` --- Provide an interactive ``Tooltip`` for each curve: ```wl In[1]:= LogLogPlot[{Tooltip[Log[x]], Tooltip[1 / x]}, {x, 1, 100}] Out[1]= [image] ``` --- Create filled plots: ```wl In[1]:= LogLogPlot[{x, 1 / x}, {x, 0.01, 100}, Filling -> 1] Out[1]= [image] ``` --- Use a theme with a frame, grid lines, and an automatic legend: ```wl In[1]:= LogLogPlot[{10 / (x ^ 2 - 6x + 10), 100 / (x ^ 2 + 100)}, {x, 0.1, 1000}, PlotTheme -> "Detailed"] Out[1]= [image] ``` Use a more vibrant theme: ```wl In[2]:= LogLogPlot[{10 / (x ^ 2 - 6x + 10), 100 / (x ^ 2 + 100)}, {x, 0.1, 1000}, PlotTheme -> "Marketing"] Out[2]= [image] ``` --- Create an overlay mesh: ```wl In[1]:= LogLogPlot[1 / Abs[x - 10], {x, 1, 1000}, Mesh -> 20, MeshFunctions -> {Log[#1]&}] Out[1]= [image] ``` --- Style the curve segments between mesh points: ```wl In[1]:= LogLogPlot[1 / Abs[x - 10], {x, 1, 1000}, Mesh -> 15, MeshFunctions -> {Log[#1]&}, MeshShading -> {Red, None, Blue}] Out[1]= [image] ``` --- Show multiple curves in a row of separate panels: ```wl In[1]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 10] + 1 / Abs[x - 50]}, {x, 1, 1000}, PlotLayout -> "Row"] Out[1]= [image] ``` Use a column instead of a row: ```wl In[2]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 10] + 1 / Abs[x - 50]}, {x, 1, 1000}, PlotLayout -> "Column"] Out[2]= [image] ``` Use multiple rows or columns: ```wl In[3]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 10] + 1 / Abs[x - 50], 1 / Abs[x ^ 2 - 1000], 1 / Abs[x ^ 2 - 15x + 30]}, {x, 1, 1000}, PlotLayout -> {"Row", 2}] Out[3]= [image] ``` --- Use ``ScalingFunctions`` to reverse the ``y`` axis: ```wl In[1]:= LogLogPlot[x^x, {x, 0, 10}, ScalingFunctions -> "Reverse", PlotRange -> All] Out[1]= [image] ``` --- Scale both ``x`` and ``y`` axes: ```wl In[1]:= LogLogPlot[x^x, {x, 0, 10}, ScalingFunctions -> {"Reverse", "Reverse"}] Out[1]= [image] ``` ### Options (96) #### ClippingStyle (5) Omit clipped regions of the plot: ```wl In[1]:= LogLogPlot[Exp[Sin[(x - 2)] / (x - 2) ^ 2], {x, 1, 5}, ClippingStyle -> None, PlotRange -> {1*^-1, 1*^1}, AxesOrigin -> {2, 1}] Out[1]= [image] ``` --- Show the clipped regions like the rest of the curve: ```wl In[1]:= LogLogPlot[Exp[Sin[(x - 2)] / (x - 2) ^ 2], {x, 1, 5}, ClippingStyle -> Automatic, PlotRange -> {1*^-1, 1*^1}, AxesOrigin -> {2, 1}] Out[1]= [image] ``` --- Show clipped regions with red lines: ```wl In[1]:= LogLogPlot[Exp[Sin[(x - 2)] / (x - 2) ^ 2], {x, 1, 5}, ClippingStyle -> Red, PlotRange -> {1*^-1, 1*^1}, AxesOrigin -> {2, 1}] Out[1]= [image] ``` --- Show clipped regions as thick at the bottom and red at the top: ```wl In[1]:= LogLogPlot[Exp[Sin[(x - 2)] / (x - 2) ^ 2], {x, 1, 5}, ClippingStyle -> {Red, Thick}, PlotRange -> {1*^-1, 1*^1}, AxesOrigin -> {2, 1}] Out[1]= [image] ``` --- Show clipped regions as red and thick: ```wl In[1]:= LogLogPlot[Exp[Sin[(x - 2)] / (x - 2) ^ 2], {x, 1, 5}, ClippingStyle -> Directive[Thick, Red], PlotRange -> {1*^-1, 1*^1}, AxesOrigin -> {2, 1}] Out[1]= [image] ``` #### ColorFunction (5) Color by scaled $y$ coordinate and scaled $x$ coordinate, respectively: ```wl In[1]:= Table[LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, ColorFunction -> Function[{x, y}, Evaluate[f]], PlotLabel -> f], {f, {Hue[x], Hue[y]}}] Out[1]= [image] ``` --- Color a curve red when its absolute $y$ coordinate is above 1: ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, ColorFunction -> Function[{x, y}, If[y > 1, Red, Black]], ColorFunctionScaling -> False, PlotStyle -> Thick] Out[1]= [image] ``` --- Fill with the color used for the curve: ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, ColorFunction -> Function[{x, y}, Hue[y]], Filling -> Axis] Out[1]= [image] ``` --- ``ColorFunction`` has higher priority than ``PlotStyle`` for coloring the curve: ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, ColorFunction -> "DarkRainbow", PlotStyle -> Directive[Red, AbsoluteThickness[5]]] Out[1]= [image] ``` --- Use a color function that is red at powers of 10: ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, ColorFunction -> Function[{x, y}, Hue[Log[10, y]]], PlotStyle -> Thick, ColorFunctionScaling -> False] Out[1]= [image] ``` #### ColorFunctionScaling (3) No argument scaling on the left, automatic scaling on the right: ```wl In[1]:= Table[LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, PlotStyle -> Thick, ColorFunction -> Function[{x, y}, Hue[y]], ColorFunctionScaling -> cf], {cf, {False, True}}] Out[1]= [image] ``` --- Scaling is done on a linear scale in the original coordinates: ```wl In[1]:= Table[LogLogPlot[t, {t, 0.1, 2 ^ i}, PlotStyle -> Thick, ColorFunction -> Function[{x, y}, Hue[y]]], {i, {0, 10, 20}}] Out[1]= {[image], [image], [image]} ``` --- Use a color function that is red at powers of 10: ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, ColorFunction -> Function[{x, y}, Hue[Log[10, y]]], PlotStyle -> Thick, ColorFunctionScaling -> False] Out[1]= [image] ``` #### EvaluationMonitor (3) Find the list of values sampled by ``LogLogPlot`` : ```wl In[1]:= Reap[LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, EvaluationMonitor :> Sow[x]];]//Short Out[1]//Short= {Null, {{«1»}}} ``` --- Show where ``LogLogPlot`` evaluates the function: ```wl In[1]:= data = Reap[ LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, EvaluationMonitor :> Sow[{x, 10 / (x ^ 2 - 6x + 10)}]] ][[-1, 1]]; In[2]:= ListLogLogPlot[data , Filling -> Axis] Out[2]= [image] ``` --- Count how many times the function is evaluated: ```wl In[1]:= Block[{k = 0}, LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, EvaluationMonitor :> k++];k] Out[1]= 204 ``` #### Exclusions (2) Use automatic methods for computing exclusions, in this case for a piecewise function: ```wl In[1]:= LogLogPlot[Sum[Boole[2 ^ (k - 1) < x < 2 ^ k]x / (2 ^ k - x), {k, 5}], {x, 1, 2 ^ 5}] Out[1]= [image] ``` --- Indicate that no exclusions should be computed: ```wl In[1]:= LogLogPlot[Sum[Boole[2 ^ (k - 1) < x < 2 ^ k]x / (2 ^ k - x), {k, 5}], {x, 1, 2 ^ 5}, Exclusions -> None] Out[1]= [image] ``` #### ExclusionsStyle (2) Use dashed lines to indicate the vertical asymptotes: ```wl In[1]:= LogLogPlot[Sum[Boole[2 ^ (k - 1) < x < 2 ^ k]x / (2 ^ k - x), {k, 5}], {x, 1, 2 ^ 5}, ExclusionsStyle -> Dashed] Out[1]= [image] ``` --- Use blue points to highlight the exclusions: ```wl In[1]:= LogLogPlot[Gamma[Floor[x]], {x, 1, 10}, ExclusionsStyle -> {None, Blue}] Out[1]= [image] ``` #### Filling (7) Use symbolic or explicit values: ```wl In[1]:= Table[LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 100}, Filling -> f], {f, {Axis, Top, Bottom, 1}}] Out[1]= [image] ``` --- Overlapping fills by default combine using opacity: ```wl In[1]:= LogLogPlot[{(x - 5) ^ 2 / x, x / (x - 5) ^ 2}, {x, 1, 25}, Filling -> Axis] Out[1]= [image] ``` --- Fill between curve 1 and the axis: ```wl In[1]:= LogLogPlot[{(x - 5) ^ 2 / x, x / (x - 5) ^ 2}, {x, 1, 25}, Filling -> {1 -> Axis}] Out[1]= [image] ``` --- Fill between curves 1 and 2: ```wl In[1]:= LogLogPlot[{(x - 5) ^ 2 / x, x / (x - 5) ^ 2}, {x, 1, 25}, Filling -> {1 -> {2}}] Out[1]= [image] ``` --- Fill between curves 1 and 2 with a specific style: ```wl In[1]:= LogLogPlot[{(x - 5) ^ 2 / x, x / (x - 5) ^ 2}, {x, 1, 25}, Filling -> {1 -> {{2}, Yellow}}] Out[1]= [image] ``` --- Fill between curves 1 and 2; use yellow when 1 is below 2 and green when 2 is above 1: ```wl In[1]:= LogLogPlot[{(x - 5) ^ 2 / x, x / (x - 5) ^ 2}, {x, 1, 25}, Filling -> {1 -> {{2}, {Yellow, Green}}}] Out[1]= [image] ``` --- Fill between curves 1 and $y=1$ with yellow: ```wl In[1]:= LogLogPlot[{(x - 5) ^ 2 / x, x / (x - 5) ^ 2}, {x, 1, 25}, Filling -> {1 -> {1, Yellow}}] Out[1]= [image] ``` #### FillingStyle (4) Use different fill colors: ```wl In[1]:= Table[LogLogPlot[Abs[Tan[x]], {x, 1, 10}, Filling -> Bottom, FillingStyle -> c], {c, {Red, Green, Blue, Yellow}}] Out[1]= [image] ``` --- Fill with opacity 0.5 yellow: ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 0.1, 1000}, Filling -> Bottom, FillingStyle -> Directive[Opacity[0.5], Yellow]] Out[1]= [image] ``` --- Fill with red below $y=5$ and blue above: ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 0.1, 1000}, Filling -> 1., FillingStyle -> {Red, Blue}] Out[1]= [image] ``` --- Use a variable filling style obtained from a ``ColorFunction`` : ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 0.1, 1000}, ColorFunction -> Function[{x, y}, Hue[y]], Filling -> Bottom, FillingStyle -> Automatic] Out[1]= [image] In[2]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 0.1, 1000}, ColorFunction -> Function[{x, y}, Hue[x]], Filling -> Bottom, FillingStyle -> Automatic] Out[2]= [image] ``` #### LabelingSize (4) Textual labels are shown at their actual sizes: ```wl In[1]:= LogLogPlot[{Log[x], x}, {x, 1, 10}, PlotLabels -> {"barcarole", "perilously"}] Out[1]= [image] ``` --- Image labels are automatically resized: ```wl In[1]:= LogLogPlot[{Log[x], x}, {x, 1, 10}, PlotLabels -> {[image], [image]}] Out[1]= [image] ``` --- Specify a maximum size for textual labels: ```wl In[1]:= LogLogPlot[{Log[x], x}, {x, 1, 10}, PlotLabels -> {"barcarole", "perilously"}, LabelingSize -> 30] Out[1]= [image] ``` Specify a maximum size for image labels: ```wl In[2]:= LogLogPlot[{Log[x], x}, {x, 1, 10}, PlotLabels -> {[image], [image]}, LabelingSize -> 50] Out[2]= [image] ``` --- Show image labels at their natural sizes: ```wl In[1]:= LogLogPlot[{Log[x], x}, {x, 1, 10}, PlotLabels -> {[image], [image]}, LabelingSize -> Full] Out[1]= [image] ``` #### MaxRecursion (2) The default sampling mesh: ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 0.1, 1000}, Mesh -> All] Out[1]= [image] ``` --- Each level of ``MaxRecursion`` will subdivide the initial mesh into a finer mesh: ```wl In[1]:= Table[LogLogPlot[1 / Abs[(x ^ 2 - 10x + 10)], {x, 0.5, 25}, MaxRecursion -> i, Mesh -> All, Ticks -> None], {i, {0, 3, 6}}] Out[1]= {[image], [image], [image]} ``` #### Mesh (3) Show the initial and final sampling meshes: ```wl In[1]:= Table[LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> m, MeshStyle -> Red], {m, {Full, All}}] Out[1]= [image] ``` --- Use 20 mesh levels evenly spaced in the unscaled $x$ direction: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> 20, MeshStyle -> Red] Out[1]= [image] ``` --- Use an explicit list of values for the mesh in the $x$ direction: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}}, MeshStyle -> PointSize[Medium]] Out[1]= [image] ``` #### MeshFunctions (4) Use a mesh evenly spaced in the $x$ and $y$ directions: ```wl In[1]:= Table[LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, MeshFunctions -> {Function[{x, y}, Evaluate[f]]}, Mesh -> 10, MeshStyle -> PointSize[Medium]], {f, {x, y}}] Out[1]= [image] ``` --- Mesh functions use the unscaled values in the $x$ and $y$ directions: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> 10, MeshFunctions -> {#2&}, MeshStyle -> PointSize[Medium]] Out[1]= [image] ``` --- Use ``Log`` to scale the mesh functions: ```wl In[1]:= Table[LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, MeshFunctions -> {Function[{x, y}, Evaluate[f]]}, Mesh -> 10, MeshStyle -> PointSize[Medium]], {f, {Log[x], Log[y]}}] Out[1]= [image] ``` --- Show 5 mesh levels in the $x$ direction (red) and 10 in the $y$ direction (blue): ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {5, 10}, MeshFunctions -> {#1&, #2&}, MeshStyle -> {Directive[PointSize[Medium], Red], Blue}] Out[1]= [image] ``` #### MeshShading (6) Alternate red and blue segments of equal width in the $x$ direction: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}}, MeshShading -> {Red, Blue}] Out[1]= [image] ``` --- Use ``None`` to remove segments: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}}, MeshShading -> {Red, None}] Out[1]= [image] ``` --- ``MeshShading`` can be used with ``PlotStyle`` : ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}}, PlotStyle -> Thick, MeshShading -> {Red, Blue}] Out[1]= [image] ``` --- ``MeshShading`` has higher priority than ``PlotStyle`` for styling the curve: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}}, PlotStyle -> Green, MeshShading -> {Red, Blue}] Out[1]= [image] ``` --- Use ``PlotStyle`` for some segments by setting ``MeshShading`` to ``Automatic`` : ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}}, PlotStyle -> Directive[Thick, Yellow], MeshShading -> {Red, Automatic}] Out[1]= [image] ``` --- ``MeshShading`` can be used with ``ColorFunction`` : ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {2 ^ Range[-3, 10]}, PlotStyle -> Thick, MeshShading -> {Black, Automatic}, ColorFunction -> Function[{x, y}, Hue[Log[x] / 10]]] Out[1]= [image] ``` #### MeshStyle (4) Color the mesh the same color as the plot: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}}, MeshStyle -> Automatic] Out[1]= [image] ``` --- Use a red mesh in the $x$ direction: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}}, MeshStyle -> Red] Out[1]= [image] ``` --- Use a red mesh in the $x$ direction and a blue mesh in the $y$ direction: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}, {0.001, 0.01, 0.1, 1, 10}}, MeshStyle -> {Red, Blue}, MeshFunctions -> {#1&, #2&}] Out[1]= [image] ``` --- Use big red mesh points in the $x$ direction: ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, Mesh -> {{0.5, 1, 5, 10, 50, 100, 500}}, MeshStyle -> Directive[PointSize[Large], Red]] Out[1]= [image] ``` #### PerformanceGoal (2) Generate a higher-quality plot: ```wl In[1]:= Timing[LogLogPlot[Abs[Sin[1 / x]], {x, 0.00001, 1}, PerformanceGoal -> "Quality"]] Out[1]= [image] ``` --- Emphasize performance, possibly at the cost of quality: ```wl In[1]:= Timing[LogLogPlot[Abs[Sin[1 / x]], {x, 0.00001, 1}, PerformanceGoal -> "Speed"]] Out[1]= {0.011433, [image]} ``` #### PlotHighlighting (8) Plots have interactive coordinate callouts with the default setting ``PlotHighlighting -> Automatic`` : ```wl In[1]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}] Out[1]= [image] ``` Use ``PlotHighlighting -> None`` to disable the highlighting for the entire plot: ```wl In[2]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> None] Out[2]= [image] ``` Use ``Highlighted[…, None]`` to disable highlighting for a single curve: ```wl In[3]:= LogLogPlot[{2^x, Highlighted[Gamma[x], None]}, {x, 0.01, 4.5}] Out[3]= [image] ``` --- Move the mouse over the curve to highlight it with a ball and label: ```wl In[1]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> "Ball"] Out[1]= [image] ``` Use a ball and label to highlight a specific point on the curve: ```wl In[2]:= LogLogPlot[Highlighted[Gamma[x], Placed["Ball", 2]], {x, 0.01, 4.5}] Out[2]= [image] ``` --- Move the mouse over the curve to highlight it with a label and droplines to the axes: ```wl In[1]:= LogLogPlot[Gamma[x], {x, 0.01, 4.5}, PlotHighlighting -> "Dropline"] Out[1]= [image] ``` Use a ball and label to highlight a specific point on the curve: ```wl In[2]:= LogLogPlot[Highlighted[Gamma[x], Placed["Dropline", 2]], {x, 0.01, 4.5}] Out[2]= [image] ``` --- Move the mouse over the plot to highlight it with a slice showing $y$ values corresponding to the $x$ position: ```wl In[1]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> "XSlice"] Out[1]= [image] ``` Highlight the curves at a fixed $x$ value: ```wl In[2]:= LogLogPlot[Highlighted[{2^x, Gamma[x]}, Placed["XSlice", 1]], {x, 0.01, 4.5}] Out[2]= [image] ``` --- Move the mouse over the plot to highlight it with a slice showing $x$ values corresponding to the $y$ position: ```wl In[1]:= LogLogPlot[Gamma[x], {x, 0.01, 4.5}, PlotHighlighting -> "YSlice"] Out[1]= [image] ``` --- Use a component that shows the points on the curve closest to the $x$ position of the mouse cursor: ```wl In[1]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> "XNearestPoint"] Out[1]= [image] ``` Specify the style for the points: ```wl In[2]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> {"XNearestPoint", <|"Style" -> Black|>}] Out[2]= [image] ``` --- Use a component that shows the coordinates on the curve closest to the mouse cursor: ```wl In[1]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> "XYLabel"] Out[1]= [image] ``` Use ``Callout`` options to change the appearance of the label: ```wl In[2]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> {"XYLabel", <|"Appearance" -> "Corners", "CalloutMarker" -> "Circle"|>}] Out[2]= [image] ``` --- Combine components to create a custom effect: ```wl In[1]:= LogLogPlot[{2^x, Gamma[x]}, {x, 0.01, 4.5}, PlotHighlighting -> {{"XNearestPoint", <|"Style" -> Black|>}, {"XYLabel", <|"Appearance" -> "Corners", "CalloutMarker" -> "Circle"|>}}] Out[1]= [image] ``` #### PlotInteractivity (4) Plots have interactive highlighting by default: ```wl In[1]:= LogLogPlot[x + Sin[x], {x, 1, 100}] Out[1]= [image] ``` --- Turn off all the interactive elements: ```wl In[1]:= LogLogPlot[x + Sin[x], {x, 1, 100}, PlotInteractivity -> False] Out[1]= [image] ``` --- Interactive elements provided as part of the input are disabled: ```wl In[1]:= LogLogPlot[Tooltip[x + Sin[x], "hello"], {x, 1, 100}, PlotInteractivity -> False] Out[1]= [image] ``` --- Allow provided interactive elements and disable automatic ones: ```wl In[1]:= LogLogPlot[Tooltip[x + Sin[x], "hello"], {x, 1, 100}, PlotInteractivity -> <|"User" -> True, "System" -> False|>] Out[1]= [image] ``` #### PlotLabel (1) Add an overall label to the plot: ```wl In[1]:= LogLogPlot[Log[x] ^ x, {x, 1, 10}, PlotLabel -> Log[x] ^ x] Out[1]= [image] ``` #### PlotLabels (5) Specify text to label curves: ```wl In[1]:= LogLogPlot[{Log[x], x ^ x}, {x, 1, 2π}, PlotLabels -> {"log(x)", "x^x"}] Out[1]= [image] ``` --- Place the labels above the curves: ```wl In[1]:= LogLogPlot[{x ^ Sin[x], x ^ Cos[x]}, {x, 1, 2π}, PlotLabels -> Placed["Expressions", Above]] Out[1]= [image] ``` Place the labels differently for each curve: ```wl In[2]:= LogLogPlot[{x ^ Sin[x], x ^ Cos[x]}, {x, 1, 2π}, PlotLabels -> {Placed[x ^ Sin[x], After], Placed[x ^ Cos[x], Above]}] Out[2]= [image] ``` --- ``PlotLabels -> "Expression"`` uses functions as curve labels: ```wl In[1]:= LogLogPlot[{Log[x], x ^ x}, {x, 1, 3}, PlotLabels -> "Expressions"] Out[1]= [image] ``` --- Use callouts to identify the points: ```wl In[1]:= LogLogPlot[{x, x ^ Sin[x]}, {x, 1, 10}, PlotLabels -> {Callout[x, Scaled[0.33]], Callout[x ^ Sin[x], Scaled[0.5]]}] Out[1]= [image] ``` --- Use ``None`` to not add a label: ```wl In[1]:= LogLogPlot[{x ^ Sin[x], x ^ Cos[x]}, {x, 1, 2π}, PlotLabels -> {x ^ Sin[x], None}] Out[1]= [image] ``` #### PlotLayout (2) Place each curve in a separate panel using shared axes: ```wl In[1]:= LogLogPlot[{x, x ^ 2, x ^ 3}, {x, 1, 100}, ImageSize -> Medium, PlotLayout -> "Column"] Out[1]= [image] ``` Use a row instead of a column: ```wl In[2]:= LogLogPlot[{x, x ^ 2, x ^ 3}, {x, 1, 100}, ImageSize -> Medium, PlotLayout -> "Row"] Out[2]= [image] ``` --- Use multiple columns or rows: ```wl In[1]:= LogPlot[{x, x ^ 2, x ^ 3, x + Sin[x], Log[x], Log[x]}, {x, 1, 100}, PlotLayout -> {"Column", 4}] Out[1]= [image] ``` Prefer full columns or rows: ```wl In[2]:= LogLogPlot[{x, x ^ 2, x ^ 3, x + Sin[x], Log[x], Log[x]}, {x, 1, 100}, PlotLayout -> {"Column", UpTo[4]}] Out[2]= [image] ``` #### PlotLegends (7) No legends are used by default: ```wl In[1]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 100]}, {x, 1, 1000}] Out[1]= [image] ``` --- Create a legend based on the functions: ```wl In[1]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 100]}, {x, 1, 1000}, PlotLegends -> "Expressions"] Out[1]= [image] ``` --- Create a legend with placeholder text: ```wl In[1]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 100]}, {x, 1, 1000}, PlotLegends -> Automatic] Out[1]= [image] ``` --- Specify labels for each curve: ```wl In[1]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 100]}, {x, 1, 1000}, PlotLegends -> {"one", "two"}] Out[1]= [image] ``` --- ``PlotLegends`` picks up ``PlotStyle`` values automatically: ```wl In[1]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 100]}, {x, 1, 1000}, PlotStyle -> {Red, Blue}, PlotLegends -> Automatic] Out[1]= [image] ``` --- Use ``Placed`` to position legends: ```wl In[1]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 100]}, {x, 1, 1000}, PlotStyle -> {Red, Blue}, PlotLegends -> Placed[Automatic, Below]] Out[1]= [image] ``` Place legends inside: ```wl In[2]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 100]}, {x, 1, 1000}, PlotStyle -> {Red, Blue}, PlotLegends -> Placed[Automatic, {0.875, 0.75}]] Out[2]= [image] ``` --- Use ``LineLegend`` to modify the appearance of the legend: ```wl In[1]:= LogLogPlot[{1 / Abs[x - 10], 1 / Abs[x - 100]}, {x, 1, 1000}, PlotLegends -> LineLegend["Expressions", LegendFunction -> Frame]] Out[1]= [image] ``` #### PlotPoints (1) Use more initial points to get a smoother curve: ```wl In[1]:= Table[LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, PlotPoints -> p, MaxRecursion -> 0], {p, {5, 10, 15, 25}}] Out[1]= [image] ``` #### PlotRange (1) Show the curve only where it is positive: ```wl In[1]:= LogLogPlot[1 / (x - 5), {x, 1, 10}, PlotRange -> Automatic] Out[1]= [image] ``` #### PlotStyle (6) Use different style directives: ```wl In[1]:= Table[LogLogPlot[10 / (x ^ 2 - 19x + 100), {x, 0.1, 100}, PlotStyle -> ps, Ticks -> None], {ps, {Red, Thick, Dashed, Directive[Red, Thick]}}] Out[1]= {[image], [image], [image], [image]} ``` --- By default, different styles are chosen for multiple curves: ```wl In[1]:= LogLogPlot[Evaluate[Table[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}]], {x, 0.1, 1000}] Out[1]= [image] ``` --- Explicitly specify the style for different curves: ```wl In[1]:= LogLogPlot[Evaluate[Table[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}]], {x, 0.1, 1000}, PlotStyle -> {Red, Green, Blue}] Out[1]= [image] ``` --- ``PlotStyle`` can be combined with ``ColorFunction`` : ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 19x + 100), {x, 0.1, 100}, PlotStyle -> Thick, ColorFunction -> Function[{x, y}, Hue[x]]] Out[1]= [image] ``` --- ``PlotStyle`` can be combined with ``MeshShading`` : ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 19x + 100), {x, 0.1, 100}, PlotStyle -> Directive[Opacity[0.5], Thick], Mesh -> 10, MeshFunctions -> {Log[#1]&}, MeshShading -> {Red, Blue}] Out[1]= [image] ``` --- ``MeshStyle`` by default uses the same style as ``PlotStyle`` : ```wl In[1]:= LogPlot[x ^ Sin[x], {x, 0, 10}, PlotStyle -> Red, Mesh -> All] Out[1]= [image] ``` #### PlotTheme (1) Use a theme with a frame, grid lines, and an automatic legend: ```wl In[1]:= LogLogPlot[{10 / (x ^ 2 - 6x + 10), 100 / (x ^ 2 + 100)}, {x, 0.1, 1000}, PlotTheme -> "Detailed"] Out[1]= [image] ``` Turn off the grid lines: ```wl In[2]:= LogLogPlot[{10 / (x ^ 2 - 6x + 10), 100 / (x ^ 2 + 100)}, {x, 0.1, 1000}, PlotTheme -> "Detailed", GridLines -> None] Out[2]= [image] ``` #### RegionFunction (2) Show the curve where $x y<2$ : ```wl In[1]:= LogLogPlot[Sum[i / (x ^ 2 - 2 i 0.99 x + i ^ 2), {i, {1, 10, 100}}], {x, 0.1, 1000}, RegionFunction -> Function[{x, y}, x y < 2]] Out[1]= [image] ``` --- Exclude the region where $\frac{1}{2} Function[{x, y}, Not[1 / 2 < y < 2]]] Out[1]= [image] ``` #### ScalingFunctions (2) By default, both axes have a log scale: ```wl In[1]:= LogLogPlot[Exp[Sin[(x - 2)] / (x - 2) ^ 2], {x, 0, 25}] Out[1]= [image] ``` --- Reverse the direction of the ``y`` axis: ```wl In[1]:= LogLogPlot[Sin[x], {x, 0, 25}, ScalingFunctions -> "Reverse"] Out[1]= [image] ``` Reverse the direction of both axes: ```wl In[2]:= LogLogPlot[Sin[x], {x, 0, 25}, ScalingFunctions -> {"Reverse" , "Reverse"}] Out[2]= [image] ``` ### Properties & Relations (4) ``LogLogPlot`` samples more points where it needs to: ```wl In[1]:= LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 10}, Mesh -> All] Out[1]= [image] ``` --- ``LogLogPlot`` is a special case of ``Plot`` for curves: ```wl In[1]:= {LogLogPlot[1 / (x - 5) ^ 2, {x, 1, 10}], Plot[Log[1 / (Exp[x] - 5) ^ 2], {x, Log[1], Log[10]}, AxesOrigin -> {0, -3}]} Out[1]= {[image], [image]} ``` --- Use ``LogPlot`` and ``LogLinearPlot`` for logarithmic plots in the other directions: ```wl In[1]:= LogPlot[Gamma[x], {x, 0, 10}] Out[1]= [image] ``` --- Use ``ListLogPlot`` for data: ```wl In[1]:= {ListLogLogPlot[Table[{x, 10 / (x ^ 2 - 6x + 10)}, {x, 1, 10, 0.1}]], LogLogPlot[10 / (x ^ 2 - 6x + 10), {x, 1, 10}]} Out[1]= {[image], [image]} ``` ## See Also * [`ListLogLogPlot`](https://reference.wolfram.com/language/ref/ListLogLogPlot.en.md) * [`LogPlot`](https://reference.wolfram.com/language/ref/LogPlot.en.md) * [`LogLinearPlot`](https://reference.wolfram.com/language/ref/LogLinearPlot.en.md) * [`Plot`](https://reference.wolfram.com/language/ref/Plot.en.md) * [`ParametricPlot`](https://reference.wolfram.com/language/ref/ParametricPlot.en.md) ## Tech Notes * [Some Special Plots](https://reference.wolfram.com/language/tutorial/GraphicsAndSound.en.md#31896) ## Related Guides * [Function Visualization](https://reference.wolfram.com/language/guide/FunctionVisualization.en.md) ## History * [Introduced in 2007 (6.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn60.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) ▪ [2016 (10.4)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn104.en.md) ▪ [2016 (11.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn110.en.md) ▪ [2018 (11.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn113.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) ▪ [2023 (13.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn133.en.md) ▪ [2025 (14.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn143.en.md)