# Generating a broken or snipped axis in ListPlot

I have two data sets, data1 and data2. For example:

data1 = {{1, 1.1}, {2, 1.5}, {3, 0.9}, {4, 2.3}, {5, 1.1}};
data2 = {{1, 1001.1}, {2, 1001.5}, {3, 1000.9}, {4, 1002.3}, {5, 1001.1}};
ListPlot[data1, PlotRange -> All, Joined -> True, Mesh -> Full, PlotStyle -> Red]
ListPlot[data2, PlotRange -> All, Joined -> True, Mesh -> Full, PlotStyle -> Blue]


Their $y$-values are in vastly different regimes, but their oscillations in $y$ are comparable, and I'd like to compare them visually using ListPlot. But if I simply overlay them, it is nearly impossible to see and compare their oscillations, because of the scaling:

Show[{
ListPlot[data1, PlotRange -> {{1, 5}, {-100, All}}, Joined -> True, Mesh -> Full,
PlotStyle -> Red, AxesOrigin -> {1, -50}],
ListPlot[data2, Joined -> True, Mesh -> Full, PlotStyle -> Blue]
}]


Is there a way to "break" or "snip" the $y$ axis so that I can compare data1 and data2 on the same plot? There is no data in the range ~3 to ~1000, so I would like to snip this $y$-range out, if possible, and perhaps include a jagged symbol to show that this has been done.

• Very very strongly related: mathematica.stackexchange.com/questions/627/1-plot-2-scale-axis Commented Jul 12, 2012 at 15:28
• @Ajasja Yes, that is similar, but not identical to this question. In that question, they ask for two different axes/scales, one on each side. I am asking for a snipped axis. While the two approaches accomplish similar things, they are different, since I would like to show how the blue set of data (data2) are above the red set of data (data1). Commented Jul 12, 2012 at 15:35
• @Andrew Ajasja wasn't the one that voted to close, that was me — I didn't catch the snipped axes requirement at first. I agree that there is a subtle difference and not a duplicate.
– rm -rf
Commented Jul 12, 2012 at 16:03
• I've got a function that does this, on my laptop at home. Will post this evening (although somebody will surely beat me to it :))
– JxB
Commented Jul 12, 2012 at 16:16
• Also, W|A does a snipped axis (see, e.g. this). I wonder if it'll be included as an option in MMA 9? Commented Jul 13, 2012 at 17:14

## 4 Answers

Here is a solution that uses a BezierCurve to indicate a "snipped" axes. The function snip[x] places the mark on the axes at relative position x (0 and 1 being the ends). The function getMaxPadding gets the maximum padding on all sides for both plots (based on this answer). The two plots are then aligned one over the other, with the max padding applied for both.

snip[pos_] := Arrowheads[{{Automatic, pos,
Graphics[{BezierCurve[{{0, -(1/2)}, {1/2, 0}, {-(1/2), 0}, {0, 1/2}}]}]}}];
getMaxPadding[p_List] := Map[Max, (BorderDimensions@
Image[Show[#, LabelStyle -> White, Background -> White]] & /@ p)~Flatten~{{3}, {2}}, {2}] + 1
p1 = ListPlot[data1, PlotRange -> All, Joined -> True, Mesh -> Full, PlotStyle -> Red,
AxesStyle -> {None, snip[1]}, PlotRangePadding -> None, ImagePadding -> 30];
p2 = ListPlot[data2, PlotRange -> All, Joined -> True, Mesh -> Full, PlotStyle -> Blue,
Axes -> {False, True}, AxesStyle -> {None, snip[0]}, PlotRangePadding -> None, ImagePadding -> 30];

Column[{p2, p1} /. Graphics[x__] :>
Graphics[x, ImagePadding -> getMaxPadding[{p1, p2}], ImageSize -> 400]]


• Nice one, oh hypnotoad! Commented Jul 12, 2012 at 16:35
• @YvesKlett it sort of forces you to upvote him, doesn't it? All hail the Hypnotoad! Commented Jul 12, 2012 at 17:58
• @rcollyer well ,here goes: ALL GLORY TO THE HYPNOTOAD! Commented Jul 12, 2012 at 19:29
• R.M. this looks nice but (for me) it only works at one particular size since if I resize the graphic it overlaps incorrectly. I'm not sure if that's what you're referring to at the bottom of the answer. Either way, can you fix it? Commented Jul 13, 2012 at 5:40
• @Mr.Wizard That's more an indictment of GraphicsColumn, which overlaps (eventually) when resizing if a particular negative spacing is set (alternately, widens for positive spacing). For example, try: GraphicsColumn[{#, #}, Spacings -> -10] &@Plot[, {x, 0, 1}]. I've used Column now, and you shouldn't have this issue if you use the ImageSize option to set the size
– rm -rf
Commented Jul 13, 2012 at 15:13

This solution shifts data around and makes new ticks for the y axis.

compressYAxis[plot_,plotRange1_,plotRange2_] will modify the y axis of the supplied plot to exclude the region between the upper limit of plotRange1 and the lower limit of plotRange2. With your data, here is the plot with a compressed y axis:

data1 = {{1, 1.1}, {2, 1.5}, {3, 0.9}, {4, 2.3}, {5, 1.1}};
data2 = {{1, 1001.1}, {2, 1001.5}, {3, 1000.9}, {4, 1002.3}, {5, 1001.1}};

p = ListLinePlot[{data1, data2}, PlotRange -> All,
PlotLabel -> "Example of a compressed y axis",
AxesLabel -> {"x", "y"}];

compressYAxis[p, {0, 3}, {999, 1003}]


You will have to fiddle with this if you want tick subdivisions or a different background colour; the compression marks could be improved too.

The definition is

Clear[compressYAxis];
compressYAxis[plot_, range1_, range2_] :=
Module[{ytick1, ytick2, epilog1, target},
ytick1 = FindDivisions[range1, 5] /. y_?NumericQ :> {y, y} /. {y_?NumericQ, _} /; y >= range1[[2]] :> Sequence[];
ytick2 = FindDivisions[range2, 5] /. y_?NumericQ :> {y - range2[[1]] + range1[[2]], y} /. {y_?NumericQ, _} /; y <= range1[[2]] :> Sequence[];
epilog = Options[plot, Epilog][[1, 2]];
target = Subtract @@ Reverse@range1/(Subtract @@ Reverse@range1 + Subtract @@ Reverse@range2);
Show[plot /. {x_?NumericQ, y_?NumericQ /; y > range2[[1]]} :> {x, y - range2[[1]] + range1[[2]]},
PlotRange -> {range1[[1]], range1[[2]] + Subtract @@ Reverse@range2},
Ticks -> {Automatic, Join[ytick1, ytick2]},
Epilog -> Join[epilog, {White, Rectangle[Scaled[{-0.1, 0.98 target}], Scaled[{1.1, 1.02 target}]], Black, Text[Rotate["\\", \[Pi]/2], Scaled[{0, 0.98 target}], {-1.5, 0}], Text[Rotate["\\", \[Pi]/2], Scaled[{0, 1.02 target}], {-1.5, 0}]}]]
]

• @Andrew As promised. It's hawkish, and needs Mma v7 or greater. This approach could work quite nicely if (once?) AbsoluteOptions is fixed so that it returns suitable values for Ticks. As it stands, R.M's solution looks more robust.
– JxB
Commented Jul 13, 2012 at 4:35
• In the Module parameter list there is a epilog1 variable, however in the following code you used epilog (without the 1). This should probably be corrected.
– shrx
Commented Oct 5, 2015 at 7:45

### ScalingFunctions

We can use custom piecewise linear ScalingFunctions which efectively makes the interval $$[3,1000]$$ very short and add a glyph to indicate the break using Epilog or AxesStyle to

ClearAll[sf, isf, inset]
sf[t1_, t2_, gap_: 1/10][x_] := Piecewise[{{x, x <= t1}, {t1 + gap/(t2 - t1) (x - t1),
t1 <= x <= t2}, {t1 + gap + (x - t2), x >= t2}}]
isf[t1_, t2_, gap_: 1/10][x_] := InverseFunction[sf[t1, t2, gap]][x]

head = Graphics[{Antialiasing -> True,EdgeForm[None], FaceForm[White],
Polygon[{{-1, -1/6}, {1, 5/6}, {1, 1/6}, {-1, -5/6}}], Black,
CapForm["Butt"], AbsoluteThickness[1],
Line[{{{-1, -5/6}, {1, 1/6}}, {{-1, -1/6}, {1, 5/6}}}]}];
inset[pos_: Scaled[{0.005, .55}], size_: {1/3, 1/3}] := Inset[head, pos, Automatic, size]

{t1, t2} = {Ceiling[#[[1, 2]]], Floor[#[[2, 1]]]} &@
(CoordinateBounds[#][[2]]&/@ {data1, data2});
{yrange1, yrange2} = {Floor[#, .5], Ceiling[#2, .5]} & @@@
(CoordinateBounds[#][[2]] & /@ {data1, data2});
ticks = Join @@ (ChartingFindTicks[{0, 1}, {0, 1}][##] & @@@ {yrange1, yrange2});


Using inset[] as Epilog:

ListLinePlot[{data1, data2}, PlotStyle -> Thick,
ScalingFunctions -> {"Linear", {sf[t1, t2], isf[t1, t2]}},
Ticks -> {Automatic, ticks}, PlotRangeClipping -> False,
Epilog -> inset[], ImageSize -> Medium, AspectRatio -> Automatic]


Using head as Arrowheads in AxesStyle:

ListLinePlot[{data1, data2}, PlotStyle -> Thick,
ScalingFunctions -> {"Linear", {sf[t1, t2], isf[t1, t2]}},
Ticks -> {Automatic, ticks}, PlotRangeClipping -> False,
ImageSize -> Medium, AspectRatio -> Automatic,
AxesStyle -> {Automatic, Arrowheads[{{.05, .55, MapAt[
GeometricTransformation[#, RotationTransform[Pi/2]] &, head, {1}]}}]}]


A modification of rm-rf's snip used with Epilog and AxesStyle:

ClearAll[snip2, inset2]
head2 = Graphics[{Antialiasing -> True, FaceForm[White],
Rectangle[{-1/3, -1/2}, {2/3, 1/2}],
{#, Translate[#, {1/2, 0}]} & @
BezierCurve[{{0, -(1/2)}, {1/2, 0}, {-(1/2), 0}, {0, 1/2}}]}];
snip2[pos_] := Arrowheads[{{Automatic, pos, head2}}];
inset2[pos_: Scaled[{0.005, .55}], size_: {1/3, 1/3}] := Inset[MapAt[
GeometricTransformation[#, RotationTransform[Pi/2]] &, head2, {1}],
pos, Automatic, size]

ListLinePlot[{data1, data2}, PlotStyle -> Thick,
ScalingFunctions -> {"Linear", {sf[t1, t2], isf[t1, t2]}},
Ticks -> {Automatic, ticks}, PlotRangeClipping -> False,
Epilog -> inset2[], ImageSize -> Medium, AspectRatio -> Automatic]


ListLinePlot[{data1, data2}, PlotStyle -> Thick,
ScalingFunctions -> {"Linear", {sf[t1, t2], isf[t1, t2]}},
Ticks -> {Automatic, ticks}, PlotRangeClipping -> False,
AxesStyle -> {Automatic, snip2[.55]}, ImageSize -> Medium,
AspectRatio -> Automatic]


### TranslationTransform

We can translate data2 and modify vertical tick labels taking the translation into account:

data2translated = TranslationTransform[{0, -997}] @ data2;
ticks2 = Join[ChartingFindTicks[{0, 1}, {0, 1}][##] & @@ yrange1,
ChartingFindTicks[#, # + 997][## & @@ #] &@(yrange2 - 997)];
ListLinePlot[{data1, data2translated },
PlotStyle -> Thick, PlotRangeClipping -> False,
ImageSize -> Medium, AspectRatio -> Automatic,
AxesStyle -> {Automatic, snip2[.55]},
Ticks -> {Automatic, ticks2}]


Now there is a package in Mathematica which handles all of this without effort.

You just need to use the package and does the job in just one line!

ResourceFunction["PlotGrid"][{{plot2}, {plot1}}, "MergeAxes" -> "ZigZag", Spacings -> {0, 5}]


Just store your plots in one variable, and add the Frame-> True option to them:

plot1 = ListPlot[data1, Frame -> True, PlotRange -> All, Joined -> True, Mesh -> Full, PlotStyle -> Red];
plot2 = ListPlot[data2, Frame -> True, PlotRange -> All, Joined -> True, Mesh -> Full, PlotStyle -> Blue];
`

Here you can find more documentation on how to tweak it according to your needs: https://resources.wolframcloud.com/FunctionRepository/resources/PlotGrid/

Based on this Q&A: Broken y axis at multiple locations