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See for example this picture produced with R:

You can see there is a small white space between the x-axis and the y-axis, so that the axes do not cross. How can I do this with Mathematica, for a ListPlot or a Histogram?

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This can be done more-or-less easily with a combination of options for AxesOrigin, PlotRange, and PlotRangePadding and the CustomTicks package (for easy outward-facing ticks).

Needs["CustomTicks`"];

GapAxes[plot_Graphics, ticks : {{x__}, {y__}}, scalefactor_: Automatic] := With[
   {prange = ticks[[All, 1 ;; 2]],
    s = Flatten@{scalefactor /. Automatic -> 0.02 {1, 1/(AspectRatio /. Options[plot])}}},
   Show[plot,
    Ticks -> {LinTicks[x], LinTicks[y]},
    PlotRange -> (prange + Subtract @@@ prange {{First@s, 0}, {Last@s, 0}}),
    PlotRangePadding -> (Subtract @@@ prange {{First@s, 0}, {Last@s, 0}}),
    AxesOrigin -> (prange[[All, 1]] + Subtract @@@ prange {First@s, Last@s})
    ]
   ];
  1. plot can be any plot or chart.
  2. ticks gives the arguments of the LinTicks functions which specify the axes ticks. x and y must each contain a range specification (which also doubles as the PlotRange specifiation) as the first two items, but they may also include as additional items any of the other arguments that may be passed to LinTicks (TickDirection -> Out, perhaps).
  3. The optional argument scalefactor specifies how far to separate the axes from the plot as a fraction of the total image dimensions. If scalefactor is not specified, the axes are separated by 2% of the total width.

Examples

data = RandomVariate[HalfNormalDistribution[1/150], 500];

GapAxes[
 Histogram[data, {100}], 
 {{0, 700, TickDirection -> Out}, {0, 200, TickDirection -> Out}}
 ]

chart

GapAxes[
 Plot[Tan[x], {x, -3, 3}], 
 {{-3, 3, TickDirection -> Out}, {-6, 6, TickDirection -> Out}}
 ]

plot


Notes:

  1. It remains to be seen how robust this GapAxes function will prove to be, but the basic method should be pretty universal.

  2. To see the whole plot when the axes are short, additional ImagePadding may be needed.

    GapAxes[
     Histogram[data, {100}, ImagePadding -> {{Automatic, 50}, {Automatic, Automatic}}], 
     {{0, 600, TickDirection -> Out}, {0, 200, TickDirection -> Out}}
     ]
    

chart2

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This is tedious.. manually drawing the axes.

 GraphicsRow[{Histogram[data],
      Show[{Histogram[data  , PlotRangePadding -> Scaled[.2], 
            Axes -> False,
            PlotRange -> {{-3, 3}, {0, 100}}], 
      Graphics[{Line[{Scaled[{.2, .15}], Scaled[{.8, .15}]}],
                Line[Scaled /@ {{#, .15}, {#, .1}}] & /@ Range[.2, .8, .1],
            Text[#, Scaled[{.6 (# + 3)/6 + .2, .04}], {0, 0}] & /@ 
                  Range[-3, 3, 1],
             Text[Rotate[ #, Pi/2], 
              Scaled[{.04, (#/100) .6 + .2 }], {0, 0}] & /@ 
               Range[0, 100, 25],
            Line[Scaled /@ {{.06, #}, {.1, #}}] & /@ Range[.2, .8, .1],
            Line[Scaled /@ {{.1, .2}, {.1, .8}}]}]}]}]

enter image description here

a bit of caution, I'm not certain the axes are precisely aligned.

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Not a real answer. But you can try to put your plot in Inset[], then add another Inset[] for x-axis and yet another Inset[] for y-axis and then stitch all scales together… Something like this (nothing is stitched)

Graphics[{Transparent, Rectangle[], 
  Inset[ListPlot[{1, 2, 3, 4, 0}, Axes -> False, Joined -> True, 
    InterpolationOrder -> 0, Filling -> Bottom], {0, 0}, {0.1, -0.1}, 
   1], Inset[
   ListPlot[{}, AxesStyle -> Red, Axes -> {False, True}], {0, 
    0.05}, {0, 0}, 1],
  Inset[ListPlot[{}, AxesStyle -> Blue, Axes -> {True, False}], {0.05,
     0}, {0, 0}, 1]}]

enter image description here

This post is potentially useful for aligning three Insets

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  • 1
    $\begingroup$ try working with regular Plot for the axes then you can specify the PlotRange $\endgroup$ – george2079 Jun 16 '15 at 19:37
  • $\begingroup$ @george2079 I can specify PlotRange for ListPlot as well… like you said it's just so tedious! I actually prefer your solution, it's straightforward and quite flexible. I thought about it but got scared to draw ticks myself... $\endgroup$ – BlacKow Jun 16 '15 at 19:41
  • $\begingroup$ yes you can. Actually the other issue I had in v9 ListPlot does not like an empty list. You can give it an out of range point though to get an empty plot. $\endgroup$ – george2079 Jun 16 '15 at 19:52
  • $\begingroup$ why do you need an empty plot? $\endgroup$ – BlacKow Jun 16 '15 at 19:55
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    $\begingroup$ that's what your ListPlot[{}, .. does. Just an axis with no data. In v9 this throws an error "ListPlot called with 0 arguments" . This tricks it into working : ListPlot[{""}, ... ] $\endgroup$ – george2079 Jun 16 '15 at 20:01
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ClearAll[ticksF, axesF, labelF]
ticksF[tSide_: Left, tr_: 1, tl_: (.01), s_: {Thickness[.001]}][{minmax__}, nd_:{6, 6}] :=
 Module[{tf = tSide /. {Automatic | Left -> Identity, Right -> ({-1, 1} # &), 
   Bottom -> ((Reverse@#) &)}, 
 d = {#, Complement[Join @@ #2, #]} & @@ FindDivisions[{minmax}, nd, Method -> {}], 
 trns = tSide /. {Left -> {-tr, 0}, Right -> {tr, 0}, Bottom -> {0, -tr} }, tcks}, 
 tcks = Join[Table[{i, i, tl, s}, {i, d[[1]]}], Table[{i, "", tl/2, s}, {i, d[[2]]}]]; 
 Translate[{s, Line@Thread[tf @
  {0, Through @ {Min, Max} @ #[[All, 1]]}], {Line[{tf @ {-#3, #}, tf @ {0, #}}],
  Text[#2,  tf[{1.2  tSide /. {(Left | Bottom) -> (-1) , (Top | Right) -> 1}, 1} {#3, #}],
   If[tSide === Bottom, {Center, tSide /. {Bottom -> Top, Top -> Bottom}}, 
    {tSide /. {Left -> Right, Right -> Left}, Center}]]} & @@@ #} &@tcks, trns]]

axesF[ tr_: {1, 1}, tl_: (0.01), ar_: 1/GoldenRatio][
   {rng1 : {_, __}, nd1_: {6, 6}}, {rng2 : {_, __}, nd2_: {6, 6}}] := 
 Module[{sc = ar (Subtract @@ rng1[[{2, 1}]])/ (Subtract @@ rng2[[{2, 1}]])}, 
  {ticksF[Bottom, tr[[1]], tl][rng1, nd1], ticksF[Left, tr [[2]] sc, tl  sc][rng2, nd2]}]

labelF = Labeled[#, {Rotate[#2, 90 Degree], #3}, {Left, Bottom}] &;

Histogram

SeedRandom[1]
data = RandomVariate[HalfNormalDistribution[1/150], 500];
hst = Histogram[data, Axes -> False, 
   ImagePadding -> {Scaled /@ {.04, .05}, Scaled /@ {.04, .025}}, 
   ImageSize -> 600, PlotRangeClipping -> False, 
   Epilog -> (axesF[{5, 5}, 5][{{0, 700}}, {{0, 120}}]), 
   BaseStyle -> {FontSize -> 14}];
labelF[hst, Style["labely", 20, "Panel"], Style["labelx", 20, "Panel"]]

enter image description here

ListPlot

lp = ListPlot[data, Axes -> False, 
   ImagePadding -> {Scaled /@ {.04, .05}, Scaled /@ {.04, .025}}, 
   ImageSize -> 600, PlotRangeClipping -> False, 
   Epilog -> (axesF[{20, 20}, 20][{{0, Length@data}}, {{0, 1.1 Max[data]}}]), 
   BaseStyle -> {FontSize -> 14}];
labelF[lp, Style["labely", 20, "Panel"], Style["labelx", 20, "Panel"]]

enter image description here

BarChart

bc = BarChart[d2 = HistogramList[data][[2]], Axes -> False, 
   AxesOrigin -> {0, 0}, 
   ImagePadding -> {Scaled /@ {.025, .025}, Scaled /@ {.05, .025}}, 
   ImageSize -> 600, AspectRatio -> ar, PlotRangeClipping -> False, 
   Epilog -> (axesF[{5, 0}, 5][{{1, 1 + Length@d2}, {Length@d2, 1}}, {{0, 120}}]), 
   BaseStyle -> {FontSize -> 14}];
labelF[bc, Style["labely", 20, "Panel"], Style["labelx", 20, "Panel"]]

enter image description here

Plot

plot = Plot[{Sin[x], Cos[x]}, {x, -2 Pi, 2 Pi}, Axes -> False, 
  ImagePadding -> {Scaled /@ {.05, .05}, Scaled /@ {.065, .05}}, 
  ImageSize -> 600, PlotRange -> {{-2 Pi, 2 Pi}, {-1, 1}}, 
  PlotRangeClipping -> False, 
  Epilog -> (axesF[{1.1, 1.7}, .1][{{-2 Pi, 2 Pi, Pi/2}, {8, 2}}, {{-1, 1}}]), 
  BaseStyle -> {FontSize -> 14}]
labelF[plot, Style["labely", 20, "Panel"], Style["labelx", 20, "Panel"]]

enter image description here

Note: With some additional effort, some of the manual settings can be automated using Scaled and/or extracting plot range.

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