How do I plot a histogram with hatched shading?

Question

I can plot an ordinary histogram with blue shading and black borders like this:

T = RandomVariate[NormalDistribution[0, 1], 10000];
Histogram[T, 30]

And I can simulate hatching like this:

T = RandomVariate[NormalDistribution[0, 1], 10000];
Histogram[T, 30, ChartElements -> Graphics[{Black, Line[{{0, 0}, {1, 1}}]}]]

How can I get the hatching and the black borders at the same time?

Answer 1

I was sure Histogram can be modified to have the hatching style. Little late but what about this!

g[{{xmin_, xmax_}, {ymin_, ymax_}}, ___] := Module[{yval, line},
  yval = Range[ymin, ymax, 15];
  line = Line /@ Transpose@{Most@({xmin, #} & /@ yval),Rest@({xmax, #} & /@ yval)};
  {FaceForm[White],Polygon[{{xmin, ymin}, {xmax, ymin}, {xmax, ymax}, {xmin, ymax}}],
   Orange, line}];
T = RandomVariate[NormalDistribution[0, 1], 10000];
Histogram[T, 30, ChartElementFunction -> g,
ChartBaseStyle -> EdgeForm[{Thin, Darker@Orange}], Frame -> True]

Check in the function where yval is defined with Range[ymin, ymax, 15] one can change the $15$ to change the amount of hatching. You also have total control of the Graphics primitive used in the ChartElementFunction so you can use many more Directive for example Opacity and all.

BR

Answer 2

I would do something like:

t = RandomVariate[NormalDistribution[0, 1], 10000];
a = Histogram[t, 30, ChartStyle -> White];
b = Histogram[t, 30, 
  ChartElements -> Graphics[{Black, Line[{{0, 0}, {1, 1}}]}]];
Show[a, b]

Answer 3

Here is extended version of PlatoManiac's solution which allows changing of the direction of the hatching and also tuning the distance between hatches:

g[step_?NumberQ][{{xmin_, xmax_}, {ymin_, ymax_}}, ___] := 
  Module[{yval, lines, xstart, xend},
   yval = Range[ymin, ymax, Abs[step]];
   If[step > 0, {xstart, xend} = {xmin, xmax}, {xstart, xend} = {xmax, xmin}];
   lines = Transpose@{{xstart, #} & /@ Most[yval], {xend, #} & /@ Rest[yval]};
   lines = Join[lines, {{{xstart, Last@yval}, 
           {xstart + ((xend - xstart) (ymax - Last@yval))/Abs[step], ymax}}}];
   {FaceForm[None], Rectangle[{xmin, ymin}, {xmax, ymax}], 
                                               CapForm["Butt"], Line[lines]}];

Now

data = RandomVariate[NormalDistribution[0, 1], 10000];
Histogram[data, 30, "PDF", ChartElementFunction -> g[-.006], 
 ChartBaseStyle -> {Directive[{EdgeForm[{Thin, Black}], Black}]}, 
 Frame -> True]

gives

And now one can combine several histograms with different hatchings:

data1 = RandomVariate[NormalDistribution[0, 1], 500];
data2 = RandomVariate[NormalDistribution[2, 1/2], 500];
h1 = Histogram[data1, 30, "PDF", ChartElementFunction -> g[.0260], 
   ChartBaseStyle -> Directive[{EdgeForm[{Thin, Black}], Black, Thin}], 
   Frame -> True];
h2 = Histogram[data2, 30, "PDF", ChartElementFunction -> g[-.0180], 
   ChartBaseStyle -> Directive[{EdgeForm[{Thin, Black}], Black, Thin}], 
   Frame -> True];
Show[h1, h2, PlotRange -> All, BaseStyle -> Antialiasing -> False]

The histogram can be optimized by joining adjacent line segments into solid lines and deleting auxiliary points. Here is an example:

data = RandomVariate[NormalDistribution[0, 1], 100];
hist = Histogram[data, 30, "PDF", ChartElementFunction -> g[-.0160], 
  ChartBaseStyle -> {Directive[{EdgeForm[{Thin, Black}], Black}]}, Frame -> True];

hatchings = Cases[hist, (Line | LineBox)[{x__List}] /; Dimensions[{x}][[2]] == 2 :> x, {0, Infinity}];
hist2 = DeleteCases[hist, (Line | LineBox)[{x__List}] /; Dimensions[{x}][[2]] == 2, {0, Infinity}];

ClearAll[coeff, a, b, x1, x2, y1, y2];
coeff[{{x1_, y1_}, {x2_, y2_}}] /; x1 != x2 = {a, b} /. First@Solve[{a x1 + b == y1, a x2 + b == y2}, {a, b}];
Show[hist2, 
 Graphics[{Line@
    Flatten[Map[SortBy[Flatten[#, 1], Last][[{1, -1}]] &, 
      (Split[#, #1[[2]] == #2[[1]] || #1[[1]] == #2[[2]] &] & /@ 
        Gather[hatchings, coeff[#1] == coeff[#2] &]), {2}], 1]}]]

Answer 4

You can use the PDF of a HistogramDistribution for the outline.

dist = HistogramDistribution[T, 30]

p1 = Plot[PDF[dist, t], {t, -4, 4}, PlotStyle -> Black, 
   Exclusions -> None, PlotPoints -> 100];

p2 = Histogram[T, 30, "PDF", 
   ChartElements -> Graphics[{Black, Line[{{0, 0}, {1, 1}}]}]];

Show[p1, p2]

The problem here is that it isn't a frequency histogram but a density histogram.

If you want to get counts you need to multiply by the bin width and sample size.

p1 = Plot[
  Differences[dist["BinDelimiters"]][[1]]*10^4*PDF[dist, t], {t, -4, 
   4}, PlotStyle -> Black, Exclusions -> None, PlotPoints -> 100]

Edit:

If you don't want to use HistogramDistribution you can also try HistogramList.

ListLinePlot[
 Thread[{Most[First[#]], Last[#]}] &[HistogramList[T, 30]], 
 InterpolationOrder -> 0, PlotStyle -> Black]

Answer 5

Since Mathematica 12.1 it is possible to do this with HatchFilling:

Histogram[RandomReal[{0, 10}, 100], 10, 
 ChartStyle -> HatchFilling /@ (Range[0, 9] π/10)]

Answer 6

Using the method from this answer using System`BarFunctionDump`TextureBar for the option ChartElementFunction together with Texture as ChartStyle. Images to be used with Texture are created using the function hatchF.

ClearAll[hatchF]
hatchF[mf_List: {# &, #2 &}, mesh_List: {50, 50}, 
  style_: GrayLevel[.5], opts : OptionsPattern[]] := 
 ParametricPlot[{x, y}, {x, 0, 1}, {y, 0, 1}, Mesh -> mesh, 
  MeshFunctions -> mf, MeshStyle -> style, BoundaryStyle -> None, 
  opts, Frame -> False, PlotRangePadding -> 0, ImagePadding -> 0, Axes -> False]

Examples:

SeedRandom[123]
data1 = RandomVariate[NormalDistribution[0, 1], 10000];
data2 = RandomVariate[NormalDistribution[2, 1/2], 500];

Histogram[data1, 10, "PDF", 
 Frame -> True, ImageSize -> 500,
 ChartElementFunction -> System`BarFunctionDump`TextureBar, 
 ChartStyle -> Texture[hatchF[{# - #2 &}, {120}, Gray, PlotStyle -> None, 
    MeshShading -> {Gray, White}]]]

t1 = hatchF[{# - #2 &}, {80}, Gray, PlotStyle->Yellow, MeshShading -> {Gray, Automatic}];
t2 = hatchF[{# - #2 &, #2 + # &}, {50, 50}, Gray, ColorFunction -> "Rainbow", 
   MeshShading -> {{GrayLevel[.5], Automatic}, {Automatic, GrayLevel[.6]}}];
t3 = hatchF[{# - #2 &}, {80}, White, 
   MeshShading -> {GrayLevel[.5], Automatic}, ColorFunction -> "Rainbow"];
t4 = hatchF[{#2 + # &}, {90}, Blue, ColorFunction -> "DeepSeaColors"];

h1 = Histogram[data1, 10, "PDF", 
   ChartElementFunction -> System`BarFunctionDump`TextureBar, 
   ChartStyle -> Texture[t1], Frame -> True, ImageSize -> 400];
h2 = Histogram[data1, 10, "PDF", 
   ChartElementFunction -> System`BarFunctionDump`TextureBar, 
   ChartStyle -> Texture[t2], Frame -> True, ImageSize -> 400];

Row[{h1, h2}]

Histogram[{data1, data2}, 20, "PDF", 
  ChartElementFunction -> System`BarFunctionDump`TextureBar, 
  ChartStyle -> {Texture[t3], Texture[t4]},
  Frame -> True, ImageSize -> 500]