Drawing minor gridlines

Question

What's the best (most elegant, shortest, easiest to read) way to add minor grid lines to a plot?

Here is an example:

data = Table[{x, Log@x}, {x, 100}];
ListPlot[data, Frame -> True, GridLines -> Automatic]

But this gives gridlines only at the position of the major frameticks. I'm looking for an easy way to automatically generate minor grid lines at the positions of minor frameticks (in a style different from the major gridlines).

Here is an example (yes, made in excel)

I guess I could write half a page of code to generate both the frame ticks and the gridlines, but it seems like an overkill.

I realize this is very similar to this question, but if I have to enter the ranges manually for each plot then I might as well draw my plots in excel.

Answer 1

Not elegant, but at least it's quite short :)

makeGrid[{minX_, maxX_}, {minY_, MaxY_}, {xStep_, yStep_}] := 
 {AbsoluteThickness[.25],
   Table[{If[Mod[x, 10] == 0, Black, LightGray], 
     Line[{{x , -100}, {x , 100}}]}, {x, minX, maxX, xStep}],
   Table[{If[Mod[y, 1] == 0, Black, LightGray], 
     Line[{{-100, y}, {100, y}}]}, {y, minY, MaxY, yStep}]}

ListPlot[data, Frame -> True, 
 Prolog -> makeGrid[{0, 100}, {0, 10}, {10, .1}]]

Answer 2

This is what came to my mind

myGridDivision[{min_, max_}, {major_, majorStyle_}, {minor_, minorStyle_}] :=
 Function[divisions,
   Join[{#, majorStyle} & /@ divisions[[1]],
    {#, minorStyle} & /@ Complement[Flatten[#[[2]]], #[[1]]] &@ divisions]
   ][FindDivisions[{min, max}, {major, minor}]]

ListPlot[data, Frame -> True,
 FrameTicks -> {{True, False}, {True, False}},
 PlotRange -> {{0, 100}, {0, 5}},
 GridLines -> {
   myGridDivision[{0, 100}, {5, GrayLevel[.5]}, {5, GrayLevel[.8]}],
   myGridDivision[{0, 5}, {5, GrayLevel[.5]}, {5, GrayLevel[.8]}]
   }]

You can always set min/max to far more negative/positive large than the actual range of the plot to avoid manully determine the range.

Unfortunately, for some custom set FrameTicks cases, it seems not possible to auto-determine the FrameTicks setting using AbsoluteOptions[(*graphics*), FrameTicks] after the plot has been generated.. Maybe a home-made frame-ticks generator along with this one would be good.

Answer 3

Update 2: If it is ok to have minor and major gridlines with the same style, then the simplest solution is to use Full as the option setting:

ListPlot[data, Frame -> True, GridLines -> {Full, Full}]

AFAIK, this setting is not documented.

Update: A more convenient approach is to use the function Charting`FindTicks:

ClearAll[gridLinesF2]
gridLinesF2[majorstyle_: Thick, minorstyle_: Thin] := Replace[
   DeleteDuplicatesBy[Charting`FindTicks[{0, 1}, {0, 1}][##][[All, ;; 2]], First], 
     {{a_, ""} :> {a, minorstyle}, {a_, b_} :> {a, majorstyle}}, 1] &

ListPlot[data, Frame -> True, GridLines -> {gridLinesF2[Blue, Green], gridLinesF2[]}]

Original answer:

GridLines option setting can be a function. Using FindDivisions (as in Silvia's answer) without specific values for min and max (i.e., letting FindDivisions use automatically generated min and max values) and using {6, 6} as the second argument we get major and minor GridLines that match automatic ticks.

ClearAll[gridLinesF]
gridLinesF[style1_: Directive[Thickness[.003], GrayLevel[.5]], 
  style2_: Directive[Thin, GrayLevel[.9]], divs_:{6, 6}] := 
 Join[Thread[{#, style1}], 
   Thread[{DeleteCases[DeleteDuplicates[Join @@ #2], Alternatives @@ #], style2}]] & @@
 FindDivisions[{##}, divs] &

Examples:

data = Table[{x, Log@x}, {x, 100}];
ListPlot[data, Frame -> True, GridLines -> {gridLinesF[], gridLinesF[]}]

ListPlot[{RandomInteger[100], RandomReal[127]} + # & /@ data, 
 Frame -> True, GridLines -> {gridLinesF[], gridLinesF[]}]

Graphics[Circle[], Frame -> True, GridLines -> {gridLinesF[Red], gridLinesF[Blue]}]

Graphics[{}, PlotRange -> {{0, 1}, {0, 1}}, Frame -> True, 
 GridLines -> {gridLinesF[Directive[Thickness[.01], Red], Orange], 
   gridLinesF[Directive[Thickness[.01], Blue], Green]}]

Answer 4

I think it is quite useful since it is automatically applicaple:

data = Table[{x, Log@x}, {x, 100}];
plot = ListPlot[data, Frame -> True, GridLines -> Automatic]
{leftTicks, bottomTicks} = 
AbsoluteOptions[plot, FrameTicks][[ 1, 2, {2, 1}]];

we are taking FrameTicks from automatic plot, then we are taking labeled ticks as thicker GridLines and rest as thinner:

horizontalGridLines = 
leftTicks /. {x_?NumericQ, y_String, z__} :> {x, 
 [email protected]} /. {x_?NumericQ, y_?NumericQ, z__} :> {x, Black}

verticalGridLines = 
bottomTicks /. {x_?NumericQ, y_String, z__} :> {x, 
 [email protected]} /. {x_?NumericQ, y_?NumericQ, z__} :> {x, Black}

ListPlot[data, Frame -> True, 
GridLines -> {verticalGridLines, horizontalGridLines}]

Answer 5

Using elements from Kuba's great answer this is what I came up with:

addMajorMinorGridLines[plot_, majorStyle_, minorStyle_] := 
 Block[{leftTicks, bottomTicks, horizontalGridLines, 
   verticalGridLines},
  {leftTicks, bottomTicks} = AbsoluteOptions[plot, FrameTicks][[1, 2, {2, 1}]];
  horizontalGridLines = 
   leftTicks /. {x_?NumericQ, y_String, z__} :> {x, minorStyle} 
            /. {x_?NumericQ, y_?NumericQ, z__} :> {x, majorStyle};

  verticalGridLines = 
   bottomTicks /. {x_?NumericQ, y_String, z__} :> {x, minorStyle} 
               /. {x_?NumericQ, y_?NumericQ, z__} :> {x, majorStyle};
  Show[plot, GridLines -> {verticalGridLines, horizontalGridLines}]
  ]


plot = ListPlot[data, Frame -> True, GridLines -> Automatic, PlotStyle -> Red];
addMajorMinorGridLines[plot, Directive[Thick, Black], Directive[Thin, [email protected]]]

Answer 6

You just need:

GridLines -> {Range[0, 100, 5], Range[0, 5, 0.2]}

data = Table[{x, Log @ x}, {x, 100}];

ListPlot[data,
  Frame -> True,
  GridLines -> {Range[0, 100, 5], Range[0, 5, 0.2]},
  PlotRange -> {{0, 100}, {0, 5}}]