# Drawing minor gridlines

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.

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Maybe could use similar methods in this question. – Silvia Apr 26 '13 at 8:43
Somewhat related: (54613) – Mr.Wizard Jul 1 '15 at 14:57

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}]]


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+1 for Prolog. Had a similar one. :) – Silvia Apr 26 '13 at 10:16
@Silvia so that's where I'd seen it before! :) Still, good practice to code these things up without looking sometimes... – cormullion Apr 26 '13 at 10:26
Good practice indeed :) – Silvia Apr 26 '13 at 10:35

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.

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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,
GrayLevel@.9} /. {x_?NumericQ, y_?NumericQ, z__} :> {x, Black}

verticalGridLines =
bottomTicks /. {x_?NumericQ, y_String, z__} :> {x,
GrayLevel@.9} /. {x_?NumericQ, y_?NumericQ, z__} :> {x, Black}

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

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AbsoluteOptions[plot, FrameTicks] won't work for some kinds of custom setting FrameTicks, say FrameTicks -> {{True, False}, {True, False}}. – Silvia Apr 26 '13 at 9:17
So do not set it for first plot. It is only to get values we need. But I agree that exact values of FrameTicks given by user in final plot may not match those GridLines in general case. – Kuba Apr 26 '13 at 9:19
Good call! (+1) – Silvia Apr 26 '13 at 9:22

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];

How will you deal with plot with non-integer ticks, say plot = ListPlot[data, Frame -> True, FrameTicks -> {{{-1, 0, 1}, None}, {{0, Pi, 2 Pi, 3 Pi}, None}}]? – Silvia Apr 26 '13 at 10:11
@Ajasja I would say re-constructing a ListGridPlot from Graphics and primitives. :) – Silvia Apr 26 '13 at 12:59