How to choose the numbers shown on the axes of a plot in mathemetica?

Question

I have already checked all the examples and settings in the Mathematica documentation center, but couldn't find any example on how to choose the numbers that will be shown on the axes.

How do I change plot axis numbering like 2,4,6,.. to PI,2PI,3PI,...?

Answer 1

You can find an example here:

Ticks -> {{Pi, 2 Pi, 3 Pi}, {-1, 0, 1}}

Answer 2

Howard has already given the correct answer in the case where you want the labels Pi, 2 Pi etc to be at the values Pi, 2 Pi etc.

Sometimes you might want to use substitute tick labels at particular values, without rescaling data.

One of the other examples in the documentation shows how:

Plot[Sin[x], {x, 0, 10}, 
 Ticks -> {{{Pi, 180 \[Degree]}, {2 Pi, 360 \[Degree]}, {3 Pi, 
  540 \[Degree]}}, {-1, 1}}]

I have a suite of small custom functions for formatting Ticks the way I want them. This is probably too much information if you are just starting out, but it is worth knowing that you can use any number format and substitute anything into your ticks if desired.

myTickGrid[min_, max_, seg_, units_String, len_?NumericQ, 
  opts : OptionsPattern[]] := 
 With[{adj = OptionValue[UnitLabelShift], bls = OptionValue[BottomLabelShift]}, 
Table[{i, 
If[i == max, 
 DisplayForm[AdjustmentBox[Style[units, LineSpacing -> {0, 12}], 
   BoxBaselineShift ->  If[StringCount[units, "\n"] > 0, adj + 2, adj]]], 
 If[i == min, 
  DisplayForm@AdjustmentBox[Switch[i, _Integer, 
     NumberForm[i, DigitBlock -> 3, 
      NumberSeparator -> "\[ThinSpace]"], _, N[i]], 
    BoxBaselineShift -> bls], 
  Switch[i, _Integer, NumberForm[i, DigitBlock -> 3, 
    NumberSeparator -> "\[ThinSpace]"], _, N[i]]]], {len, 0}}, {i,
 If[Head[seg] === List, Union[{min, max}, seg], Range[min, max, seg]]}]]

And setting:

Options[myTickGrid] = {UnitLabelShift -> 1.3, BottomLabelShift -> 0}
SetOptions[myTickGrid, UnitLabelShift -> 1.3, BottomLabelShift -> 0]

Example:

Plot[Erfc[x], {x, -2, 2}, Frame -> True, 
 FrameTicks -> {myTickGrid[-2, 2, 1, "x", 0.02, UnitLabelShift -> 0], 
   myTickGrid[0, 2, {0.25, .5, 1, 1.8}, "Erfc(x)", 0.02]}]

Answer 3

Ticks also accepts a function, which will save you the trouble of listing the points manually or having to change the max value each time. Here's an example:

xTickFunc[min_, max_] := 
 Table[{i, i, 0.02}, {i, Ceiling[min/Pi] Pi, Floor[max/Pi] Pi, Pi}]
Plot[Sinc[x], {x, -5 Pi, 5 Pi}, Ticks -> {xTickFunc, Automatic}, 
 PlotRange -> All]

If you want more flexibility in customizing your ticks, you might want to look into LevelScheme.