Set plot axes to be positive in both directions

Question

How can I set the axes of a plot to be positive in both directions, along the lines of this image?

I've looked through some questions on how to change the axis direction (here, here and here) but they obviously don't fully answer my problem, and I've not got further than the options given in those questions. Presumably the answer lies in the Ticks function, but I'm not sure how to implement it.

Edit

I am aware of custom labels and tick positions from the documentation, but am curious about a more automatic way to do it. I was thinking along the lines of the accepted answer to How to change the axes' origin and direction?, where this is given as a way of reversing the axis direction.

x = Sin /@ Range[0, 2 π, 0.1];
ListPlot[-x, Ticks -> {Automatic, Function[{xmin, xmax}, 
    Table[{i, -i, {0.02, 0}}, {i, N@FindDivisions[{xmin, xmax}, 10]}]]}]

Is there a similar method I could use based on xmin, xmax and N@FindDivisions[], or is custom labels the way forward?

Answer 1

Here is one way to do what you are asking for.

tickSpec[i_Integer] /; Mod[i, 10] == 0 := {i, Abs[i]}
tickSpec[i_Integer] := {i, ""}
With[{nTicks = 13}, 
  ticks[xmin_, xmax_] := Table[tickSpec @ i, {i, FindDivisions[{xmin, xmax}, nTicks]}]]

Plot[{}, {x, -30, 30},
  PlotRange -> {Full, {-30, 30}},
  AspectRatio -> Automatic,
  Frame -> True,
  Axes -> False,
  FrameTicks -> {{ticks, None}, {ticks, None}}]