Export to PDF - scaling grids of plots and text size

Question

Sometimes I have occasion to make big grids of plots. As a toy example:

lots = GraphicsGrid[
Table[With[{a = RandomInteger[{1, 17}], b = RandomInteger[{1, 17}]},
  ParametricPlot[Sin[t^2] { Cos[a t], Sin[b t]}, {t, 0, 2 \[Pi]}, 
     PlotRange->{{-1, 1}, {-1, 1}}, Frame->True]], {15}, {7}]]

Which is a 7 by 15 grid of plots. For ease of viewing, printing and wider distribution; I will often export this to a pdf.

Export["lots.pdf", lots]

This results in a completely rubbish view. You get giant text labels and a graph too small to even see. This can be rectified by fiddling with the scaling:

Export["lots.pdf", lots, ImageSize->2000]

Now the text labels are more in proportion with the graph size. But how do I know what ImageSize should be? It depends on how big your graphic grid is, but I know not the voodoo required to get a good result.

Alternatively, how can I get the text size to be proportional to the graph size?

Answer 1

You should investigate in the Scaled function:

lots = GraphicsGrid[
   Table[With[{a = RandomInteger[{1, 17}], 
      b = RandomInteger[{1, 17}]}, 
     ParametricPlot[Sin[t^2] {Cos[a t], Sin[b t]}, {t, 0, 2 \[Pi]}, 
      PlotRange -> {{-1, 1}, {-1, 1}}, Frame -> True, 
      ImageSize -> Scaled[1]]], {15}, {7}]];
Export["lots.pdf", lots]

Answer 2

Why this happens?

The reason for this behaviour is that Mathematica works with two kinds of units:

• plot coordinates---the same thing you see on the axes

• offset coordinates---these are in printer's points

Plot coordinates scale with the figure: if you print the figure (or export to PDF) at twice the size, objects specified on plot coordinates double in size. But offset coordinates do not scale: if the font size is 10 pt, it will be 10 pt no matter how big the figure.

The default graphics size is 360 pt wide (12.7 cm). When you specify the size using ImageSize, it is also understood in points. When using a 10 pt font size and having seven figures in a row, this'll make the tick labels pretty crowded.

This behaviour can cause problems (especially because the space left for the tick labels is also determined in offset coordinates), but can be very useful too when one needs to ensure that the fonts of the exported figure are at the correct size (e.g. 8 pt and no smaller).

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Possible solutions

Now that you understand why this happens, you can make a good judgement about what ImageSize to choose when exporting, and what font size to use.

Sometimes it's desirable to have the text scale with the figure: Mathematica has a third kind of unit for this, Scaled units (as @halirutan described). This lets you specify e.g. the font size as a fraction of the plot range width:

Plot[Sin[x], {x, 0, 10}, BaseStyle -> {FontSize -> Scaled[0.04]}]

When you resize this, the text scales with the figure.

For completeness, there is also a fourth type of unit, ImageScaled. This lets you specify sizes as a fraction of the full figure width, including the space left for tick labels (not only the plot range---i.e. the area inside the frame).

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I find that this multitude of unit types is useful sometimes (when exporting figures to size), but at other times it makes it really difficult to achieve what I want, especially when trying to make tightly packed plot grids and specify the full size of the grid. Related: Sizing cells in a GraphicsGrid/GraphicsRow