Be careful if you export to pdf a Row[] of graphic objects, because my experience on the Mac is that the size of the Row[] in the pdf will be smaller than expected almost by 30%. For example:

dsk = Graphics[{Circle[], Text["abc"]}, ImageSize -> 250]
Export[NotebookDirectory[] <> "dsk.pdf", dsk]
twoDsks = Row[{dsk, dsk}]
Export[NotebookDirectory[] <> "twodsks.pdf", twoDsks]

In the notebook, twoDsks is twice as wide as dsk, but twodsks.pdf is only 360 pt wide, when I would expect 500 pt. The fonts are also downscaled compared with dsk.pdf. Same problem with Column. I have already reported this issue to Tech Support.

Mark,

The problem seems to be the ImageResize[]. This operation breaks the sizing. I would report this to support. The difference seems to be that when you resize, it becomes an Image, The original is a Graphics object. If all the objects are Graphics objects it seems to work fine.

If you Rasterize the Images and specify the ImageSize, it works again:

jSet = ImageCrop[
   ImageResize[
    JuliaSetPlot[cPts[[1]], ColorFunction -> "RedGreenSplit", 
     Frame -> False, 
     ImageSize -> {{480}, {227}}], {{480}, {227}}], {480, 227}, 
   Padding -> "Fixed"];
jSetrr = Rasterize[jSet, ImageSize -> 480 ]
Column[{mSet, jSetrr}]

I think that when the Graphics gets converted to Image it must get the DPI changed.

I hope this helps.

Regards,

Neil

pts={{0.0667205, 0.863948}, {-0.921531, 0.248067}, {0.349526, 
  0.596629}, {-0.788888, 0.126608}}

They are points generated on the fly in a specific region of the Mandelbrot set. I later change them to complex numbers.

Thanks, Neil, for responding. I apparently did not make myself clear. The part of the output I'm having trouble with is the MandelbrotSetPlot object above the Julia set, which is an image. The Mandelbrot graphic was made with this code:

cPts= {0.0667205 + 0.863948 I, -0.921531 + 0.248067 I, 
 0.349526 + 0.596629 I, -0.788888 + 0.126608 I};

mSet=MandelbrotSetPlot[
 Epilog -> {PointSize[Large], Blue, Point[pts[[1]]], Red, 
   Point[pts[[2]]], Gray, Point[pts[[3]]], Black, Point[pts[[4]]]},
 PlotRange -> {{-1.53, .53}, {-1.1, 1.1}}, Frame -> False,
 ColorFunction -> (If[#3 == 1, GrayLevel[.85], White] &),
 ImageSize -> 300];

The Julia Set was made with this code:

jSet = ImageCrop[ImageResize[
    JuliaSetPlot[cPts[[1]],
     ColorFunction -> "RedGreenSplit",
     Frame -> False,
     ImageSize -> {{480}, {227}}], {{480}, {227}}],
   {480, 227}, Padding -> "Fixed"];

When I try to apply your solution to get what I really want, it shrinks both objects down to thumbnail size. (Don't be fooled by the large size of the screen shot, that's a result of taking a screen shot on a retina display, I think):

Mark,

I have had the same problem before. The issue is you must specify a size for EVERY plot (not necessarily a number, i.e. Medium works). Once they are fixed, the combination is trivial:

I don't have your plots so I randomly grabbed some examples from the documentation:

g1 = MandelbrotSetPlot[ImageSize -> 400]
g2 = JuliaSetPlot[-1, ImageSize -> 400]
g3 = ParametricPlot[{{2 r Cos[t], r Sin[t]}, {r Cos[t], 
    2 r Sin[t]}}, {t, 0, 2 Pi}, {r, 0, 1}, Mesh -> False, 
  ImageSize -> 200]
Row[{g3, Column[{g1, g2}]}]

This will have repeatable alignment and will respond well to grid/row/column spacing and adjustments. I like to pick a number for the size because everything lines up well. I hope this helps.

Neil