Across the back. "X" shape. Attached to upper and lower shelves. Pinned in the middle.
Without a lot of searching or thought I see some aluminum bar stock at Home Despot.
http://www.homedepot.com/p/Everbilt...at-Bar-with-1-8-in-Thickness-802577/204273946
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Cut it to length. Drill holes at each end to screw into back of shelf. Smooth off exposed edge. Join in centre where the two pieces will cross with a short carriage bolt, nut, and washer.
Any similar material will do. Remember that what will add the rigidity with a cross brace is the fact that one member will be in tension when things start to twist, so the material need not be super great in compression.
Here's an old pic of the back of my gear racks (to illustrate the point). Pardon the clutter, but if you look closely, you will see a cross brace attached to each of the four sections. In my case, even with all the heavy gear, it's overkill since each shelf does a good job of bracing the one beside it - and because the shelves attach to mutual vertical columns etc. But the braces came with the shelves (and with a turntable on top of one shelf, any extra rigidity is a good thing) so I used them. (I've done the same with tall open-back bookcases that are much more similar in design to Chuck's shelves. With closed-back shelves, the backing becomes the cross brace.)
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With a little searching I could probably find other sources of suitable material to use for the bracing, but I think the aluminum bar stock would look good, and would certainly be effective - not to mention relatively inexpensive at the price shown in the above link.
Hope that answers the question.
Jeff