HOWEVER: If you have an image manipulation package that allows you to 'stretch' around the images a bit, using the flipped images per above and then fooling around with the center (without messing with the edges) may give a decent-ish result.
For simplicity, let us only discuss the X coordinate case.
(Sadly, we only get a 0,5x0,5 piece of patternmatched wood out of a 1x1 piece of original wood if one uses this exact setup, but...)
At the left edge of the output image, do NOT place the left edge of the scanned wood! Instead the middle (X = 0.5 in input wood) are used, so we go from (left of output) = (0.5X of input) and (right of output) = (1.0 X of input). However, we cross-dissolve this with another image, who has (left of output = 0.0 X of input) and (right of output) = (0.5 X of input).
This gives us the exact 0.5 condition at the edges, with a smooth cross dissolve over the actual texture. Works quite OK for wood.
I myself use all three with increasingly good results going from the first idea listed here to the last. Of course, an increasing workload is imposed for each step down the list too :-)
The best result is the handmade one, even if the cross-dissolved can look good too. However, it can appear a bit blurrish in the 50%-50% regions, and they can sometimes show as "blurred crosses" on the surfaces.
Perhaps an ideal one would be the cross dissolve with some kind of triangulation morph of the image so one could assemble them to look good near the middle so the crossdissolve won't look blurred.