I think Matt Newsome was the one who told me how the mills do that to make the "Shadow tartans".

Basically, you have the same color wool, but 1 set of strands are spun one direction (clockwise) and 1 set is spun counterclockwise. When you weave them, you change the set of strands from clockwise to counter for a few threads and then back again. Weave the whole pattern this way.

When you look at the tartan in DIRECT light, it's tough to tell there's a pattern there. When you look at it on an angle, the light reflects differently off of the clockwise than it does the counterclockwise, so the tartan appears.

Neat, huh?