[Charlie Cogar]"I have 16 squares on-screen, 4 rows, 4 columns, and would like to build left-to-right as each square flips and the image changes. "
You could use the Card Wipe Effect. It isn't an easy effect for newbies. There are a LOT of parameters to tweak. There are a lot of cool things that are easily overlooked. For example, you could make a luminance map in Photoshop (or precomp one in AE) to control the card turning sequence. So you have to read up on it, you have to look for tutorials on it, and then you also have to just PLAY with it.
See what I mean about the basics?
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