Want to follow along at home? Download the project files above (This includes the grid jpeg and an AE 4.1 project file).
Step 1:
Make a comp, and put your grid on the bottom layer.

Step 2:
Make a solid that's as wide as the comp, and a bit taller than one grid row. Call it Track Matte 1.

Step 3:
Position Track Matte 1 over the bottom row of the grid. Here's what it looks like:

Step 4:
Duplicate Track Matte 1 and rename it Track Matte 2. Reposition it to obscure the next row up. Repeat this step as many times as necessary.

Step 5:
Figure out how much time you want between dissolves. Let's say it's a second. Put Track Matte 1 at 1 second, Track Matte 2 at 2 seconds, and so on. Precomp all the Track Matte layers. Call it Dissolve Precomp.

Step 6:
Figure out how long you want the dissolves to last. Open Dissolve Precomp. Go to the in point of the bottom layer, Track Matte 1. Set an Opacity keyframe of 0% at the in point, and a 100% Opacity keyframe at the end of the dissolve. Copy these two opacity keyframes.
Step 7:
Go to in point on the next layer up, Track Matte 2. Set any old opacity keyframe. Paste in the Opacity keyframes from Track Matte 1. Repeat this step for all of your layers.. When you're done, your precomp will look like this:

Step 8:
Go back to the original comp. Go to your grid layer. Set the layer up so that it uses an Alpha Inverted Matte of the layer above it, which is Dissolve Precomp.

Step 9:
Do a Ram Preview and watch with satisfaction. Here's what it will look like:
Download the movie here (if you haven't already.)
Simple, huh? Learn to use track mattes. Love 'em. They can save you both time and money.
--Dave LaRonde
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Want to discuss this technique? Go to Creative COW's After Effects forum.