...anything from manually arranging a ton of solids to creating a shape layer array with the repeater to using effects like Card Dance. Entirely depends on what kind of animation you plan on doing.
Here's is everything that I did to both layers in my example.
That is only one of about 10 ways that I can think of to recreate the effect. It's all about layering. The other mosaic transitions could be created using similar techniques, then the two comps could be combined in a master comp to transition from one effect to the next. I would not do both in one comp.
I added a time*360 expression to the fractal noise evolution to get the grid to animate then rendered a preview. This is what the animation looks like:
It's even better with sound...
This will get you started.