I cut in Final Cut and whenever I see this effect I always wonder how they do it. Watch until the 2.26 mark. Is there a tiling effect in final cut? How would they have done this, especially since its all so symmetrical and each circle has a different image in it.
It may NOT be Final Cut. They could be using After Effects or some other program, BUT. You can certainly pull this off with alot of tedious work and photoshop. Create your masks in photoshop import them into final cut and mix down the video clip with the mask. From that point you shouldn't hav any issues.
This is actually easier to do than you might first think, but it requires some lateral thinking. In Apple Motion, you can generate particles and map specific video to the particles. The particles can actually be any shape you want. If you look at the wider versions of the polkadot shot, there are only a few clips, each repeating. So you build the effect once for each source, and just copy-paste it and add the camera fly-out move in 3-d.
...and it's not too tough in After Effects, either.
I count about 8 distinct clips, and less if you like messing with color effects.
Each clip is in its own comp nested in a main comp with a circle mask applied, then duplicated and positioned as necessary.
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I would do it in AE or Motion rather than in Final Cut, because the overall quality can be better due to the virtual 3d camera moves you can apply to a high rez comp. You could build and keyframe all those tracks in the NLE timeline, but getting the camera pull-out effect would be harder.