> the direction of movement of any individual covers a much smaller portion of their possible movement directionsNumber of adjacent bins versus fraction of unoccupied bins. The latter is what matters (ie density). Plus the physical and mental ability to rapidly and accurately select and maneuver into one of them. Plus (and this is really the crux of the thing) some sort of hardcoded behavior that makes the risk of conflicting independent choices vanishingly small.
A concrete example of that last part is TCAS. [0] That's what birds seem to have built in that other animals lack.
> it's much easier to form a "wave" in 2d, and this wave covers a much larger portion of their potential movement options
Not true. Waves in a 3D medium are themselves 3D. Go check out a fluid dynamics simulation.
I think what you might be trying to get at is dissipation within a volume. Cubed versus squared. But that's not the issue here. Dense pockets will occur from time to time in such a system regardless of dimensionality. The question is collision frequency for a given density. Birds are ~0 whereas humans (and most other animals) are really quite bad.
> birds don't explode upon most collisions
It's a fair point (and humorous) however irrelevant because my entire point there is that I've never seen birds collide to begin with. Even if they did explode it wouldn't matter.
Note that unlike human pilots autonomous aircraft are capable of forming dense swarms without colliding. (At least assuming the software was designed with that in mind.)
[0] https://en.wikipedia.org/wiki/Traffic_collision_avoidance_sy...