Desperately Balanced

So I was watching a flock of birds today as I walked toward the train...

There was a large bunch of small, dark birds (for all you ornithologists out there) perched on a nearby roof and set of power lines. They would all fly up, do a circle or two, and then return to their resting positions. I noticed two things that were particularly interesting to me:

1) The birds at the tail end of the flock cut the corner. When the front end of the flock turned, then the rest of the flock would also change direction, but not simply by following. The birds right behind the front would follow the birds in front of them, but the birds at the very end would aim for where the front of the flock was. Just like cutting the corner in racing, they'd get a little bit ahead of the birds they'd previously been right behind. The further up in the flock you look, the more amount of following and the less cutting the corner.

Let's say that the flock is a line of birds numbered 1 through N, where 1 is the lead bird and N is the last bird in the flock. After bird 1 turns, we wait some unspecified small amount of time (X) and then try to characterize what the birds are doing. The tail bird (N) is now aiming straight at bird 1, "cutting the corner". Bird N-1 is partially following the bird ahead of it (N-2) and partially cutting the corner. And the ratio continues to shift, let's say that halfway through the flock (bird N/2) the bird is 1/2 following the bird ahead of it and 1/2 cutting the corner.

This explains the way that the flock shape "shifts" as it moves around.

2) The flock can be viewed as a "cloud" of birds, but when a flock is turning there appear to be areas of denser and emptier birdiness. The distribution of birds does not appear to be equal. Well, I don't think that's what is really happening. The natural assumption is that in the denser areas the birds are, say, 4 inches apart instead of 8 inches apart like the rest of the flock. But I think the inter-bird distance is the same throughout, what changes is the cross-section depth of the flock. The area that appears to be twice as dense is actually twice as wide, but since the flock doesn't lend itself to fine distance discrimination (e.g., it's hard for your eye to lock on and say "The closest bird is X far away and the farthest bird is Y far away", along the axis of eyesight) it just looks denser.

#1 and #2, of course, lead me to think that the 2d representation of a flock of birds we get drastically reduces the actual size and shape of the flock. I think that we view a flock as a somewhat regularly shaped oval of birds, but in fact it's probably this incredibly lumpy mass with lumps sticking out in all 3 dimensions. And most incredibly, that it's a shape with smooth contours - the lumps are rolling hills, not mesas.