Applied Mathematics - Starlings in Flight

During early-spring, I saw a few European Starlings in our backyard at the bird feeder, but there have not been any in our backyard for months (1). At that time, I didn't realize that during the winter they are covered in white spots, and then turn dark in summer - the yellow beak was the characteristic that settled it for me that what I was looking at were starlings. These birds are native to most of temperate Europe and western Asia. Northeastern populations migrate south and west in winter to Europe, and further south to areas where it does not breed in the Iberian Peninsula and north Africa. Starlings have been introduced to Australia, New Zealand, North America, and South Africa - the first brought to North America by Shakespeare enthusiasts in the nineteenth century. European Starlings are now among the continent’s most numerous songbirds. For much of the year, they wheel through the sky and mob lawns in big, noisy flocks.

My son's Facebook page had a link to a flock of starlings in flight - complex amorphous formations that turned and folded into itself.

The video clip is dubbed over with music titled Forgive by an artist called Burial (2). I saw swarms of starlings in Oregon when out in newly established grass seed fields in early spring. They would land en mass in fields, and peck small holes in the soil between the grass seedlings. Though there was no way to plan ahead for making measurements to prove our hunch, we were pretty sure that the starlings were a natural control measure of gray garden slugs - another introduction into North America from Europe. The size of the flocks I saw in Oregon came nowhere close to the size of the one in the photograph to the side, or the video. A quick Google search turned up the abstract below from a scientific journal article that describes how the motion of birds in flight can be described mathematically in physical terms for particles, as well as information about Burial and his music. Using the Google translator, the English for the Russian title of the video is Birds Before the Tornado.

While watching the starling video, I remembered when growing up in the hot Central Valley of California, how in summer gnats would swarm together in their own distinctive fashion at dusk, while the air was perfectly still after a 105° F day. Across and down the road from my 

house, I would stir up the layer of dust on a short dirt road that led back to an old barn behind an abandoned farm house. As I shuffled my feet back and forth, the cloud would hover a foot above the ground below my knees like fog, while the gnats silently swam in unison above my head. I could stand there for what seemed like a long time - barefooted, only wearing short pants -  and squeeze the alkali dirt that felt like talcum power with my toes. That place off the asphalt was a refuge from the heat that still lingered in the pavement, as were the white painted lines - the only other cool place to walk back home where the shower was the next stop before my bed.

A computer simulation of gnats swarming can be found at this link.  The underlying assumptions used in the simulation are that gnats are always in flight motion - never stationary, and individual gnats will seek to stay within a given distance of the rest of the swarm. Given these assumptions it is natural that they will tend to fly in circular patterns around a common center. The simulation allows for gusts of wind to originate from the point of the mouse click and blow outward. Each gnat is affected by the gust in inverse proportion to its distance from the origin, and in a direction away from the origin. As I mentioned above, when I watched the swarms of gnats, the evenings were still - no wind at all, except for my breath that I held when the swarm came near me so I wouldn't swallow them.
___________________________________

Flocks, Herds, and Schools: A Distributed Behavioral Model
  
Abstract. The aggregate motion of a flock of birds, a herd of land animals, or a school of fish is a beautiful and familiar part of the natural world. But this type of complex motion is rarely seen in computer animation. This paper explores an approach based on simulation as an alternative to scripting the paths of each bird

individually. The simulated flock is an elaboration of a particle system, with the simulated birds being the particles. The aggregate motion of the simulated flock is created by a distributed behavioral model much like that at work in a natural flock; the birds choose their own course. Each simulated bird is implemented as an independent actor that navigates according to its local perception of the dynamic environment, the laws of simulated physics that rule its motion, and a set of behaviors programmed into it by the "animator." The aggregate motion of the simulated flock is the result of the dense interaction of the relatively simple behaviors of the individual simulated birds. (3)
___________________________________

(1) However, I have seen starlings in our neighbors' yards across the street from our front yard. Sometime I need to begin doing an inventory of birds in front, because I suspect there may be other species present there. Our backyard, and those of our next door neighbors have virtually no turf, and are heavily wooded. In contrast, the neighboring yards up and down on the street side in front of our house are dominated by turf, and of course the open area caused by the road.

(2) Burial’s self-titled debut album was released May 15, 2006. While the genre is usually filed under dubstep, ambient and garage often get used to describe the album. The album was very unique and fresh when first released and quickly  Burial rose to the top of the dubstep scene. At that time, his real name was not known and he released his music simply using Burial - nothing like a little drama and mystery to stir up interest,  even though the artist wasn't looking for any.

(3) Reynolds, C. W. (1987) Flocks, Herds, and Schools: A Distributed Behavioral Model, in Computer Graphics, 21(4) (SIGGRAPH '87 Conference Proceedings) pages 25-34.