flock of birds LO21791

Leo Minnigh (L.D.Minnigh@library.tudelft.nl)
Tue, 1 Jun 1999 11:44:24 +0200 (MET DST)

Replying to LO21774 --

Dear Arthur, dear LO'ers,

Arthur Battram made a very interesting contribution: the organisation
within a flock of birds, a school of fish, a cloud of insects, or a herd
of buffaloes. It seems that there is a strong tendency in natural life
where individuals show a strong will to self organise. The examples given
by Arthur are very instructive.

A couple of years ago I made analogies between thought movements (or
activities in the brain) and the flock of birds. At that time I was not
aware of theoretical backgrounds. Even now, my knowledge is very limited
and based on some popular scientific contributions in my news paper.
However, observing the movements of bird flocks is so fascinating that the
subject attracts my attention continuously.

Arthur mentioned the simple rules that Craig Reynolds has used in his
computer program. Craig was also facinated by the flock of birds which
made the strangest caprioles above the cemetery in Culver City. In 1987 he
formulated his three basic rules for his Boid computerprogram:

>1. It tried to maintain a minimum distance from other objects in the
>environment, including other boids.
>2. It tried to match velocities with boids in its neighbourhood.
>3. It tried to move toward the perceived centre of mass of boids in its

I like here to mention some other contributions to this phenomenon. This
is based on a article in my newspaper (NRC, 12 december 1998). The
scientific community made some progress, but still based on Reynolds'
There were some hesitations against the simple rules:

a. Do animals 'know' these rules? Are they realy following these rules?
b. In the computerprogram it is assumed that every individual behaves
according to these rules. It assumes ideal boids that react in a ideal
manner to impacts from outside the boid. It seems not unrealistic that in
nature there is at least one individual that reacts too late, or that it
forgets to ajust its speed. The birds in the neibourhood must react on
that not-ideal behaviour, which has its effects on the whole group.
c. The individuals at the front of the flock have difficulties (moving
inward to the central mass) with the general movement of the flock.

The first one who was thinking seriously on these hesitations was the
Hongarian physicist Tamas Vicsek. Originally, he was not so interested in
birds, but in bacteria. Colonies of bacteria, such as the bacillus
subtilis forms spontaneously circles. With a microscope and video camera
one can observe that these circles turn around. Some clockwise, others
anti clockwise. Vicsek compared this with magnetic fields. With iron
filings this was easily immitated. His assumptions even went further. Each
iron atom is a tiny magnet itself, that reacts on its neighbours; like the
birds in a flock, or the colony of bacteria. The computer simmulations of
Vicsek demonstrate that flocks of birds could also be described as a
'magnetic' model.
So far, Vicsek's theory differs not so much from Reynolds' rules. But
Vicsek hoped that he could deal with 'bad' behaviour in the flock with his
model. Magnetism only works if the temperature is not too high. It should
be below the Curie-temperature. Under the influence of heat, small
disturbences will occur in the magnetic characteristics. And Vicsek hoped
that he was able to cope with behavioural disturbences of individuals.
However, his own thoughts were the kill of his theory. The chaotic
behaviour with rising temperatures was so much that the total coherency of
the flock or colony was disturbed completely. So Vicsek's conclusion was
that flocks or herds could only exist if each individual behaves in a
perfect manner.

So, ther must be something else to cope with the problem of bad behaviour.
At the fall of 1994, two physicists of the IBM laboratory in New York,
John Toner and Yuhai Tu became intrigued by this problem. Nearly four
years later they published a paper in Physical Review E: 'Quantitative
theory of flocking' (october 1998). They used Vicsek's model of magnetic
interactions, but they broke with all former theories, because they didn't
look at the individuals. Toner and Tu consider the flock as a whole. The
physical analogy that they used is that of a liquid. Comparisons with
running water, for instance, don't consider either individual water
molecules. In the same way a flock of birds might behave as a quatity of
running water.
Again an analogy. But one with some extra's, since in this model for the
first time the effect of misbehaviour is taken into acount. To understand
this, one may think of a pan of water that is heated. Convection will
occur: hot water rises from the bottom to create space for cold water.
This is a most efficient way of coping with temperature differences. Local
disturbences are in this way 'smeared out' over the whole.And according to
Toner and Tu it is precisely this which occurs in bird flocks. In their
model, even with considerable margins of error (for instance if a couple
of birds are flying in the wrong direction, creating a local 'temperature
rise'), it does not lead to the split-up of the flock.

But all these theories give little attention to the function of animal
behaviour. Why prefer animals to migrate in groups? That is the critical
question, which most physicists seem to forget. The answer to this
question will possibly give more clues than all the physical theories.

It was the Brittish evolutionary biologist Hamilton who wrote some words
on this question. In his paper 'Geometry for the selfish herd' he proposed
that a group is better resistant against attacks from outside the group.
To save energy, preditors will always attack the nearestby individual. The
pray never knows however, where the attack will take place. So therefore
it is better for the pray to surround itself with other individuals of the
group. These latter are automatically closer to the presumed preditor. As
soon as a potential pray find itself on the side of the group, it will try
immediately to enter the group. It is as if the centre of the group
generates a strong attracting force. This 'force' is according to Hamilton
the cohesian of the group.

And here, we see again that the third rule of Reynolds comes into play.
Although it seems to me slightly different: an individual likes to
surround itself by other individuals.

Well Arthur, most of these other models are strongly related to the
original boids of Reynolds. I just liked to add some additional
information. Especially, the Toner-Tu theory (by considering the flock as
a whole, like a liquid) diserves attention.

Thank you to point us to a most interesting natural phenomena.

dr. Leo D. Minnigh
Library Technical University Delft
PO BOX 98, 2600 MG Delft, The Netherlands
Tel.: 31 15 2782226
Let your thoughts meander towards a sea of ideas.


Leo Minnigh <L.D.Minnigh@library.tudelft.nl>

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