(~) ~ Computer Graphics, Volume 21, Number 4, July 1987
Flocks, Herds, and Schools: A Distributed Behavioral Model
Craig W. Reynolds
Symbolics Graphics Division
1401 Westwood Boulevard
Los Angeles, California 90024
(Electronic mail: cwr@Symbolics.COM)
Abstract
The aggregate motion of a flock of birds, a herd of land ani-
mals, 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 natu-
ral flock; the birds choose their own course. Each simulated
bird is implemented as an independent actor that navigates ac-
cording 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 aggre-
gate motion of the simulated flock is the result of the dense
interaction of the relatively simple behaviors of the individual
simulated birds.
Categories and Subject Descriptors: 1.2.10 [Artificial Intelli-
gence]: Vision and Scene Understanding; 1.3.5 [Computer
Graphics]: Computational Geometry and Object Modeling;
1.3.7 [Computer Graphics]: Three-Dimensional Graphics and
Realism--Animation; 1.6.3 [Simulation and Modeling[: Appli-
cations.
General Terms: Algorithms, design.
Additional Key Words, and Phrases: flock, herd, school, bird,
fish, aggregate motion, particle system, actor, flight, behav-
ioral animation, constraints, path planning.
Introduction
The motion of a flock of birds is one of nature's delights.
Flocks and related synchronized group behaviors such as
schools of fish or herds of land animals are both beautiful to
watch and intriguing to contemplate. A flock* exhibits many
contrasts. It is made up of discrete birds yet overall motion
seems fluid; it is simple in concept yet is so visually complex,
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it seems randomly arrayed and yet is magnificently synchro-
nized. Perhaps most puzzling is the strong impression of inten-
tional, centralized control. Yet all evidence indicates that flock
motion must be merely the aggregate result of the actions of
individual animals, each acting solely on the basis of its own
local perception of the world.
One area of interest within computer animation is the de-
scription and control of all types of motion. Computer anima-
tors seek both to invent wholly new types of abstract motion
and to duplicate (or make variations on) the motions found in
the real world. At first glance, producing an animated, com-
puter graphic portrayal of a flock of birds presents significant
difficulties. Scripting the path of a large number of individual
objects using traditional computer animation techniques would
be tedious. Given the complex paths that birds follow, it
is
doubtful this specification could be made without error. Even
if a reasonable number of suitable paths could be described, it
is unlikely that the constraints of flock motion could be main-
tained (for example, preventing collisions between all birds at
each frame). Finally, a flock scripted in this manner would be
hard to edit (for example, to alter the course of all birds for a
portion of the animation). It is not impossible to script flock
motion, but a better approach is needed for efficient, robust,
and believable animation of flocks and related group motions.
This paper describes one such approach. This approach
assumes a flock is simply the result of the interaction between
the behaviors of individual birds. To simulate a flock we simu-
late the behavior of an individual bird (or at least that portion
of the bird's behavior that allows it to participate in a flock). To
support this behavioral "control structure" we must also simu-
late portions of the bird's perceptual mechanisms and aspects
of the physics of aerodynamic flight. If this simulated bird
model has the correct flock-member behavior, all that should
be required to create a simulated flock is to create some in-
stances of the simulated bird model and allow them to inter-
act. **
Some experiments with this sort of simulated flock are de-
scribed in more detail in the remainder of this paper. The suc-
*In this paperflock refers generically to a group of objects that
exhibit this general class of polarized, noncolliding, aggregate
motion. The term polarization is from zoology, meaning align-
ment of animal groups. English is rich with terms for groups of
animals; for a charming and literate discussion of such words see
An Exultation of Larks. [16]
**This paper refers to these simulated bird-like, "bird-old" objects
generically as "boids" even when they represent other sorts of
creatures such as schooling fish.
25
~ SIGGRAPH '87, Anaheim, July 27-31, 1987
cess and validity of these simulations is difficult to measure
objectively. They do seem to agree well with certain criteria
[25] and some statistical properties [23] of natural flocks and
schools which have been reported by the zoological and behav-
ioral sciences. Perhaps more significantly, many people who
view these animated flocks immediately recognize them as a
representation of a natural flock, and find them similarly de-
lightful to watch.
Our
Forefiocks
The computer graphics community has seen simulated bird
flocks before. The Electronic Theater at SIGGRAPH '85 pre-
sented a piece labeled "motion studies for a work in progress
entitled 'Eurythmy'" [4] by Susan Amkraut, Michael Girard,
and George Karl from the Computer Graphics Research Group
of Ohio State University. In the film, a flock of birds flies up
out of a minaret and, passing between a series of columns, flies
down into a lazy spiral around a courtyard. All the while the
birds slowly flap their wings and avoid collision with their
flockmates.
That animation was produced using a technique completely
unlike the one described in this paper and apparently not spe-
cifically intended for flock modeling. But the underlying con-
cept is useful and interesting in its own right. The following
overview is based on unpublished communications [3]. The
software is informally called "the force field animation sys-
tem." Force fields are defined by a 3 x 3 matrix operator that
transform from a point in space (where an object is located) to
an acceleration vector; the birds trace paths along the "phase
portrait" of the force field. There are "rejection forces"
around each bird and around static objects. The force field
associated with each object has a bounding box, so object in-
teractions can be culled according to bounding box tests. An
incremental, linear time algorithm finds bounding box inter-
sections. The "animator" defines the space field(s) and sets
the initial positions, orientations, and velocities of objects. The
rest of the simulation is automatic.
Karl Sims of MIT's Media Lab has constructed some be-
haviorally controlled animation of groups of moving objects
(spaceships, inchworms, and quadrupeds), but they are not or-
ganized as flocks [35]. Another author kept suggesting [28,
29, 30] implementing a flock simulation based on a distributed
behavioral model.
Particle Systems
The simulated flock described here is closely related to
parti-
cle systems
[27], which are used to represent dynamic "fuzzy
objects" having irregular and complex shapes. Particle systems
have been used to model fire, smoke, clouds, and more re-
cently, the spray and foam of ocean waves [27]. Particle sys-
tems are collections of large numbers of individual particles,
each having its own behavior. Particles are created, age, and
die off. During their life they have certain behaviors that can
alter the particle's own state, which consists of
color, opacity,
location,
and
velocity.
Underlying the bold flock model is a slight generalization
of particle systems. In what might be called a "subobject sys-
tem," Reeves's dot-like particles are replaced by an entire geo-
metrical object consisting of a full local coordinate system and
a reference tO a geometrical shape model. The use of shapes
instead of dots is visually significant, but the more fundamen-
tal difference is that individual subobjects have a more com-
plex geometrical state: they now have orientation.
Another difference between bold flocks and particle sys-
tems is not as well defined. The behavior of boids is generally
more complex than the behaviors for particles as described in
the literature. The present bold behavior model might be about
one or two orders of magnitude more complex than typical
particle behavior. However this is a difference of degree, not of
kind. And neither simulated behavior is nearly as complex as
that of a real bird.
Also, as presented, particles in particle systems do not in-
teract with one another, although this is not ruled out by defini-
tion. But birds and hence boids must interact strongly in
order
to flock correctly. Bold behavior is dependent not only on
in-
ternal state
but also on
external state.
Actors and Distributed Systems
The behavioral model that controls the boid's flight and flock-
ing is complicated enough that rather than use an
ad hoc
ap-
proach, it is worthwhile to pursue the most appropriate formal
computational model. The behaviors will be represented as
rules or programs in some sense, and the internal state of each
bold must be held in some sort of data structure. It is conve-
nient to encapsulate these behaviors and state as an
object,
in
the sense of object-oriented programming systems [10, 11,
21]. Each
instance
of these objects needs a computational
process
to apply the behavioral programs to the internal data.
The computational abstraction that combines process, proce-
dure, and state is called an
actor
[12, 26, 2]. An actor is
essentially a virtual computer that communicates with other
virtual computers by
passing messages.
The actor model has
been proposed as a natural structure for animation control by
several authors [28, 13, 29, 18]. It seems particularly apt for
situations involving interacting characters and behavior simula-
tion. In the literature of parallel and distributed computer sys-
tems, flocks and schools are given as examples of robust
self-organizing distributed systems [15].
Behavioral Animation
Traditional hand-drawn eel animation was produced with a me-
dium that was completely inert. Traditional computer anima-
tion uses an active medium (computers running graphics
software), but most animation systems do not make much use
of the computer's ability to automate motion design. Using
different tools, contemporary computer animators work at al-
most the same low level of abstraction as do eel animators.
They tell their story by directly describing the motion of their
characters. Shortcuts exist in both media; it is common for
computer animators and eel animators to use helpers to inter-
polate between specified keyframes. But little progress has
been made in automating motion description; it is up to the
animator to translate the nuances of emotion and characteriza-
tion into the motions that the character performs. The animator
cannot simply tell the character to "act happy" but must tedi-
ously specify the motion that conveys happiness.
Typical computer animation models only the shape and
physical properties of the characters, whereas
behavioral
or
character-based
animation seeks to model the behavior of the
character. The goal is for such simulated characters to handle
many of the details of their actions, and hence their motions.
These
behaviors
include a whole range of activities from sim-
ple path planning to complex "emotional" interactions be-
tween characters. The construction of behavioral animation
characters has attracted many researchers [19, 21, 13, 14, 29,
26
(~ ~ Computer Graphics, Volume 21, Number 4, July 1987
ii llll ii
30, 41, 40], but it is still a young field in which more work is
needed.
Because of the detached nature of the control, the person
who creates animation with character simulation might not
strictly be an
animator.
Traditionally, the animator is directly
responsible for all motion in animation production [40]. It
might be more proper to call the person who directs animation
via simulated characters a
meta-animator,
since the animator is
less a designer of motion and more a designer of behavior.
These behaviors, when acted out by the simulated characters,
lead indirectly to the final action. Thus the animator's job be-
comes somewhat like that of a theatrical director: the charac-
ter's performance is the indirect result of the director's
instructions to the actor. One of the charming aspects of
the
work reported here is not knowing how a simulation is going to
proceed from the specified behaviors and initial conditions;
there are many unexpected, pleasant surprises. On the other
hand, this charm starts to wear thin as deadlines approach and
the unexpected annoyances pop up. This author has spent a lot
of time recently trying to get uncooperative flocks to move as
intended ("these darn boids seem to have a mind of their
own! ").
speed. A minimum speed
can also be specified but defaults to
zero. A
maximum acceleration,
expressed as a fraction of the
maximum speed, is used to truncate over-anxious requests for
acceleration, hence providing for smooth changes of speed and
heading. This is a simple model of a creature with a finite
amount of available energy.
Many physical forces are not supported in the current bold
model.
Gravity
is modeled but used only to define banking
behavior. It is defined procedurally to allow the construction of
arbitrarily shaped fields. If each bold was accelerated by grav-
ity each frame, it would tend to fall unless gravity was coun-
tered by
lift
or
buoyancy.
Buoyancy is aligned against gravity,
but aerodynamic lift is aligned with the boid's local "up" di-
rection and related to velocity. This level of modeling leads to
effects like normally level flight, going faster when flying
down (or slower up), and the "stall" maneuver. The speed
limit parameter could be more realistically modeled as a fric-
tional
drag,
a backward pointing force related to velocity. In
the current model steering is done by directing the available
thrust
in the appropriate direction. It would be more realistic to
separately model the
tangential
thrusting forces and the
lateral
steering forces, since they normally have different magnitudes.
Geometric Flight
A fundamental part of the bold model is the geometric ability
to
fly.
The motion of the members of a simulated school or
herd can be considered a type of "flying" by glossing over the
considerable intricacies of wing, fin, and leg motion (and in
the case of herds, by restricting freedom of motion in the third
dimension). In this paper the term
geometric flight
refers to a
certain type of motion along a path: a dynamic, incremental,
rigid geometrical transformation of an object, moving along
and tangent to a 3D curve. While the motion is rigid, the ob-
ject's underlying geometric model is free to articulate or
change shape within this "flying coordinate system." Unlike
more typical animated motion along predefined spline curves,
the shape of a flight path is not specified in advance.
Geometric flight is based on incremental translations along
the objecrs "forward direction" its local positive Z axis.
These translations are intermixed with
steering--rotations
about the local X and Y axes
(pitch
and
yaw),
which realign
the global orientation of the local Z axis. In real flight, turning
and moving happen continuously and simultaneously. Incre-
mental geometric flight is a discrete approximation of this;
small linear motions model a continuous curved path. In ani-
mation the motion must increment at least once per frame.
Running the simulation at a higher rate can reduce the discrete
sampling error of the flight model and refine the shape of mo-
tion blur patterns.
Flight modeling makes extensive use of the object's own
coordinate system. Local space represents the "boid's eye
view;" it implies measuring things relative to the boid's own
position and orientation. In Cartesian terms, the lefl/right axis
is X, up/down is Y, and forward/back is Z. The conversion of
geometric data between the local and global reference frames is
handled by the geometric operators
localize
and
globalize.
It is
convenient to use a local scale so that the unit of length of the
coordinate system is one
body length.
Biologists routinely
specify flock and school statistics in terms of body lengths.
Geometric flight models conservation of momentum. An
object in flight tends to stay in flight. There is a simple model
of viscous speed damping, so even if the bold continually ac-
celerates in one direction, it will not exceed a certain
maximum
Banking
Geometric flight relates translation, pitch, and yaw, but does
not constrain
roll,
the rotation about the local Z axis. This
degree of freedom is used for
banking--rolling
the object to
align the local Y axis with the (local XY component of the
total) acceleration acting upon it. Normally banking is based
on the lateral component of the acceleration, but the tangential
component can be used for certain applications. The lateral
components are from steering and gravity. In straight flight
there is no radial force, so the gravitational term dominates and
banking aligns the object's -Y axis with "gravitational down"
direction. When turning, the radial component grows larger
and the "accelerational down" direction swings outward, like a
pendulum hanging from the flying object. The magnitude of
the turning acceleration varies directly with the object's veloc-
ity and with the curvature of its path (so inversely with the
radius of its turn). The limiting case of infinite velocity resem-
bles banking behavior in the absence of gravity. In these cases
the local + Y (up) direction points directly at the center of
curvature defined by the current turn.
Direclion
of
Ftighl
4
Bank
Figure 1.
With correct banking (what pilots call a
coordinated turn)
the object's local space remains aligned with the "perceptual"
or "accelerational" coordinate system. This has several advan-
tages: it simplifies the bird's (or pilot's) orientation task, it
27
~/~ SIGGRAPH '87, Anaheim, July 27-31, 1987
keeps the lift from the airfoils of the wings pointed in the most
efficient direction ("accelerational up"), it keeps the passen-
gers' coffee in their cups, and most importantly for animation,
it makes the flying boid fit the viewer's expectation of how
flying objects should move and orient themselves. On the other
hand, realism is not always the goal in animation. By simply
reversing the angle of bank we obtain a cartoony motion that
looks like the object is being flung outward by the centrifugal
force of the turn.
Boids and Turtles
The incremental mixing of forward translations and local rota-
tions that underlies geometric flight is the basis of "turtle
graphics" in the programming language Logo [5]. Logo was
first used as an educational tool to allow children to learn ex-
perimentally about geometry, arithmetic, and programming
[22]. The Logo turtle was originally a little mechanical robot
that crawled around on large sheets of paper laid on the class-
room floor, drawing graphic figures by dragging a felt tip
marker along the paper as it moved. Abstract turtle geometry is
a system based on the frame of reference of the turtle, an ob-
ject that unites position and heading. Under program control
the Logo turtle could move forward or back from its current
position, turn left or right from its current heading, or put the
pen up or down on the paper. The turtle geometry has been
extended from the plane onto arbitrary manifolds and into 3D
space [1]. These "3d turtles" and their paths are exactly equiv-
alent to the boid objects and their flight paths.
Natural Flocks, Herds, and Schools
"... and the thousands of fishes moved as a huge beast, piercing
the water. They appeared united, inexorably bound to a common
fate. How comes this unity?"
--Anonymous, 17th century (from Shaw)
For a bird to participate in a flock, it must have behaviors
that allow it to coordinate its movements with those of its
flockmates. These behaviors are not particularly unique; all
creatures have them to some degree. Natural flocks seem to
consist of two balanced, opposing behaviors: a desire to stay
close to the flock and a desire to avoid collisions within the
flock [34]. It is clear why an individual bird wants to avoid
collisions with its flockrnates. But why do birds seem to seek
out the airborne equivalent of a nasty traffic jam? The basic
urge to join a flock seems to be the result of evolutionary
pressure from several factors: protection from predators, statis-
tically improving survival of the (shared) gene pool from at-
tacks from predators, profiting from a larger effective search
pattern in the quest for food, and advantages for social and
mating activities [33].
There is no evidence that the complexity of natural flocks
is bounded in any way. Flocks do not become "full" or "over-
loaded" as new birds join. When herring migrate toward their
spawning grounds, they run in schools extending as long as 17
miles and containing millions of fish [32]. Natural flocks seem
to operate in exactly the same fashion over a huge range of
flock populations. It does not seem that an individual bird can
be paying much attention to each and every one of its flock-
mates. But in a huge flock spread over vast distances, an indi-
vidual bird must have a localized and filtered perception of the
rest of the flock. A bird might be aware of three categories:
itself, its two or three nearest neighbors, and the rest of the
flock [23].
These speculations about the "computational complexity"
of flocking are meant to suggest that birds can flock with any
number of flockmates because they are using what would be
called in formal computer science a constant time algorithm.
That is, the amount of "thinking" that a bird has to do in order
to flock must be largely independent of the number of birds in
the flock. Otherwise we would expect to see a sha W upper
bound on the size of natural flocks when the individual birds
became overloaded by the complexity of their navigation task.
This has not been observed in nature.
Contrast the insensitivity to complexity of real flocks with
the situation for the simulated flocks described below. The
complexity of the flocking algorithm described is basically
O(N2). That is, the work required to run the algorithm grows
as the square of the flock's population. We definitely
do see
an
upper bound on the size of simulated flocks implemented as
described here. Some techniques to address this performance
issue are discussed in the section Algorithmic Considerations.
Simulated Flocks
To build a simulated flock, we start with a boid model that
supports geometric flight. We add behaviors that correspond to
the opposing forces of collision avoidance and the urge to join
the flock. Stated briefly as rules, and in order of decreasing
precedence, the behaviors that lead to simulated flocking are:
1. Collision Avoidance: avoid collisions with nearby
flockmates
2. Velocity Matching: attempt to match velocity with nearby
flockmates
3. Flock Centering: attempt to stay close to nearby flockmates
Velocity is a vector quantity, referring to the combination of
heading and speed. The manner in which the results from each
of these behaviors is reconciled and combined is significant
and is discussed in more detail later. Similarly, the meaning
nearby in these rules is key to the flocking process. This is also
discussed in more detail later, but generally one boid's aware-
ness of another is based on the distance and direction of the
offset vector between them.
Static collision avoidance and dynamic velocity matching
are complementary. Together they ensure that the members of a
simulated flock are free to fly within the crowded skies of the
flock's interior without running into one another. Collision
avoidance is the urge to steer away from an imminent impact.
Static collision avoidance is based on the relative position of
the flockmates and ignores their velocity. Conversely, velocity
matching is based only on velocity and ignores position. It is a
predictive version of collision avoidance: if the boid does a
good job of matching velocity with its neighbors, it is unlikely
that it will collide with any of them any time soon. With veloc-
ity matching, separations between boids remains approximately
invariant with respect to ongoing geometric flight. Static colli-
sion avoidance serves to establish the minimum required sepa-
ration distance; velocity matching tends to maintain it.
Flock centering makes a boid want to be near the center of
the flock. Because each boid has a localized perception of the
world, "center of the flock" actually means the center of the
nearby flockmates. Flock centering causes the boid to fly in a
direction that moves it closer to the centroid of the nearby
boids. If a boid is deep inside a flock, the population density in
its neighborhood is roughly homogeneous; the boid density is
28
~' Computer Graphics, Volume 21, Number 4, July 1987
approximately the same in all directions. In this case, the cem
troid of the neighborhood boids is approximately at the center
of the neighborhood, so the flock centering urge is small. But
if a boid is on the boundary of the flock, its neighboring boids
are on one side. The centroid of the neighborhood boids is
displaced from the center of the neighborhood toward the body
of the flock. Here the flock centering urge is stronger and the
flight path will be deflected somewhat toward the local flock
center.
Real flocks sometimes split apart to go around an obstacle.
To be realistic, the simulated flock model must also have this
ability. Flock centering correctly allows simulated flocks to
bifurcate. As long as an individual boid can stay close to its
nearby neighbors, it does not care if the rest of the flock turns
away. More simplistic models proposed for flock organization
(such as a
central force
model or a
follow the designated leader
model) do not allow splits.
The flock model presented here is actually a better model
of a school or a herd than a flock. Fish in murky water (and
land animals with their inability to see past their herdmates)
have a limited, short-range perception of their environment.
Birds, especially those on the outside of a flock, have excellent
long-range "visual perception." Presumably this allows widely
separated flocks to join together. If the flock centering urge
was completely localized, when two flocks got a certain dis-
tance apart they would ignore each other. Long-range vision
seems to play a part in the incredibly rapid propagation of a
"maneuver wave" through a flock of birds. It has been shown
that the speed of propagation of this wavefront reaches three
times the speed implied by the measured startle reaction time
of the individual birds. The explanation advanced by Wayne
Ports is that the birds perceive the motion of the oncoming
"maneuver wave" and time their own turn to match it [25].
Potts refers to this as the "chorus line" hypothesis.
Arbitrating Independent Behaviors
The three behavioral urges associated with flocking (and others
to be discussed below) each produce an isolated suggestion
about which way to steer the boid. These are expressed as
acceleration requests.
Each behavior says: "if I were in
charge, I would accelerate in
that
direction." The acceleration
request is in terms of a 3D vector that, by system convention,
is truncated to unit magnitude or less. Each behavior has sev-
eral parameters that control its function; one is a "strength," a
fractional value between zero and one that can further attenuate
the acceleration request. It is up to the
navigation module
of
the boid brain to collect all relevant acceleration requests and
then determine a single behaviorally desired acceleration. It
must combine, prioritize, and arbitrate between potentially
conflicting urges. The
pilot module
takes the acceleration de-
sired by the navigation module and passes it to the
flight mod-
ule,
which attempts to fly in that direction.
The easiest way to combine acceleration requests is to aver-
age them. Because of the included "strength" factors, this is
actually a weighted average. The relative strength of one be-
havior to another can be defined this way, but it is a precarious
interrelationship that is difficult to adjust. An early version of
the boid model showed that navigation by simple weighted av-
eraging of acceleration requests works "pretty well." A bold
that chooses its course this way will fly a reasonable course
under typical conditions. But in critical situations, such as po-
tential collision with obstacles, conflicts must be resolved in a
timely manner. During high-speed flight, hesitation or indeci-
sion is the wrong response to a brick wall dead ahead.
The main cause of indecision is that each behavior might
be shouting advice about which way to turn to avoid disaster,
but if those acceleration requests happen to lie in approxi-
mately opposite directions, they will largely cancel out under a
simple weighted averaging scheme. The boid would make a
very small turn and so continue in the same direction, perhaps
to crash into the obstacle. Even when the urges do not cancel
out, averaging leads to other problems. Consider flying over a
gridwork of city streets between the skyscrapers; while "'fly
north" or "fly east" might be good ideas, it would be a bad
idea to combine them as "fly northeast."
Techniques from artificial intelligence, such as expert sys-
tems, can be used to arbitrate conflicting opinions. However, a
less complex approach is taken in the current implementation.
Prioritized acceleration allocation
is based on a strict priority
ordering of all component behaviors, hence of the consider-
ation of their acceleration requests. (This ordering can change
to suit dynamic conditions.) The acceleration requests are con-
sidered in priority order and added into an accumulator. The
magnitude
of each request is measured and added into another
accumulator. This process continues until the sum of the accu-
mulated magnitudes gets larger than the
maximum acceleration
value, which is a parameter of each boid. The last acceleration
request is trimmed back to compensate for the excess of accu-
mulated magnitude. The point is that a fixed amount of accel-
eration is under the control of the navigation module; this
acceleration is parceled out to satisfy the acceleration request
of the various behaviors in order of priority. In an emergency
the acceleration would be allocated to satisfy the most pressing
needs first; if all available acceleration is "'used up," the less
pressing behaviors might be temporarily unsatisfied. For exam-
ple, the flock centering urge could be correctly ignored tempo-
rarily in favor of a maneuver to avoid a static obstacle.
Simulated Perception
The bold model does not directly simulate the senses used by
real animals during flocking (vision and hearing) or schooling
(vision and fishes' unique "lateral line" structure that provides
a certain amount of pressure imaging ability [23, 24]). Rather
the perception model tries to make available to the behavior
model approximately the same information that is available to a
real animal as the end result of its perceptual and cognitive
processes.
This is primarily a matter of filtering out the surplus infor-
mation that is available to the software that implements the
boid's behavior. Simulated boids have direct access to the geo-
metric database that describes the exact position, orientation,
and velocity of all objects in the environment. The real bird's
information about the world is severely limited because it per-
ceives through imperfect senses and because its nearby flock-
mates hide those farther away. This is even more pronounced in
herding animals because they are all constrained to be in the
same plane. In fish schools, visual perception of neighboring
fish is further limited by the scattering and absorption of light
by the sometimes murky water between them. These factors
combine to strongly localize the information available to each
animal.
Not only is it unrealistic to give each simulated boid perfect
and complete information about the world, it is just plain
wrong and leads to obvious failures of the behavior model.
Before the current implementation of localized
flock centering
behavior was implemented, the flocks used a central force
model. This leads to unusual effects such as causing all mem-
bers of a widely scattered flock to simultaneously converge
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