+Figure 1. +
+
+
+ +
+Craig W. Reynolds
+Symbolics Graphics Division
+
+[obsolete addresses removed 2] +
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. + +
Categories and Subject Descriptors: 1.2.10 [Artificial +Intelligence]: 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]: Applications. + +
General Terms: Algorithms, design.b + +
Additional Key Words, and Phrases: flock, herd, school, +bird, fish, aggregate motion, particle system, actor, flight, +behavioral animation, constraints, path planning. + +
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, it seems +randomly arrayed and yet is magnificently synchronized. Perhaps most +puzzling is the strong impression of intentional, 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 description and +control of all types of motion. Computer animators 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, computer 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 maintained (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 simulate 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 simulate 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 instances of the simulated bird model and allow them to +interact.** + +
Some experiments with this sort of simulated flock are described +in more detail in the remainder of this paper. The success 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 behavioral 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 delightful to watch. + +
The computer graphics community has seen simulated bird flocks +before. The Electronic Theater at SIGGRAPH `85 presented 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 specifically +intended for flock modeling. But the underlying concept 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 system." 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 interactions can be culled according to bounding box +tests. An incremental, linear time algorithm finds bounding box +intersections. 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 behaviorally +controlled animation of groups of moving objects (spaceships, +inchworms, and quadrupeds), but they are not organized as flocks [35]. Another author kept suggesting [28, 29, 30] implementing a flock simulation based on a +distributed behavioral model. + +
The simulated flock described here is closely related to particle +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 recently, the +spray and foam of ocean waves [27]. Particle +systems 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 boid flock model is a slight generalization of +particle systems. In what might be called a "subobject system," +Reeves's dot-like particles are replaced by an entire geometrical +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 fundamental difference is that +individual subobjects have a more complex geometrical state; they now +have orientation. + +
Another difference between boid flocks and particle systems 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 boid 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 interact +with one another, although this is not ruled out by definition. But +birds and hence boids must interact strongly in order to flock +correctly. Boid behavior is dependent not only on internal state but +also on external state. + +
The behavioral model that controls the boid's flight and flocking +is complicated enough that rather than use an ad hoc approach, 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 boid must be held in some sort +of data structure. It is convenient 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, procedure, +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 +simulation. In the literature of parallel and distributed computer +systems, flocks and schools are given as examples of robust +self-organizing distributed systems [15]. + +
Traditional hand-drawn cel animation was produced with a medium +that was completely inert. Traditional computer animation 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 almost the same low level of abstraction as do cel +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 cel animators to use helpers to interpolate +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 characterization into the motions that the +character performs. The animator cannot simply tell the character to +"act happy" but must tediously 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 simple path planning to complex "emotional" +interactions between characters. The construction of behavioral +animation characters has attracted many researchers [19, 21, 13, 14, 29, 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 he an +animator. Traditionally, the animator is directly responsible for all +motion in animation production [40]. It might he +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 becomes somewhat like that of a +theatrical director: the character'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!"). + +
A fundamental part of the boid 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 object'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 +object's "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. Incremental geometric flight is a +discrete approximation of this; small linear motions model a +continuous curved path. In animation 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 motion 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 left/right axis is X, up/down is +Y, and forward/pack 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 boid continually accelerates in one +direction, it will not exceed a certain maximum 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 boid +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 boid was accelerated by gravity each frame, it +would tend to fall unless gravity was countered by lift or +buoyancy. Buoyancy is aligned against gravity, but aerodynamic lift is +aligned with the boid's local "up" direction 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 frictional 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 relates translation, pitch, and yaw, but does not +constrain roil, 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 velocity and with the +curvature of its path (so inversely with the radius of its turn). The +limiting case of infinite velocity resembles 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. + +
+
+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 advantages: it +simplifies the bird's (or pilot's) orientation task, it keeps the lift +from the airfoils of the wings pointed in the most efficient direction +("accelerational up"), it keeps the passengers 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. + +
The incremental mixing of forward translations and local rotations +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 experimentally +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 classroom 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 object 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 equivalent to the boid +objects and their flight paths. + +
"...and the thousands off 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 flockmates. 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, statistically improving +survival of the (shared) gene pool from attacks 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 "overloaded" 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 flockmates. But in a huge flock spread over +vast distances, an individual 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 sharp upper bound on the size of natural flocks when +the individual birds became overloaded by the complexity of their +navigation task. This has not be 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(N 2 ). 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. + +
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: + +
+
+
+
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 awareness 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 a way 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 velocity matching, separations between boids remains +approximately invariant with respect to ongoing geometric +flight. Static collision avoidance serves to establish the minimum +required separation 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 approximately the same in all +directions. In this case, the centroid 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 distance 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 Potts 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. + +
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 several 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 desired by the +navigation module and passes it to the flight module, which attempts +to fly in that direction. + +
The easiest way to combine acceleration requests is to average +them. Because of the included "strength" factors, this is actually a +weighted average. The relative strength of one behavior 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 averaging of acceleration requests works +"pretty well." A boid that chooses its course this way will fly a +reasonable course under typical conditions. But in critical +situations, such as potential collision with obstacles, conflicts must +be resolved in a timely manner. During high-speed flight, hesitation +or indecision 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 approximately 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 systems, +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 consideration of their acceleration +requests. (This ordering can change to suit dynamic conditions.) The +acceleration requests are considered 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 +accumulated 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 accumulated +magnitude. The point is that a fixed amount of acceleration 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 example. the flock centering urge could +be correctly ignored temporarily in favor of a maneuver to avoid a +static obstacle. + +
The boid 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 +information that is available to the software that implements the +boid's behavior. Simulated boids have direct access to the geometric +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 perceives through imperfect +senses and because its nearby flockmates 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 members of a widely scattered +flock to simultaneously converge toward the flock's centroid. An +interesting result of the experiments reported in this paper is that +the aggregate motion that we intuitively recognize as "flocking" (or +schooling or herding) depends upon a limited, localized view of the +world. + +
The behaviors that make up the flocking model are stated in terms +of "nearby flockmates." In the current implementation, the +neighborhood is defined as a spherical zone of sensitivity centered at +the boid's local origin. The magnitude of the sensitivity is defined +as an inverse exponential of distance. Hence the neighborhood is +defined by two parameters: a radius and exponent. There is reason to +believe that this field of sensitivity should realistically be +exaggerated in the forward direction and probably by an amount +proportional to the boid's speed. Being in motion requires an +increased awareness of what lies ahead, and this requirement increases +with speed. A forward-weighted sensitivity zone would probably also +improve the behavior in the current implementation of boids at the +leading edge of a flock, who tend to get distracted by the flock +behind them. Because of the way their heads and eyes are arranged, +real birds have a wide field of view (about 300 degrees), but the zone +of overlap from both eyes is small (10 to 15 degrees). Hence the bird +has stereo depth perception only in a very small, forward-oriented +cone. Research is currently under way on models of forward-weighted +perception for boids. + +
In an early version of the flock model, the metrics of attraction +and repulsion were weighted linearly by distance. This spring-like +model produced a bouncy flock action, fine perhaps for a cartoony +characterization, but not very realistic. The model was changed to use +an inverse square of the distance. This more gravity-like model +produced what appeared to be a more natural, better damped flock +model. This correlated well with the carefully controlled quantitative +studies that Brian Partridge made of the spatial relationships of +schooling fish [23]; he found that "a fish is +much more strongly influenced by its near neighbors than it is by the +distant members of the school. The contribution of each fish to the +[influence] is inversely proportional to the square or the cube of the +distance." In previous work he and colleagues [23, 24] demonstrated that +fishes school based on information from both their visual system and +from their "lateral line" organ which senses pressure waves. The area +of a perspective image of the silhouette of an object (its "visual +angle") varies inversely with the square of its distance, and that +pressure waves traveling through a 3D medium like water fall off +inversely with the cube of the distance. + +
The boid perception model is quite ad hoc and avoids actually +simulating vision. Artificial vision is an extremely complex problem +[38] and is far beyond the scope of this +work. But if boids could "see" their environment, they would be better +at path planning than the current model. It is possible to construct +simple maze like shapes that would confuse the current boid model but +would be easily solved by a boid with vision. + +
The flocking model described above gives boids an eagerness to +participate in an acceptable approximation of flock like motion. Boids +released near one another begin to flock together, cavorting and +jostling for position. The boids stay near one another (flock +centering) but always maintain prudent separation from their +neighbors' (collision avoidance), and the flock quickly becomes +"polarized"-its members heading in approximately the same direction at +approximately the same speed (velocity marching); when they change +direction they do it in synchronization. Solitary boids and smaller +flocks join to become larger flocks, and in the presence of external +obstacles (discussed below), larger flocks can split into smaller +flocks. + +
For each simulation run, the initial position (within a specified +ellipsoid), heading, velocity, and various other parameters of the +boid model are initialized to values randomized within specified +distributions. A restartable random number generator is used to allow +repeatability. This randomization is not required; the boids could +just as well start out arranged in a regular pattern, all other +aspects of the flock model are completely deterministic and +repeatable. + +
When the simulation is run, the flock's first action is a reaction +to the initial conditions. If the boids started out too closely +crowded together, there is an initial "flash expansion" where the +mutual desire to avoid collision drives the boids radially away from +the site of the initial over-pressure. If released in a spherical +shell with a radius smaller than the "neighborhood" radius, the boids +contract toward the sphere's center; otherwise they begin to coalesce +into small flockettes that might themselves begin to join together. If +the boids are confined within a certain region, the smaller flocks +eventually conglomerate into a single flock if left to wander long +enough. + +
The behaviors discussed so far provide for the ability of +individual birds to fly and participate in happy aimless flocking. But +to combine flock simulations with other animated action, we need more +direct control over the flock. We would like to direct specific +action at specific times (for example, "the flock enters from the left +at :02.3 seconds into the sequence, turns to fly directly upward at +:03.5, and is out of the frame at :04.0"). + +
The current implementation of the boid model has several +facilities to direct the motion and timing of the flock action. First, +the simulations are run under the control of a general-purpose +animation scripting system [36]. The details of +that scripting system are not relevant here except that, in addition +to the typical interactive motion control facilities, it provides the +ability to schedule the invocation of user-supplied software (such as +the flock model) on a frame-by-frame basis. This scripting facility is +the basic tool used to describe the timing of various flock +actions. It also allows flexible control over the time-varying values +of parameters, which can be passed down to the simulation +software. Finally the script is used to set up and animate all +nonbehavioral aspects of the scene, such as backgrounds, lighting, +camera motion, and other visible objects. + +
The primary tool for scripting the flock's path is the migratory +urge built into the boid model. In the current model this urge is +specified in terms of a global target, either as a global direction +(as in "going Z for the winter") or as a global position-a target +point toward which all birds fly. The model computes a bounded +acceleration that incrementally turns the boid toward its migratory +target. + +
With the scripting system. we can animate a dynamic parameter +whose value is. a global position vector or a global direction +vector. This parameter can be passed to the flock, which can in turn +pass it along to all boids, each of which sets its own "migratory goal +register." Hence the global migratory behavior of all birds can be +directly controlled from the script. (Of course, it is not necessary +to alter all boids at the same time, for example, the delay could be a +function of their present position in space. Real flocks do not change +direction simultaneously [25], but rather the +turn starts with a single bird and spreads quickly across the flock +like a shock wave.) + +
We can lead the flock around by animating the goal point along the +desired path, somewhat ahead of the flock. Even if the migratory goal +point is changed abruptly the path of each boid still is relatively +smooth because of the flight model's simulated conservation of +momentum. This means that the boid's own flight dynamics implement a +form of smoothing interpolation between "control points." + +
+
+
The most interesting motion of a simulated flock comes from +interaction with other objects in the environment. The isolated +behavior of a flock tends to reach a steady state and becomes rather +sterile. The flock can be seen as a relaxation solution to the +constraints implied by its behaviors. For example, the conflicting +urges of flock centering and collision avoidance do not lead to +constant back and forth motion, but rather the boids eventually strike +a balance between the two urges (the degree of damping controls how +soon this balance is reached). Environmental obstacles and the boid's +attempts to navigate around them increase the apparent complexity of +the behavior of the flock. (In fact the complexity of real flocks +might be due largely to the complexity of the natural environment.) + +
Environmental obstacles are also important from the standpoint of +modeling the scene in which we wish to place the flock. If the flock +is scripted to fly under a bridge and around a tree, we must be able +to represent the geometric shape and dimension of these obstacles. The +approach taken here is to independently model the "shape for +rendering" and the "shape for collision avoidance." The types of +shapes currently used for environmental obstacles are much less +complicated than the models used for rendering of computer graphic +models. The current work implements two types of shapes of +environmental collision avoidance. One is based on the force field +concept, which works in undemanding situations but has some +shortcomings. The other model called steer-to-avoid is more robust and +seems closer in spirit to the natural mechanism. + +
The force field model postulates a field of repulsion force +emanating from the obstacle out into space; the boids are increasingly +repulsed as they get closer to the obstacle. This scheme is easy to +model; the geometry of the field is usually fairly simple and so an +avoidance acceleration can be directly calculated from the field +equation. These models can produce good results, such as in "Eurythmy" +[4], but they also have drawbacks that are +apparent on close examination. If a boid approaches an obstacle +surrounded by a force field at an angle such that it is exactly +opposite to the direction of the force field, the boid will not turn +away. In this case the force field serves only to slow the boid by +accelerating it backwards and provides no side thrust at all. The +worst reaction to an impending collision is to fail to turn. Force +fields also cause problems with "peripheral vision." The boid should +notice and turn away from a wall as it flies toward it, but the wall +should be ignored if the boid is flying alongside it. Finally, force +fields tend to be too strong close up and too weak far away; avoiding +an obstacle should involve long-range planning rather than panicky +corrections at the last minute. + +
Steer-to-avoid is a better simulation of a natural bird guided by +vision. The boid considers only obstacles directly in front of it. (It +finds the intersection, if any, of its local Z axis with the +obstacle.) Working in local perspective space, it finds the silhouette +edge of the obstacle closest to the point of eventual impact. A radial +vector is computed which will aim the boid at a point one body length +beyond that silhouette edge (see figure 2). Currently steer-to avoid +has been implemented for several obstacle shapes: spheres, cylinders, +planes, and boxes. Collision avoidance for arbitrary convex polyhedral +obstacles is being developed. + +
+
+Figure 2. +
Obstacles are not necessarily fixed in space; they can be animated +around by the script during the animation. Or more interestingly, the +obstacles can be behavioral characters. Sparrows might flock around a +group of obstacles that is in fact a herd of elephants. Similarly, +behavioral obstacles might not merely be in the way; they might be +objects of fear such as predators. It has been noted [25] that natural flocking instincts seem to be +sharpened by predators. + +
The model of polarized noncolliding aggregate motion has many +applications, visual simulation of bird flocks in computer animation +being one. Certain modifications yield a fish school model. Further +modifications, such as [imitation to a 2D surface and the ability to +follow the terrain, lead to a herd model. Imagine a herd of PODA-style +legged creatures [9], using Karl Sims' techniques +for locomotion over uneven, complex terrain [35]. Other applications are less obvious. Traffic +patterns, such as the flow of cars on a freeway, is a flock-like +motion. There are specialized behaviors, such as being constrained to +drive within the lanes, but the basic principles that keep boids from +colliding are just as applicable on the freeway. We could imagine +creating crowds of "extras" (human or otherwise) for feature +films. However the most fun are the offbeat combinations possible in +computer graphics by mixing and matching: a herd of pogo sticks, a +flock of Pegasus-like winged horses, or a traffic jam of spaceships on +a 3D interplanetary highway. + +
One serious application would be to aid in the scientific +investigation of flocks, herds, and schools. These scientists must +work almost exclusively in the observational mode; experiments with +natural flocks and schools are difficult to perform and are likely to +disturb the behaviors under study. It might be possible, using a more +carefully crafted model of the realistic behavior of a certain species +of bird, to perform controlled and repeatable experiments with +"simulated natural flocks." A theory of flock organization can be +unambiguously tested by implementing a distributed behavioral model +and simply comparing the aggregate motion of the simulated flock with +the natural one. + +
A naive implementation of the basic flocking algorithm would grow +in complexity as the order of the square of the flock's population +("O(N2)"). Basically this is because each boid must reason about +each of the other boids, even if only to decide to ignore it. This +does not say the algorithm is slow or fast, merely that as the size of +the problem (total population of the flock) increases, the complexity +increases even faster. Doubling the number of boids quadruples the +amount of time taken. + +
However, as stated before, real birds are probably not as +sensitive to the total flock population. This gives hope that the +simulated boid could be taught to navigate independently of the total +population. Certainly part of the problem is that we are trying to run +the simulation of the whole flock on a single computer. The natural +solution is to use distributed processing, as the real flock does. If +we used a separate processor for each boid, then even the naive +implementation of the flocking algorithm would be O(N), or linear with +respect to the population. But even that is not good enough. It still +means that as more boids are added to the flock, the complexity of the +problem increases. + +
What we desire is a constant time algorithm, one that is +insensitive to the total population. Another way to say this is that +an N2 algorithm would be OK if there was an efficient way +to keep N very small. Two approaches to this goal are currently under +investigation. One is dynamic spatial partitioning of the flock; the +boids are sorted into a lattice of "bins" based on their position in +space. A boid trying to navigate inside the flock could get quick +access to the flockmates that are physically nearby by examining the +"bins" near its current position. Another approach is to do +incremental collision detection (x`nearness testing"). General +collision detection is another N2 algorithm, but if one +does collision detection incrementally, based on a partial solution +that described the situation just a moment before, then the algorithm +need worry only about the changes and so can run much faster, assuming +that the incremental changes are small. The incremental collision +detection algorithm used in Girard's PODA system [9] apparently achieves constant time performance in +the typical case. + +
The boids software was written in Symbolics Common Lisp. The code +and animation were produced on a Symbolics 3600 Lisp Machine, a +high-performance personal computer. The flock software is implemented +in Flavors, the object-oriented programming extensions to Symbolics +Common Lisp. The geometric aspects of the system are layered upon +S-Geometry, an interactive geometric modeler [37]. Boids are based on the flavor 3D:OBJECT, which +provides their geometric abilities. The flock simulations are invoked +from scripts created and animated with the S Dynamics [36] animation system, which also provided the +real-time playback facility used to view the motion tests. The +availability of this graphical toolkit allowed the author to focus +immediately on the issues unique to this project. One example of the +value of this substrate is that the initial version of the flock +model, including implementation, testing, debugging, and the +production of seven short motion tests was accomplished in the ten +days before the SIGGRAPH `86 conference. + +
The boid software has not been optimized for speed. But this +report would be incomplete without a rough estimate of the actual +performance of the system. With a flock of 80 boids, using the naive +O(N2) algorithm (and so 6400 individual boid-to-boid +comparisons), on a single Lisp Machine without any special hardware +accelerators, the simulation ran for about 95 seconds per frame. A +ten-second (300 frame) motion test took about eight hours of real time +to produce. + +
This paper has largely ignored the internal animation of the +geometrical model that provides the visual representation of the +boid. The original motion tests produced with these models all show +flocks of little abstract rigid shapes that might be paper +airplanes. There was no flapping of wings nor turning of heads. and +there was certainly no character animation. These topics are all +important and pertinent to believable animation of simulated +flocks. But the underlying abstract nature of flocking as +polarized. noncolliding aggregate motion is largely independent of +these issues of internal shape change and articulation. This notion is +supported by the fact that most viewers of these simulations identify +the motion of these abstract objects as "flocking" even in the absence +of any internal animation. + +
But doing a believable job of melding these two aspects of the +motion is more than a matter of concatenating the action of an +internal animation cycle for the character with the motion defined by +geometrical flight. There are important issues of synchronization +between the current state of the flight dynamics model, and the +amplitude and frequency of the wing motion cycle. Topics of current +development include internal animation. synchronization, and +interfaces between the simulation-based flock model and other more +traditional. interactive animation scripting systems. We would like to +allow a skilled computer animator to design a bird character and +define its "wing flap cycle" using standard interactive modeling and +scripting techniques. and then be able to take this cyclic motion and +"plug it in" to the flock simulation model causing the boids in the +flock to fly according to the scripted cycle. + +
The behaviors that have been discussed in this paper are all +simplistic, isolated behaviors of low complexity. The boids have a +geometric and kinematic state. but they have no significant mental +state. Real animals have more elaborate, abstract behaviors than a +simple desire to avoid a painful collision: they have more complex +motivations than a simple desire to fly to a certain point in +space. More interesting behavior models would take into account +hunger, finding food, fear of predators, a periodic need to sleep, and +so on. Behavior models of this type have been created by other +investigators [6, 19, 21], but they have not yet been implemented for the +boid model described here. + +
This paper has presented a model of polarized. noncolliding +aggregate motion. such as that of flocks. herds. and schools. The +model is based on simulating the behavior of each bird +independently. Working independently. the birds try both to stick +together and avoid collisions with one another and with other objects +in their environment. The animations showing simulated flocks built +from this model seem to correspond to the observer's intuitive notion +of what constitutes "flock-like motion." However it is difficult to +objectively measure how valid these simulations are. By comparing +behavioral aspects of the simulated flock with those of natural +flocks. we are able improve and refine the model. But having +approached a certain level of realism in the model. the parameters of +the simulated flock can be altered at will by the animator to achieve +many variations on flock-like behavior. + +
I would like to thank flocks. herds. and schools for existing; +nature is the ultimate source of inspiration for computer graphics and +animation. I would also like to acknowledge the contributions to this +research provided by workers in a wonderfully diverse collection of +pursuits: + +
To the natural sciences of behavior, evolution, and zoology: for +doing the hard work, the Real Science, on which this computer graphics +approximation is based. To the Logo group who invented the appropriate +geometry, and so put us in the driver's seat. To the Actor semantics +people who invented the appropriate control structure, and so gave the +boid a brain. To the many developers of modern Lisp who invented the +appropriate programming language. To my past and present colleagues at +MIT, III, and Symbolics who have patiently listened to my speculations +about flocks for years and years before I made my first boid fly. To +the Graphics Division of Symbolics, Inc., who employ me, put up with +my nasty disposition, provide me with fantastic computing and graphics +facilities, and have generously supported the development of the work +described here. And to the field of computer graphics, for giving +professional respectability to advanced forms of play such as reported +in this paper. + +
+
+
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
Freeman and Company. San Francisco, 1970, +pp. 452480.
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+
+
+ +
+
Permission to copy without fee all or part of this material is +granted provided that the copies are not made or distributed for +direct commercial advantage, the ACM copyright notice and the title of +the publication and its date appear, and notice is given that copying +is by permission of the Association for Computing Machinery. To copy +otherwise, or to republish requires a fee and/or specific permission. + +
(C)1987 ACM-0-89791-227-6/87/007/0025 $00.75 + +
+
+