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Flocking (behavior)

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Flocking behavior is the behavior exhibited when a group of birds, called a flock, are foraging or in flight There are parallels with the shoaling behavior of fish, the swarming behavior of insects, and herd behavior of land animals

Computer simulations and mathematical models which have been developed to emulate the flocking behaviors of birds can generally be applied also to the "flocking" behavior of other species As a result, the term "flocking" is sometimes applied, in computer science, to species other than birds

This article is about the modelling of flocking behavior From the perspective of the mathematical modeller, "flocking" is the collective motion of a large number of self-propelled entities and is a collective animal behavior exhibited by many living beings such as birds, fish, bacteria, and insects It is considered an emergent behavior arising from simple rules that are followed by individuals and does not involve any central coordination

Flocking behavior was first simulated on a computer in 1987 by Craig Reynolds with his simulation program, Boids This program simulates simple agents boids that are allowed to move according to a set of basic rules The result is akin to a flock of birds, a school of fish, or a swarm of insects


  • 1 Flocking rules
  • 2 Measurement
  • 3 Algorithmic complexity
  • 4 Applications
  • 5 See also
  • 6 References
  • 7 Other sources
  • 8 External links

Flocking rules

Basic models of flocking behavior are controlled by three simple rules:

  1. Separation - avoid crowding neighbors short range repulsion
  2. Alignment - steer towards average heading of neighbors
  3. Cohesion - steer towards average position of neighbors long range attraction

With these three simple rules, the flock moves in an extremely realistic way, creating complex motion and interaction that would be extremely hard to create otherwise

The basic model has been extended in several different ways since Reynolds proposed it For instance, Delgado-Mata et alextended the basic model to incorporate the effects of fear Olfaction was used to transmit emotion between animals, through pheromones modelled as particles in a free expansion gas Hartman and Benesintroduced a complementary force to the alignment that they call the change of leadership This steer defines the chance of the bird to become a leader and try to escape Hemelrijk and Hildenbrandtused attraction, alignment and avoidance and extended this with a number of traits of real starlings:first, birds fly according to fixed wing aerodynamics, while rolling when turning thus losing lift, second they coordinate with a limited number of interaction neighbours of 7 like in real starlings, third, they try to stay above a sleeping site like starlings do at dawn and when they happen to move outwards from the sleeping site, they return to it by turning, fourth, they move at relative fixed speed The authors showed that the specifics of flying behaviour as well as large flocksize and low number of interaction partners were essential to the creation of the variable shape of flocks of starlings


Measurements of bird flocking have been made using high-speed cameras, and a computer analysis has been made to test the simple rules of flocking mentioned above It is found that they generally hold true in the case of bird flocking, but the long range attraction rule cohesion applies to the nearest 5-10 neighbors of the flocking bird and is independent of the distance of these neighbors from the bird In addition, there is an anisotropy with regard to this cohesive tendency, with more cohesion being exhibited towards neighbors to the sides of the bird, rather than in front or behind This is no doubt due to the field of vision of the flying bird being directed to the sides rather than directly forward or backward

Another recent study is based on an analysis of high speed camera footage of flocks above Rome, and uses a computer model assuming minimal behavioural rules

Algorithmic complexity

In flocking simulations, there is no central control; each bird behaves autonomously In other words, each bird has to decide for itself which flocks to consider as its environment Usually environment is defined as a circle 2D or sphere 3D with a certain radius representing reach

A basic implementation of a flocking algorithm has complexity On2 - each bird searches through all other birds to find those which fall into its environment

Possible improvements:-

  • bin-lattice spatial subdivision Entire area the flock can move in is divided into a large number of bins Each bin stores which birds it contains Each time a bird moves from one bin to another, lattice has to be updated
    • Example:2D3D grid in a 2D3D flocking simulation
    • Complexity:Onk, k is number of surrounding bins to consider; just when bird's bin is found in O1

Lee Spector, Jon Klein, Chris Perry and Mark Feinstein studied the emergence of collective behavior in evolutionary computation systems

Bernard Chazelle proved that under the assumption that each bird adjusts its velocity and position to the other birds within a fixed radius, the time it takes to converge to a steady state is an iterated exponential of height logarithmic in the number of birds This means that if the number of birds is large enough, the convergence time will be so great that it might as well be infinite This result applies only to convergence to a steady state For example, arrows fired into the air at the edge of a flock will cause the whole flock to react more rapidly than can be explained by interactions with neighbors, which are slowed down by the time delay in the bird's central nervous systems—bird-to-bird-to-bird


Flock-like behavior in humans may occur when people are drawn to a common focal point or when repelled, as below:a crowd fleeing from the sound of gunfire

In Cologne, Germany, two biologists from the University of Leeds demonstrated a flock-like behavior in humans The group of people exhibited a very similar behavioral pattern to that of a flock, where if 5% of the flock would change direction the others would follow suit When one person was designated as a predator and everyone else was to avoid him, the flock behaved very much like a school of fish

Flocking has also been considered as a means of controlling the behavior of Unmanned Air Vehicles UAVs

Flocking is a common technology in screensavers, and has found its use in animation Flocking has been used in many films to generate crowds which move more realistically Tim Burton's Batman Returns 1992 featured flocking bats, and Disney's The Lion King 1994 included a wildebeest stampede

Flocking behaviour has been used for other interesting applications It has been applied to automatically program Internet multi-channel radio stations It has also been used for visualizing informationand for optimization tasks

See also

  • Crowd


  1. ^ O'Loan, OJ; Evans, MR 1999 "Alternating steady state in one-dimensional flocking" Journal of Physics A:Mathematical and General IOP Publishing 32 8:L99 arXiv:cond-mat/9811336 doi:101088/0305-4470/32/8/002 
  2. ^ Reynolds, Craig W 1987 "Flocks, herds and schools:A distributed behavioral model" ACM SIGGRAPH Computer Graphics 21 pp 25–34 
  3. ^ Delgado-Mata C, Ibanez J, Bee S, et al 2007 "On the use of Virtual Animals with Artificial Fear in Virtual Environments" New Generation Computing 25 2:145–169 doi:101007/s00354-007-0009-5 
  4. ^ Hartman C, Benes B 2006 "Autonomous boids" Computer Animation and Virtual Worlds 17 3-4:199–206 doi:101002/cav123 
  5. ^ Hemelrijk, C K; Hildenbrandt, H 2011 "Some Causes of the Variable Shape of Flocks of Birds" PLOS ONE 6 8 doi:101371/journalpone0022479 
  6. ^ Feder, Toni October 2007 "Statistical physics is for the birds" Physics Today 60 10:28–30 doi:101063/12800090 
  7. ^ Hildenbrandt, H; Carere, C; Hemelrijk, CK 2010 "Self-organized aerial displays of thousands of starlings:a model" Behavioral Ecology 21 6:1349–1359 doi:101093/beheco/arq149 
  8. ^ Hemelrijk, CK; Hildenbrandt, H 2011 "Some causes of the variable shape of flocks of birds" PLOS ONE 6 8:e22479 doi:101371/journalpone0022479 
  9. ^ Project Starflag
  10. ^ Swarm behaviour model by University of Groningen
  11. ^ Spector, L; Klein, J; Perry, C; Feinstein, M 2003 "Emergence of Collective Behavior in Evolving Populations of Flying Agents" Proceedings of the Genetic and Evolutionary Computation Conference GECCO-2003 Springer-Verlag Retrieved 2007-05-01 
  12. ^ Bernard Chazelle, The Convergence of Bird Flocking, J ACM 61 2014
  13. ^ "http://psychcentralcom/news/2008/02/15/herd-mentality-explained/1922html" Retrieved on October 31st 2008
  14. ^ Gabbai, J M E 2005 "Complexity and the Aerospace Industry:Understanding Emergence by Relating Structure to Performance using Multi-Agent Systems" Manchester:University of Manchester Doctoral Thesis 
  15. ^ Ibanez J, Gomez-Skarmeta AF, Blat J 2003 "DJ-boids:emergent collective behavior as multichannel radio station programming" Proceedings of the 8th international conference on Intelligent User Interfaces pp 248–250 doi:101145/604045604089 
  16. ^ Moere A V 2004 "Time-Varying Data Visualization Using Information Flocking Boids" Proceedings of the IEEE Symposium on Information Visualization pp 97–104 doi:101109/INFVIS200465 
  17. ^ Cui Z, Shi Z 2009 "Boid particle swarm optimisation" International Journal of Innovative Computing and Applications 2 2:77–85 doi:101504/IJICA2009031778 

Other sources

  • Cucker, Felipe; Steve Smale 2007 "The Mathematics of Emergence" PDF Japanese Journal of Mathematics 2:197 doi:101007/s11537-007-0647-x Retrieved 2008-06-09 
  • Shen, Jackie Jianhong 2008 "Cucker–Smale Flocking under Hierarchical Leadership" SIAM J Applied Math 68 3:694 doi:101137/060673254 Retrieved 2008-06-09 

External links

  • Craig Reynolds' Boids page
  • Iztok Lebar Bajec's fuzzy logic based flocking publications
  • Live In-Browser 3D Simulation of Bird Flocking Behavior in Unity3D - Open Source implementation for Windows, Linux and Mac
  • Another Flocking Simulator - A simple flocking applet which lets you control a number of parameters to create flocks that behave like birds, insects, bacteria, etc
  • NetLogo, a free software for multi-agent modeling, simulation, and the like, including a flocking simulation
  • VisualBots - Freeware multi-agent simulator in Microsoft Excel - Visual Basic syntax
  • Murmurations of starlings

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