# Flocking with speed variations

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### WHAT IS IT?

This model is an attempt to mimic the flocking of birds. (The resulting motion also resembles schools of fish.) The flocks that appear in this model are not created or led in any way by special leader birds. Rather, each bird is following exactly the same set of rules, from which flocks emerge.

The birds follow three rules: "alignment", "separation", and "cohesion". "Alignment" means that a bird tends to turn so that it is moving in the same direction that nearby birds are moving. "Separation" means that a bird will turn to avoid another bird which gets too close. "Cohesion" means that a bird will move towards other nearby birds (unless another bird is too close). When two birds are too close, the "separation" rule overrides the other two, which are deactivated until the minimum separation is achieved.

The three rules affect only the bird's heading. Each bird always moves forward at the same constant speed.

### HOW TO USE IT

First, determine the number of birds you want in the simulation and set the POPULATION slider to that value. Press SETUP to create the birds, and press GO to have them start flying around.

The default settings for the sliders will produce reasonably good flocking behavior. However, you can play with them to get variations:

Three TURN-ANGLE sliders control the maximum angle a bird can turn as a result of each rule.

VISION is the distance that each bird can see 360 degrees around it.

### THINGS TO NOTICE

Central to the model is the observation that flocks form without a leader.

There are no random numbers used in this model, except to position the birds initially. The fluid, lifelike behavior of the birds is produced entirely by deterministic rules.

Also, notice that each flock is dynamic. A flock, once together, is not guaranteed to keep all of its members. Why do you think this is?

After running the model for a while, all of the birds have approximately the same heading. Why?

Sometimes a bird breaks away from its flock. How does this happen? You may need to slow down the model or run it step by step in order to observe this phenomenon.

### THINGS TO TRY

Play with the sliders to see if you can get tighter flocks, looser flocks, fewer flocks, more flocks, more or less splitting and joining of flocks, more or less rearranging of birds within flocks, etc.

You can turn off a rule entirely by setting that rule's angle slider to zero. Is one rule by itself enough to produce at least some flocking? What about two rules? What's missing from the resulting behavior when you leave out each rule?

Will running the model for a long time produce a static flock? Or will the birds never settle down to an unchanging formation? Remember, there are no random numbers used in this model.

### EXTENDING THE MODEL

Currently the birds can "see" all around them. What happens if birds can only see in front of them? The IN-CONE primitive can be used for this.

Is there some way to get V-shaped flocks, like migrating geese?

What happens if you put walls around the edges of the world that the birds can't fly into?

Can you get the birds to fly around obstacles in the middle of the world?

What would happen if you gave the birds different velocities? For example, you could make birds that are not near other birds fly faster to catch up to the flock. Or, you could simulate the diminished air resistance that birds experience when flying together by making them fly faster when in a group.

Are there other interesting ways you can make the birds different from each other? There could be random variation in the population, or you could have distinct "species" of bird.

### NETLOGO FEATURES

Notice the need for the SUBTRACT-HEADINGS primitive and special procedure for averaging groups of headings. Just subtracting the numbers, or averaging the numbers, doesn't give you the results you'd expect, because of the discontinuity where headings wrap back to 0 once they reach 360.

### CREDITS AND REFERENCES

This model is inspired by the Boids simulation invented by Craig Reynolds. The algorithm we use here is roughly similar to the original Boids algorithm, but it is not the same. The exact details of the algorithm tend not to matter very much -- as long as you have alignment, separation, and cohesion, you will usually get flocking behavior resembling that produced by Reynolds' original model. Information on Boids is available at http://www.red3d.com/cwr/boids/.

To refer to this model in academic publications, please use: Wilensky, U. (1998). NetLogo Flocking model. http://ccl.northwestern.edu/netlogo/models/Flocking. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 1998 Uri Wilensky. All rights reserved. See http://ccl.northwestern.edu/netlogo/models/Flocking for terms of use.

## Comments and Questions

turtles-own [ flockmates ;; agentset of nearby turtles nearest-neighbor ;; closest one of our flockmates speed ] to setup clear-all crt population [ set color yellow - 2 + random 7 ;; random shades look nice set size 1.5 ;; easier to see setxy random-xcor random-ycor set speed 1.0 ] end to go ask turtles [ flock ] ;; the following line is used to make the turtles ;; animate more smoothly. repeat 5 [ ask turtles [ fd speed / 5 ] display ] ;; for greater efficiency, at the expense of smooth ;; animation, substitute the following line instead: ;; ask turtles [ fd speed ] tick end to flock ;; turtle procedure find-flockmates if any? flockmates [ find-nearest-neighbor ifelse distance nearest-neighbor < minimum-separation [ separate ] [ align cohere ] set speed (speed + mean [speed] of flockmates) / 2 ] set speed speed + random-normal 0 random-acceleration if (not allow-move-backward? and speed < 0) [ set speed 0 ] end to find-flockmates ;; turtle procedure set flockmates other turtles in-radius vision end to find-nearest-neighbor ;; turtle procedure set nearest-neighbor min-one-of flockmates [distance myself] end ;;; SEPARATE to separate ;; turtle procedure turn-away ([heading] of nearest-neighbor) max-separate-turn end ;;; ALIGN to align ;; turtle procedure turn-towards average-flockmate-heading max-align-turn end to-report average-flockmate-heading ;; turtle procedure ;; We can't just average the heading variables here. ;; For example, the average of 1 and 359 should be 0, ;; not 180. So we have to use trigonometry. let x-component sum [sin heading] of flockmates let y-component sum [cos heading] of flockmates ifelse x-component = 0 and y-component = 0 [ report heading ] [ report atan x-component y-component ] end ;;; COHERE to cohere ;; turtle procedure turn-towards average-heading-towards-flockmates max-cohere-turn end to-report average-heading-towards-flockmates ;; turtle procedure ;; "towards myself" gives us the heading from the other turtle ;; to me, but we want the heading from me to the other turtle, ;; so we add 180 let x-component mean [sin (towards myself + 180)] of flockmates let y-component mean [cos (towards myself + 180)] of flockmates ifelse x-component = 0 and y-component = 0 [ report heading ] [ report atan x-component y-component ] end ;;; HELPER PROCEDURES to turn-towards [new-heading max-turn] ;; turtle procedure turn-at-most (subtract-headings new-heading heading) max-turn end to turn-away [new-heading max-turn] ;; turtle procedure turn-at-most (subtract-headings heading new-heading) max-turn end ;; turn right by "turn" degrees (or left if "turn" is negative), ;; but never turn more than "max-turn" degrees to turn-at-most [turn max-turn] ;; turtle procedure ifelse abs turn > max-turn [ ifelse turn > 0 [ rt max-turn ] [ lt max-turn ] ] [ rt turn ] end ; *** NetLogo 4.1beta3 Model Copyright Notice *** ; ; This model was created as part of the project: CONNECTED MATHEMATICS: ; MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL ; MODELS (OBPML). The project gratefully acknowledges the support of the ; National Science Foundation (Applications of Advanced Technologies ; Program) -- grant numbers RED #9552950 and REC #9632612. ; ; Copyright 1998 by Uri Wilensky. All rights reserved. ; ; Permission to use, modify or redistribute this model is hereby granted, ; provided that both of the following requirements are followed: ; a) this copyright notice is included. ; b) this model will not be redistributed for profit without permission ; from Uri Wilensky. ; Contact Uri Wilensky for appropriate licenses for redistribution for ; profit. ; ; This model was converted to NetLogo as part of the projects: ; PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING ; IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. ; The project gratefully acknowledges the support of the ; National Science Foundation (REPP & ROLE programs) -- ; grant numbers REC #9814682 and REC-0126227. ; Converted from StarLogoT to NetLogo, 2002. ; ; To refer to this model in academic publications, please use: ; Wilensky, U. (1998). NetLogo Flocking model. ; http://ccl.northwestern.edu/netlogo/models/Flocking. ; Center for Connected Learning and Computer-Based Modeling, ; Northwestern University, Evanston, IL. ; ; In other publications, please use: ; Copyright 1998 Uri Wilensky. All rights reserved. ; See http://ccl.northwestern.edu/netlogo/models/Flocking ; for terms of use. ; ; *** End of NetLogo 4.1beta3 Model Copyright Notice ***

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Josh Unterman

## turtles move backward

that seems bad

## Posted about 15 years ago

Forrest Stonedahl

## Yeah, so what?

I think it's cute to see them wriggle backwards. But if you don't like it, just use the ALLOW-MOVE-BACKWARDS? switch. ;-)

## Posted about 15 years ago