turtles-own [ flockmates ;; agentset of nearby turtles nearest-neighbor ;; closest one of our flockmates ] globals [ mate_sizes ;; list of number of flockmates for each turtle group_lists ;; list of turtle ids in each extended group group_sizes ;; list of number in each extended group plot_legend ] to setup ca cct population [ rt random-int-or-float 360.0 setxy (random-int-or-float screen-size-x) (random-int-or-float screen-size-y) set color hsb (heading / 360) 1. 1. ] histograms set-plot-pen-mode 1 end to go ask turtles [ flock ] group-set ;; new histograms ;;new end to histograms ifelse toggle_plot [ ;set-current-plot "Histogram of number of flock mates" ;set-plot-xlabel "Number of flockmates (neighbots)" set plot_legend "Histogram of number of flock mates" set-plot-x-range 0 population set-plot-y-range 0 population set-histogram-num-bars population histogram-list mate_sizes ] [ ;set-current-plot "Histogram of direction" ;set-plot-xlabel "Direction of turtle" set plot_legend "Histogram of direction (0 & 360 is up)" set-plot-x-range 0 360 set-plot-y-range 0 population set-histogram-num-bars 18 histogram-from turtles [heading] ] end to group-set ;; find list of groups in flockmates - returns: mate_sizes group_lists group_sizes locals [ temp fm ;; temp list t-list ;; list of who = [ 0 1 2 ... ] a-list ;; list of "who" that is in flockmate agentsets i-list ;; list of agents that have been inserted g-list ;; list of agents in each group t-loop a-loop flocktmp;; list of flockmates for current agent n-list again ;; flag to continue seach within a group for new members ] set t-list [] set g-list [] set group_lists [] set i-list [] set t-list values-from turtles [who] set a-list [] repeat population [set a-list fput [] a-list] ; set up list with one entry per agent (t-list is convienent) foreach t-list ;; create a list equivalent to agentset flockmate - called "a-list" [ set fm value-from (turtle ?) [ flockmates] ;; returns agentset (not list as suggested in manual) set temp values-from fm [who] ; list of flockmates for ? if length temp > 0 [set a-list replace-item ? a-list (sentence ? temp)] ] set n-list filter [length item ? a-list > 0] t-list while [ length n-list > 0 ] [ set g-list item (item 0 n-list) a-list set again true while [again] [ set again false foreach t-list ;; Loop over all agents [ set t-loop ? set flocktmp item t-loop a-list if (not member? t-loop i-list and not empty? flocktmp) [ foreach flocktmp ;; insert flock mates into a-list [ set a-loop ? if (not member? a-loop i-list and length item a-loop a-list > 1 and member? a-loop g-list) ;; check if this agent's flockmates have been inserted? [ set g-list replace-item (position a-loop g-list) g-list (item a-loop a-list) ;; replace with list set i-list lput a-loop i-list set g-list reduce [sentence ?1 ?2 ] g-list ;; flattens list of lists set g-list sort remove-duplicates g-list ;; remove duplicates set again true ] ] ;; end foreach over g-list - at end - have a complete group list ] ] ;; end loop over t-list and if test ;print g-list ] ;; loop over while again - continue until no new agents added set group_lists lput g-list group_lists set temp reduce [sentence ?1 ?2 ] group_lists set n-list filter [not member? ? temp] t-list set n-list filter [length item ? a-list > 0] n-list ] ; loop over while n-list ; print list "group_lists" group_lists set group_sizes sort map [ length ? ] group_lists ;print list "group sizes:" group_sizes set mate_sizes map [ length item ? a-list] t-list end to flock ;; turtle procedure find-flockmates if any flockmates [ find-nearest-neighbor ifelse distance nearest-neighbor < minimum-separation [ separate ] [ align cohere ] ] fd 1.0 set color hsb (heading / 360) 1. 1. end to find-flockmates ;; turtle procedure set flockmates (turtles in-radius vision) with [self != myself] 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. report atan mean values-from flockmates [sin heading] mean values-from flockmates [cos heading] 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 report atan mean values-from flockmates [sin (towards myself + 180)] mean values-from flockmates [cos (towards myself + 180)] 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 ;; To find the difference between two headings, we can't just ;; subtract the numbers, because 0 and 360 are the same heading. ;; For example, the difference between a heading of 5 degrees ;; and a heading of 355 degrees is 10 degrees, not 350 degrees. to-report subtract-headings [h1 h2] ifelse abs (h1 - h2) <= 180 [ report h1 - h2 ] [ ifelse h1 > h2 [ report h1 - h2 - 360 ] [ report h1 - h2 + 360 ] ] end ; *** NetLogo Model Copyright Notice *** ; ; This model was originally 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 (and was changed in the process to ; be an alternate version of the model) as part of the project: ; PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN ; CLASSROOMS. The project gratefully acknowledges the support of the ; National Science Foundation (REPP program) -- grant number REC #9814682. ; Converted from StarLogoT to NetLogo, 2002. Updated 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. ; ; *** End of NetLogo Model Copyright Notice *** @#$#@#$#@ GRAPHICS-WINDOW 250 10 704 485 18 18 12.0 1 10 1 1 1 CC-WINDOW 419 489 710 660 Command Center BUTTON 31 10 112 43 NIL setup NIL 1 T OBSERVER T BUTTON 121 11 202 44 NIL go T 1 T OBSERVER T SLIDER 10 52 233 85 population population 1 200 50 1 1 NIL SLIDER 5 181 238 214 max-align-turn max-align-turn 0.0 20.0 5.0 0.25 1 degrees SLIDER 5 215 238 248 max-cohere-turn max-cohere-turn 0 20 3.0 0.25 1 degrees SLIDER 5 249 238 282 max-separate-turn max-separate-turn 0 20 1.5 0.25 1 degrees SLIDER 10 99 233 132 vision vision 0 10 3.0 0.5 1 patches SLIDER 10 133 233 166 minimum-separation minimum-separation 0 5 1.0 0.25 1 patches PLOT 5 489 412 660 NIL NIL number in bin 0.0 25.0 0.0 20.0 true true PENS "default" 1.0 1 -16776961 false SWITCH 6 421 125 454 Toggle_plot Toggle_plot 1 1 -1000 MONITOR 1 330 245 379 Group sizes group_sizes 0 1 MONITOR 6 454 245 503 Plot being displayed plot_legend 0 1 @#$#@#$#@ 21 OCT 2003 *** The standard flocking example (Flocking) supplied with Ver 1.3 of NetLogo is modified to include changes: 1. Turtles are now color-coded by the direction they are heading. This makes the flocking behavior much more obvious to the eye: all the agents in a flock have a similar color. 2. A subroutine GROUP-SET is added that finds from the agentset FLOCKMATES the lists of turtles in extended groups implied by the individual neighbor lists. For example, if your neighbor has a neighbor that is not in your list, then the three of you will be in the same extended group list. To use the subroutine, just copy it into your program, define GLOBAL variables mate_size, group_lists and group_sizes, call GROUP-SET appropriately, provide an agentset with the neighbor lists (you can rename FLOCKMATES to whatever is your neighbor list). You may wish to comment out mate_size if you do not require it - it is included here for output. The output of GROUP-SET is three lists: - group-lists: a list of lists of the form: [ (list of turtle numbers in a extended group) (list of turtle number in another extended group) ...] The essential property is that all the sets of extended groups are disjoint in any combination (they have no common members). The order of the groups is not meaningful, and an extended group is only 2 or more turtles. - group-sizes: an ordered list of the group sizes (you may wish to remove the sorting to retain correspondence between the two lists). - mate_size: the number of neighbors for each turtle Despite the calculation being at worst an N^2 problem (where N is the number of turtles), the code typically does not consider all N^2 combinations. But you will notice a speed penalty for large N. 3. Three diagnostics are included: - Histogram of the directions of turtles - Histogram of the numbers of flockmates - Monitor of the group sizes *** THINGS TO OBSERVE ***: - look at the histogram of the directions to follow the coherence formation and the different extended groups that self-organize - compare the histogram of the number of flockmates and the group size: this illustrates how the extended group is an emergent property of the system - examine the dynamics of these diagnostics as you change the parameters (like the vision range) during a run. How quickly do the extended groups form, breakup, reform? *** AN EXAMPLE: What determines what final direction of the flock after a some time? If you repeat a simulation over and over, it is difficult to predict the final direction from visually observing the initial distribution of directions in the graphics. This illustrates the sensitivity of the final solution (the direction of an entire flock) on details of the initial distribution. * Try this experiment: - Toggle the plot to show the histogram of direction. - Set vision to the maximum (10) and the minimum distance to minumum (0). - Click SETUP, and then click GO. After the flocks align, click Go to stop. - Repeat the last step a couple of times. Note how the flock quickly aligns to one direction (observe in the histogram all individuals will be in one or two bins) because everyone sees almost everyone else (observe the extended group size). Can you predict from the initial histogram what will be the final direction? * Now try this experiment: - Repeat the first three steps from the previous example. - While running, slide the mimimun distance to both extremes. Observe the histogram. When the minimum distance is maximum, every one tries to avoid everyone else and the system will start to randomize. But note how the distribution in the histogram takes time to populate other angles. When you reduce the minimum distance to zero, the flock will quickly reorient to the original direction of the flocks. How long do you have to let the simulation run before it "forgets" the previous collective angle? Remember that the turtles have no individual memory except their direction. The answer might surprise you. Can you predict how long is long enough by looking at the histogram? *** A suggestion: To better see the formation and interactions of flock mates, try reducing the speed of the agents by replacing "fd 1.0" with "fd 0.5" Norman Johnson Theoretical Division Los Alamos National Laboratory norman@lanl.gov The following is the standard introduction: ------------------------------------------- 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 apparent 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? Is there some way to get V-shaped flocks, like migrating geese? What happens if you put walls around the edges of the screen that the birds can't fly into? Can you get the birds to fly around obstacles in the middle of the screen? 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 special procedures for subtracting two headings, and 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. 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