turtles-own [lost inside my-xcor my-ycor historyx historyy bad-move]  ; variable to store if a particular turtle is lost
globals [rand-list rand-list-nozero inside-move found]

; Called when user clicks on the setup button
to setup
  ca
  set rand-list [-1 -0.5 0 0.5 1]  ; initializes the list of random numbers (used for creating error)
  set rand-list-nozero [-0.5 -0.25 0.25 0.5]
  set inside-move [1 0 0 0 0 0 0 0 0 0]
  ; set-default-shape turtles "circle"
  create-n-turtles num-turtles
    
  ;***************************************************************************************
  ; Uncomment the following lines to see the shape they are conforming to
  ;***************************************************************************************
  ask patches
  [
    ; this series of if statements set up the vertical rectangles
    ;if ((pxcor <= -12) and (pxcor >= -15)) and ((pycor <= 15) and (pycor >= -15))
    ;[ set pcolor gray ]
    ;if ((pxcor >= 12) and (pxcor <= 15)) and ((pycor <= 15) and (pycor >= -15))
    ;[ set pcolor gray ]
    ;if ((pxcor <= -3) and (pxcor >= -6)) and ((pycor <= 15) and (pycor >= -15))
    ;[ set pcolor gray ]
    ;if ((pxcor >= 3) and (pxcor <= 6)) and ((pycor <= 15) and (pycor >= -15))
    ;[ set pcolor gray ]
    
    ; this series of if statements set up the horizontal rectangles
    ;if ((pycor <= -12) and (pycor >= -15)) and ((pxcor <= 15) and (pxcor >= -15))
    ;[ set pcolor gray ]
    ;if ((pycor >= 12) and (pycor <= 15)) and ((pxcor <= 15) and (pxcor >= -15))
    ;[ set pcolor gray ]
    ;if ((pycor <= -3) and (pycor >= -6)) and ((pxcor <= 15) and (pxcor >= -15))
    ;[ set pcolor gray ]
    ;if ((pycor >= 3) and (pycor <= 6)) and ((pxcor <= 15) and (pxcor >= -15))
    ;[ set pcolor gray ]
  ]
  
end



; Actually sets up the initial locations of the turtles
to create-n-turtles [n]
  locals [t1 t2 t3 the-neighbors]

  create-custom-turtles n
  [
    setxy ((random screen-size-x) - screen-edge-x) ((random screen-size-y) - screen-edge-y)
    set found (list 0)
    set heading random 360
    set lost true
    set inside false
    set color red
    set bad-move false
    set shape "square"
   
      set my-xcor (xcor + random-one-of rand-list-nozero)
      set my-ycor (ycor + random-one-of rand-list-nozero)
    
    set historyx (list my-xcor)
    set historyy (list my-ycor)
    
    ;************************************************************************************
    ; When turtle is first created, try to look for neighbors and triangulate position
    ;************************************************************************************
    set the-neighbors find-neighbors  ; get an agentset of 3 nearby turtles
    if(count the-neighbors = 3)  ; if we actually have 3 nearby neighbors...
    [
      let id-neighbors values-from the-neighbors [who]  ; get the id's of the turtle neighbors
      set t1 (distance-nowrap (turtle (first id-neighbors)) + random-one-of rand-list)  ; get the distance (approx) to each neighbor
      set t1 (distance-nowrap (turtle (item 1 id-neighbors)) + random-one-of rand-list)
      set t1 (distance-nowrap (turtle (last id-neighbors)) + random-one-of rand-list)
      
      ;*********************************************************************************
      ; Do the following for all 3 neighbors:
      ; - Find the distance between the neighbors
      ; - Find the angle between 2 of the neighbors and the current agent
      ; - Find the x offset using sin(angle) to one neighbor
      ; - Find the y offset using sin(angle) to other neighbor
      
      set lost false
    ]
  ]
end


; Updates the locations of the turtles
to update
  if(count turtles < num-turtles)
  [
    create-n-turtles num-turtles - count turtles
  ]
  while [count turtles > num-turtles]
  [
    ask random-one-of turtles [die]
  ]
  ask turtles [without-interruption [move]]
end


; Moves the turtles (does all the actual work for turtle movement)
to move
  locals [g cx cy the-neighbors newx newy]
    
    ; now, to move one step in the gradient you just have to
    set the-neighbors find-neighbors
    set g get-gradient the-neighbors
    set my-xcor (xcor + first g + random-one-of rand-list-nozero)
    set my-ycor (ycor + last g + random-one-of rand-list-nozero)
    
    set historyx fput my-xcor historyx  ; add latest x location to front of the list
    if (length historyx > 8)
    [ set historyx remove (last historyx) historyx ]  ; remove oldest x location from the list
    set historyy fput my-ycor historyy  ; add latest y location to front of the list
    if (length historyy > 8)
    [ set historyy remove (last historyy) historyy ]  ; remove oldest y location from the list
    
    set newx (xcor + first g)
    set newy (ycor + last g)
    
    set bad-move true  ; bad-move is when an agent inside the shape tries to move outside the shape
    
    ; this series of if statements set up when the agent is in a vertical rectangle
    if ((my-xcor <= -12) and (my-xcor >= -15)) and ((my-ycor <= 15) and (my-ycor >= -15))
    [ 
      set inside true
      set bad-move false
    ]
    if ((my-xcor >= 12) and (my-xcor <= 15)) and ((my-ycor <= 15) and (my-ycor >= -15))
    [
      set inside true
      set bad-move false 
    ]
    if ((my-xcor <= -3) and (my-xcor >= -6)) and ((my-ycor <= 15) and (my-ycor >= -15))
    [
      set inside true
      set bad-move false
    ]
    if ((my-xcor >= 3) and (my-xcor <= 6)) and ((my-ycor <= 15) and (my-ycor >= -15))
    [
      set inside true
      set bad-move false
    ]
    
    ; this series of if statements set up when the agent is in a horizontal rectangle
    if ((my-ycor <= -12) and (my-ycor >= -15)) and ((my-xcor <= 15) and (my-xcor >= -15))
    [
      set inside true
      set bad-move false
    ]
    if ((my-ycor >= 12) and (my-ycor <= 15)) and ((my-xcor <= 15) and (my-xcor >= -15))
    [
      set inside true
      set bad-move false
    ]
    if ((my-ycor <= -3) and (my-ycor >= -6)) and ((my-xcor <= 15) and (my-xcor >= -15))
    [
      set inside true
      set bad-move false
    ]
    if ((my-ycor >= 3) and (my-ycor <= 6)) and ((my-xcor <= 15) and (my-xcor >= -15))
    [
      set inside true
      set bad-move false
    ]
    
    ifelse (inside = true)
    [ 
      ifelse (bad-move = false)
      [
        set color blue
        setxy newx newy
      ]
      [
        let rand-move random-one-of inside-move
        if(rand-move = 1)
        [ 
          let offset random-one-of [-.1 -0.5 0.5 .1]
          setxy (xcor + offset) (ycor + offset)
        ]
      ]
    ]
    [ setxy newx newy ]   
      
    ; setxy (xcor + first g) (ycor + last g)
    display
end


; Returns a list of 3 neighbors
to-report find-neighbors
  locals [near tnear rand sensor neighbor t-here th-id isin]  ; declare some local variables
  set sensor 1  ; sets sensor radius initially to 1
  set rand 0;
  ; set rand random-one-of rand-list  ; get a random offset from the list
  set tnear turtles in-radius-nowrap (sensor + rand)  ; find all turtles within a certain radius
  while[(count tnear) < 5]  ; while the turtle can't find 3 neighbors
  [
    set sensor (sensor + 1)  ; increment sensor radius by 1
    ; set rand random-one-of rand-list  ; get a random offset from the list
    if(sensor >= 25) [report tnear]  ; if the sensor tries to go too far, just exit b/c it's not going to find more agents
    set tnear turtles in-radius-nowrap (sensor + rand)  ; find all turtles within a certain radius
  ]
  
  ;set t-here turtles-here
  ;set th-id values-from t-here [who]
  ;set isin false
  
  if ((count tnear) >= 5)  ; if turtle has 5 or more neighbors, prune to 3 neighbors (not including self)
  [ 
    set neighbor (random-n-of 3 tnear)
    set near values-from neighbor [who]
    
    ; foreach th-id [ if(member? ?1 near) [ set isin true ] ]
    
    ; while[isin = true]
    while[member? who near]
    [
      set neighbor (random-n-of 3 tnear)
      set near values-from neighbor [who]
      ;foreach th-id[ if(member? ? near) [ set isin true ] ]
    ]
  ]
  
  ; show near
  ; set lost false
  ; show neighbor
  
  report neighbor
end


;***********************************************************************************************
; If an agent is lost, uses data from nearby neighbors to triangulate it's own position
to find-turtle
  locals [near tnear rand]  ; declare some local variables
  set rand random-one-of rand-list  ; get a random offset from the list
  set tnear turtles in-radius-nowrap (6 + rand)  ; find all turtles within a certain radius
  set near values-from tnear [who]  ; get id's of these turtles
  set near remove who near  ; remove self from the list
  
  if (length near) < 3  ; if turtle doesn't find 3 neighbors, exit procedure and continue
  [ stop ]
  
  while [(length near) > 3]  ; if turtle has more than 3 neighbors, prune to 3 neighbors
  [ set near remove (random-one-of near) near ]
 ; set lost false
 ; show near
end
;**************************************************************************************************

; Displaces a large number of the turtles a random distance away from the original shape
to shake
  locals [x1 x2 y1 y2]
  set x1 random screen-edge-x
  set x2 (x1 - abs((random 5) + 10))
  set y1 random screen-edge-y
  set y2 (y1 - abs((random 5) + 10))
  
  ask turtles
  [
    if (xcor <= x1) and (xcor >= x2) and (ycor <= y1) and (ycor >= y2)
    [
      set lost true
      set inside false
      set color green
      setxy (xcor + (random 5) - 10) (ycor + (random 5) - 10)
    ]
  ]
end




;turtle function
; if other-node is a distance of more than d away from my perceived coordinates
;     (where I think I am: my-xcor my-ycor)
;    then report the unit vector which points towards other-node
; if other-node is a distance of less than d 
;    then report the unit vector which points away from other-node
; else report (0 0)
to-report get-unit-vector-towards [other-node]
without-interruption
[
   no-display ;turn display off to hide the jump back and forth.
   let d distance-nowrap other-node ;the real distance to other-node
   let tx xcor ;save my coordinates
   let ty ycor
   setxy my-xcor my-ycor ;temporarily place myself where I think I am.
   
   set heading towards-nowrap other-node

   ifelse (distance other-node > d) [
      report (list dx dy)
   ][
      ifelse (distance other-node < d)[
         set heading heading + 180
         report (list dx dy)
      ][
         report (list 0 0)
      ]
  ]
  ; the following 2 lines are useless because they will never get executed
  setxy tx ty ;put me back where I really am
  display
]
end

;turtle function
;reports a unit vector that is the gradient (step 2 in the algorithm) for this 
; turtle given the-neighbors.
;the-neighbors is the list of neighbors
to-report get-gradient [the-neighbors]
   let vector reduce [(list ((first ?1) + (first ?2)) ((last ?1) + (last ?2)))]
                      values-from the-neighbors [get-unit-vector-towards myself]
   let magnitude sqrt ((first vector) * (first vector) 
                  + (item 1 vector) * (item 1 vector))
   if (magnitude = 0) [ report (list 0 0) ]
   report (list (first vector / magnitude) (item 1 vector / magnitude))
end
@#$#@#$#@
GRAPHICS-WINDOW
303
10
733
461
17
17
12.0
1
10
1
1
1
0
1
1
1

CC-WINDOW
5
475
742
570
Command Center
0

SLIDER
8
60
180
93
num-turtles
num-turtles
0
2000
1006
1
1
NIL

BUTTON
8
11
71
44
NIL
setup
NIL
1
T
OBSERVER
T
NIL

BUTTON
78
11
148
44
NIL
update
NIL
1
T
OBSERVER
T
NIL

BUTTON
155
11
225
44
NIL
update
T
1
T
OBSERVER
T
NIL

BUTTON
8
106
73
139
NIL
shake
NIL
1
T
OBSERVER
T
NIL

@#$#@#$#@
Title: Shapebugs
Author: Matt Baker
Description:
This is an implementation of the Shapebugs algorithm from
<ul>
<li>Jimming Cheng, Winston Cheng, and Radhika Nagpal. <a href="http://jmvidal.cse.sc.edu/lib/cheng05a.html">&ldquo;Robust and Self-Repairing Formation Control for Swarms of Mobile Agents&rdquo;</a>. In <i>Proceedings of the Twentieth National Conference on Artificial Intelligence,</i> p. 59--64, AAAI Press. 2005</li>
</ul>

My program begins (via the setup button) by randomly dispersing the agents throughout the display.  All agents start in the lost state and assume that they are outside of the desired shape.  An agent inside the shape is assumed to have been found.

Each agent's movement is as follows:
<ul>
<li>If a neighbor reaches a minimum distance the agent repels that neighbor</li>
<li>If an agent finds itself inside of the desired shape, it will follow the above rules as long as such movement does not take it outside of the shape</li>
<li>If an agent is inside of the shape, and it determines that its next move will take it outside of the shape, it will instead do one of 2 things:
	(a) Stay still: 90% probability
	(b) Move either slightly to the right, left, up, or down: 10% probability</li>
</ul>

Agent colors:
<ul>
<li>A red agent is an agent outside of the desired shape</li>
<li>A blue agent is an agent inside of the desired shape</li>
<li>A green agent is an agent that has been displaced</li>
</ul>

Agents can be added or removed dynamically via the slider.  The shake button chooses a random square from the screen and moves all agents within that square in random directions away from their starting positions.

Note: I found that using 1,000+ agents seems to work best for modeling the shape.
@#$#@#$#@
default
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circle
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circle 2
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cow
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face happy
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face neutral
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face sad
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fish
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flag
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flower
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house
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leaf
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line
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Line -7500403 true 150 0 150 300

pentagon
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Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120

person
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Circle -7500403 true true 110 5 80
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Polygon -7500403 true true 195 90 240 150 225 180 165 105
Polygon -7500403 true true 105 90 60 150 75 180 135 105

plant
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Rectangle -7500403 true true 135 90 165 300
Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285
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Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135
Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135
Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60
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square
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Rectangle -7500403 true true 30 30 270 270

square 2
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Rectangle -7500403 true true 30 30 270 270
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star
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Polygon -7500403 true true 60 270 150 0 240 270 15 105 285 105
Polygon -7500403 true true 75 120 105 210 195 210 225 120 150 75

target
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Circle -7500403 true true 0 0 300
Circle -16777216 true false 30 30 240
Circle -7500403 true true 60 60 180
Circle -16777216 true false 90 90 120
Circle -7500403 true true 120 120 60

tree
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0
Circle -7500403 true true 118 3 94
Rectangle -6459832 true false 120 195 180 300
Circle -7500403 true true 65 21 108
Circle -7500403 true true 116 41 127
Circle -7500403 true true 45 90 120
Circle -7500403 true true 104 74 152

triangle
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Polygon -7500403 true true 150 30 15 255 285 255

triangle 2
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truck
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Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194
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Polygon -16777216 true false 238 112 252 141 219 141 218 112
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Rectangle -7500403 true true 181 185 214 194
Circle -16777216 true false 144 174 42
Circle -16777216 true false 24 174 42
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turtle
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wheel
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Circle -7500403 true true 3 3 294
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Line -7500403 true 150 285 150 15
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Circle -7500403 true true 120 120 60
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Line -7500403 true 40 84 269 221
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x
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Polygon -7500403 true true 270 75 225 30 30 225 75 270
Polygon -7500403 true true 30 75 75 30 270 225 225 270

@#$#@#$#@
NetLogo 3.0
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@