5.16-onlattice-dla.nlogo

;; The MIT License (MIT)
;;
;; Copyright (c) 2011-24 David O'Sullivan and George Perry
;;
;; Permission is hereby granted, free of charge, to any person
;; obtaining a copy of this software and associated documentation
;; files (the "Software"), to deal in the Software without restriction,
;; including without limitation the rights to use, copy, modify, merge,
;; publish, distribute, sublicense, and/or sell copies of the Software,
;; and to  permit persons to whom the Software is furnished to do so,
;; subject to the following conditions:
;;
;; The above copyright notice and this permission notice shall be included
;; in all copies or substantial portions of the Software.
;;
;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
;; OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
;; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
;; THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
;; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
;; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
;; DEALINGS IN THE SOFTWARE.
;;

extensions [ palette ]

globals [
  circle
  occupied-patches
  cluster-radius
  centre-patch
  n-occupied
]

patches-own [
  occupied?
  t-colonised
  d-to-cluster
]

to setup
  clear-all
  set centre-patch patch ((min-pxcor + max-pxcor) / 2) ((min-pycor + max-pycor) / 2)
  ask patches [
    set occupied? false
    set t-colonised -1
  ]
  set circle patches with [ceiling distance centre-patch = floor (world-width / 2)]
  ask circle [set pcolor grey]
  ask centre-patch [
    set occupied? true
    set pcolor white
    set occupied-patches self
    set t-colonised 1
    set d-to-cluster 0
    ask other patches [
      set d-to-cluster distance myself
    ]
  ]
  set n-occupied 1
  set cluster-radius 5
  reset-ticks
end

to go
  one-walker
  set cluster-radius max (list cluster-radius get-cluster-radius)
  if (any? circle with [d-to-cluster < start-radius-add])
      or (cluster-radius > ((world-width / 2) - 2)) [
    stop
  ]
 tick
end

to one-walker
  ask initiate-walker-patch [
    if show-starts? [ set pcolor red ]
    let step 0
    sprout 1 [
      let walking? true
      set hidden? true
      ; pd
      while [walking?] [
        set step step + 1
        move-to (one-of neighbors4)
        ;; if any neighbors are occupied stick to them
        if any? neighbors4 with [occupied? = true] [
          ask patch-here [
            set occupied-patches (patch-set occupied-patches self)
            set occupied? true
            set pcolor white
            set t-colonised ticks + 1
            set n-occupied n-occupied + 1
            set d-to-cluster 0
            ask other patches in-radius (start-radius-add + 1) [
              set d-to-cluster min (list d-to-cluster distance myself)
            ]
          ]
          set walking? false
          die
        ]
      ]
    ]
  ]
end

;; report furthest distance to origin
to-report get-cluster-radius
  let radius max [distance centre-patch] of occupied-patches
  if radius < 5 [ set radius 5 ]
  report radius
end

to-report initiate-walker-patch
  if (walker-starts-method = "buffer") [
    report one-of patches with [floor d-to-cluster = start-radius-add]
  ]
  if (walker-starts-method = "advancing circle") [
    ;; circle-based method
    let d 0
    let start-patch nobody
    ;; don't want to start the walker closer than 5 units from origin
    ifelse cluster-radius < 5
    [ set d 5 ]
    [ set d cluster-radius + start-radius-add ]

    ifelse d < world-width / 2 [
      let h random 359
      let start-x [pxcor] of centre-patch + (d * cos(h))
      let start-y [pycor] of centre-patch + (d * sin(h))
      set start-patch patch start-x start-y
    ]
    [
      set start-patch one-of circle
    ]
    report start-patch
  ]
  if (walker-starts-method = "fixed circle") [
    report one-of circle ;; initially slow
  ]
end

to colour-by-time
  ask occupied-patches [
    set pcolor palette:scale-gradient [[244 109 67] [255 255 191] [116 173 209]] t-colonised 0 ticks
  ]
end
@#$#@#$#@
GRAPHICS-WINDOW
257
10
667
421
-1
-1
2.0
1
10
1
1
1
0
0
0
1
-100
100
-100
100
1
1
1
ticks
100.0

MONITOR
184
170
241
215
n
n-occupied
0
1
11

BUTTON
107
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174
45
NIL
setup
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

BUTTON
181
13
244
46
NIL
go
T
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

BUTTON
18
328
139
361
colour-by-time
colour-by-time
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

SWITCH
7
151
145
184
show-starts?
show-starts?
0
1
-1000

SLIDER
74
53
246
86
start-radius-add
start-radius-add
2
20
15.0
1
1
NIL
HORIZONTAL

SLIDER
73
90
245
123
return-radius-mult
return-radius-mult
1
5
1.3
0.1
1
NIL
HORIZONTAL

CHOOSER
6
187
165
232
walker-starts-method
walker-starts-method
"advancing circle" "buffer" "fixed circle"
1

TEXTBOX
10
235
250
310
\"advancing circle\" is the method discussed in the text and in the literature; \"buffer\" method tends to produce more uniform clusters; \"fixed circle\" will start walkers from the circle shown, and is initially slow
11
0.0
1

@#$#@#$#@
## WHAT IS IT?

This model is a simulation of an _on lattice diffusion-limited aggregation_ process. See

+   Witten TA and Sander LM 1981 Diffusion-limited aggregation, a kinetic critical phenomenon. _Physical Review Letters_ **47** 1400–1403

and also Chapter 5 of

+   O'Sullivan D and Perry GLW 2013 _Spatial Simulation: Exploring Pattern and Process_. Wiley, Chichester, England.

for details of the model and related.  The examples presented in the book use the 'advancing circle" setting for the `walker-starts-method`.  Cluster characteristics are in general sensitive to the method used to determine starting locations for the random walkers that build the cluster.

## HOW TO CITE

If you mention this model in a publication, please include these citations for the model itself and for NetLogo

+   O'Sullivan D and Perry GLW 2013 _Spatial Simulation: Exploring Pattern and Process_. Wiley, Chichester, England.
+   Wilensky U 1999 NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
+   Witten TA and Sander LM 1981 Diffusion-limited aggregation, a kinetic critical phenomenon. _Physical Review Letters_ **47** 1400–1403

## COPYRIGHT AND LICENSE

The MIT License (MIT)

Copyright &copy; 2011-24 David O'Sullivan and George Perry

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to  permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
@#$#@#$#@
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airplane
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arrow
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box
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bug
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butterfly
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circle
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circle 2
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cow
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cylinder
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dot
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face happy
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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 half
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pentagon
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person
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Rectangle -7500403 true true 127 79 172 94
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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Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285
Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285
Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210
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
Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90

sheep
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Rectangle -7500403 true true 47 225 75 285
Rectangle -7500403 true true 15 75 210 225
Circle -7500403 true true 135 75 150
Circle -16777216 true false 165 76 116

square
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square 2
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star
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target
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Circle -7500403 true true 120 120 60

tree
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Rectangle -6459832 true false 120 195 180 300
Circle -7500403 true true 65 21 108
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triangle
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triangle 2
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truck
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wheel
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@#$#@#$#@
NetLogo 6.4.0
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@#$#@#$#@
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