Dissemination of Culture.nlogo

patches-own [culture walls cluster]
globals [this-cluster max-cluster num-cluster]

to setup
  clear-all
  setup-patches
  setup-links
  setup-walls
  setup-turtles
end

to go
  tick
  update-patch
  if ticks mod sample-interval = 0
    [
    update-plot
    if check-end? [stop]
    ]
end

to setup-patches
  let x 0
  let y 0
  set-default-shape turtles "square"
  repeat world-height
    [
    set x 0
    repeat world-height
      [
      ask patch x y
        [
        sprout 1 [setxy xcor ycor set color black set size 0.2]
        set pcolor white
        set culture []
        repeat num-features
          [
          set culture fput random num-traits culture
          ]
        ]
      set x x + 1
      ]
    set y y + 1
    ]
end

to setup-links
  ask turtles
    [
    create-links-with turtles-on neighbors4
      [
      set color black
      set thickness 0.2
      ]
    ]
end

to setup-walls
  let a1 0     ; 1..2
  let a2 0     ; ....
  let a3 0     ; 4..3
  let a4 0
  ask patches
    [
    ask turtles-here [set a2 who]
    ask turtles-at -1 0 [set a1 who]
    ask turtles-at 0 -1 [set a3 who]
    ask turtles-at -1 -1 [set a4 who]
    set walls (list link a1 a2 link a2 a3 link a3 a4 link a4 a1)
    update-walls
    ]
end

to setup-turtles
  ask turtles [setxy xcor + 0.5 ycor + 0.5]
end

to update-patch
  let neighbor-positions [[0 1] [1 0] [0 -1] [-1 0]]
  let neighbor random 4
  let culture-A []
  let culture-B []
  let patch-A 0
  let patch-B 0
  let P 0
  let n 0
  ask one-of patches
    [
    set culture-A culture
    set patch-A self
    ask patch-at item 0 (item neighbor neighbor-positions) item 1 (item neighbor neighbor-positions)
      [
      set culture-B culture
      set patch-B self
      ]
    set P similarity culture-A culture-B
    if (P > 0 and P < 1) and random-float 1 < P
      [
      set n difference culture-A culture-B
      set culture replace-item n culture (item n culture-B)
      update-walls
      ]
    ]
end

to update-walls
  let neighbor-positions [[0 1] [1 0] [0 -1] [-1 0]]
  let culture-A culture
  let culture-B []
  let n 0
  repeat 4
    [  
    ask patch-at item 0 (item n neighbor-positions) item 1 (item n neighbor-positions) [set culture-B culture]
    ask item n walls
      [
      set color 9.9 * similarity culture-A culture-B
      ]
    set n n + 1
    ]
end

to update-plot
  find-clusters
  set-current-plot "Connected Regions"
  set-plot-x-range 0 ticks
  set-plot-y-range 0 world-width * world-height
  set-current-plot-pen "Number"
  plotxy ticks num-cluster
  set-current-plot-pen "Largest"
  plotxy ticks max-cluster
end

to find-clusters
  set max-cluster 0
  set num-cluster 0
  let seed patch 0 0
  ask patches [set cluster nobody]
  while [seed != nobody]
    [
    ask seed
      [
      set cluster self
      set this-cluster 1
      set num-cluster num-cluster + 1
      grow-cluster
      ]
    if this-cluster > max-cluster [set max-cluster this-cluster]
    set seed one-of patches with [cluster = nobody]
    ]
end

to grow-cluster
  ask neighbors4 with [(cluster = nobody) and (culture = [culture] of myself)]
    [
    if cluster = nobody [set this-cluster this-cluster + 1]
    set cluster [cluster] of myself
    grow-cluster
    ]
end

to-report check-end?
  let end? true
  ask links
    [
    if color > 0 and color < 9.9 [set end? false]
    ]
  report end?    
end

to-report similarity [list-A list-B]
  let n 0
  let l length list-A
  let similarities 0
  repeat l
    [
    if item n list-A = item n list-B [set similarities similarities + 1]
    set n n + 1
    ]
  report similarities / l    
end

to-report difference [list-A list-B]
  let n 0
  let differences []
  repeat length list-A
    [
    if item n list-A != item n list-B [set differences lput n differences]
    set n n + 1
    ]
  report item (random length differences) differences
end
    
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@#$#@#$#@
WHAT IS IT?
-----------
This is a replication of Robert Axelrod's model of cultural dissemination, as presented in "The Dissemination of Culture: A Model with Local Convergence and Global Polarization".


HOW IT WORKS
------------
Patches are assigned a list of num-features integers which can each take on one of num-traits values. Each tag is called a feature, while it's value is called the trait.

The links in the view represent walls between patches where solid black walls mean there is no cultural similarity, and white walls mean the neighbors have the same culture.

The order of actions is as follows:
1) At random, pick a site to be active, and pick one of it's neighbors
2) With probability equal to their cultural similarity, these sites interact. The active site replaces one of the features on which they differ (if any) with the corresponding trait of the neighbor.

The model ends when no further interactions can take place.


HOW TO USE IT
-------------
Setup assigns the patches random culture based on the num-features and num-traits sliders, and updates the walls between them.

The plot "Connected Regions" has 2 pens. The black pen tracks the number of clusters of culturally identical patches, while the red pen tracks the size of the largest cluster. This is a time consuming algorithm for larger scale models, so the interval between updates is controlled by the sample-interval slider.


THINGS TO NOTICE
----------------
Q1) Try setting num-features to 5 and num-traits to 10. Under these settings, a typical culture list might be [9 6 0 3 4]. Run the model. How do the plots vary over time? Are changes gradual, or sudden?

Try running the model a few times. What different features can you see under these settings?

Q2) Try increasing num-traits to 15 and then to 20. How does this affect the final picture? Can you explain this?

Q3) With num-traits set at 20, try increasing num-features to 10. What happens now? More features means there is even more variety in culture, so the results may be surprising. What aspect of the model causes this behavior?

A1) These are the settings Axelrod uses in the paper referenced. Often, under these settings we find the culture becomes entirely uniform, and no more walls exist. The switch between generally separate cultures, and a large, connected cluster happens suddenly, where the number of clusters drops and the size of the largest cluster increases steeply.

Sometimes small islands form, and even small clusters isolated from the larger cluster by dramatic cultural differences.

A2) Increasing num-traits to 15 tends to mean the end result is several smaller clusters, through the majority of patches become connected. Further increase to 20 however tends to result in many small clusters, where the largest often occupies less than half of the total space.

A3) Though it may seem counter-intuitive, increasing num-features will tend to result in a larger cluster, and fewer islands. This is because with so many different features, the likelihood of neighbors having nothing in common is small compared with fewer features.


CREDITS AND REFERENCES
----------------------
Robert Axelrod, "The Dissemination of Culture: A Model with Local Convergence and Global Polarization"
Philip Ball - "Critical Mass"

Any suggestions or questions? e-mail: isw3@le.ac.uk
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