The Spread of a Meme Across a Social Network

globals [color-mode pop] ;; 0 = default, 1 = source, 2 = times heard, 3 = popularity

turtles-own [popularity trendy? trend-setter? interest-category trend-category trend-source times-heard]
;; popularity is a number value representing the degree of each turtle
;; trendy? is a boolean that is true if the person follows the trend
;; trend-setter? is a boolean that is true if the person is seeded the trend (i.e. the overall trend-starter)
;; interest-category is an integer representing the type of things the person is interested in
;; trend-category is an integer that represents the inherent type of thing a trend is
;; (corresponds with same values as interest-category) if the person is carrying a trend.
;; trend-source tells whether the turtle followed a trend from a friend, from the media, or both.
;; times-heard counts how many times a turtle has heard a meme

patches-own [category]
;; category is an integer that represents the inherent type of thing a trend is
;; (corresponds with same values as trend-category of a person)

;; Create people and links.

to setup
  ca
  set color-mode 0 ;; default
  set-default-shape turtles "person"
  make-node nobody ;; first node, unattached
  make-node turtle 0 ;; second node, attached to first node
  ask patches [
    set category -1 ;; -1 corresponds with "no trend", i.e. this patch is not a TV
  ]
  reset-ticks
end 

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;;;Network Procedures;;;
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;; Network and layout procedures incorporated from Preferential Attachment example model

to create-network
  make-node find-partner ;; find partner and use it as attachment
  tick
  if layout? [layout]
  if count turtles = population [ ;; We want the network to have POPULATION turtles, as set by the slider
    reset-ticks ;; reset the ticks at 0 so we can observe them for the meme-spreading section
    stop
  ]
end 

;; used for creating a new node

to make-node [old-node]
  crt 1
  [
    set color gray ;; default "no-trend" color is gray
    set interest-category random 10 ;; an "interest type" category corresponding to one of 0-9
    set trend-category -1 ;; -1 corresponds with "no trend"
    set times-heard 0
    if old-node != nobody
      [ create-link-with old-node
        ;; position new node near its partner
        move-to old-node
        fd 8
      ]
  ]
end 

;; Main preferential attachment mechanism. The more connections a node already has, the more likely
;; it is to gain another connection.

to-report find-partner
  report [one-of both-ends] of one-of links
end 

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;;;Layout Procedures;;;
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;; resize nodes, change back and forth from size based on degree to a size of 1

to resize-nodes
  ifelse all? turtles [size <= 1]
  [
    ;; a node is a circle with diameter determined by
    ;; the SIZE variable; using SQRT makes the circle's
    ;; area proportional to its degree
    ask turtles [set size sqrt count link-neighbors ]
  ]
  [
    ask turtles [set size 1]
  ]
end 

to layout
  ;; the number 3 here is arbitrary; more repetitions slows down the
  ;; model, but too few gives poor layouts
  repeat 3 [
    ;; the more turtles we have to fit into the same amount of space,
    ;; the smaller the inputs to layout-spring we'll need to use
    let factor sqrt count turtles
    ;; numbers here are arbitrarily chosen for pleasing appearance
    layout-spring turtles links (1 / factor) (7 / factor) (1 / factor)
    display  ;; for smooth animation
  ]
  ;; don't bump the edges of the world
  let x-offset max [xcor] of turtles + min [xcor] of turtles
  let y-offset max [ycor] of turtles + min [ycor] of turtles
  ;; big jumps look funny, so only adjust a little each time
  set x-offset limit-magnitude x-offset 0.1
  set y-offset limit-magnitude y-offset 0.1
  ask turtles [ setxy (xcor - x-offset / 2) (ycor - y-offset / 2) ]
end 

to-report limit-magnitude [number limit]
  if number > limit [ report limit ]
  if number < (- limit) [ report (- limit) ]
  report number
end 

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;;;Meme Procedures;;;
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;; seed a trend to one random person

to seed-trend
  ask turtles [
    set popularity count my-links
  ]
  ask n-of meme-count turtles [
    set color item (interest-category + 1) base-colors
    set trendy? true
    set trend-setter? true
    set trend-category interest-category ;; trend is given a "type" corresponding to the turtle's interest
    set times-heard 1
    set size 1.5 ;; distinguish the trend-setter
  ]
end 

;; run the model

to go
  ask turtles with [trendy? = true][ ;; ask the trendy turtles to spread the trend
    spread-trend
  ]
  ;; if media is turned on, every  ticks a TV will flash in a patch with a turtle on it.
  if media?[
    ;; a TV will appear once every MEDIA-FREQUENCY ticks
    if ticks mod (media-frequency / 2) = 0 [
      ask one-of patches with [count turtles-here > 0] [
        media-trend
      ]
    ]
    ;; reset TV patches to black
    if ticks mod media-frequency = 0 [
      ask patches with [pcolor = white][
        set category -1
        set pcolor black
      ]
    ]
  ]
  ;; fit to the chosen color-mode
     recolor
  ;; if all of the turtles now follow the trend, stop. The model is over.
  if all? turtles [trendy? = true] [stop]
  tick
end 

;; spreading the trend

to spread-trend
  ;; turtles try to spread the trend to one of their linked neighbors
  let target nobody
  set target one-of link-neighbors
  if target != nobody [
    ask target [
      ; when stubborn is on and the target is trendy, the only effect of asking the target will be to increment times heard
      ifelse stubborn? and member? self (turtles with [trendy? = true])  [ set times-heard times-heard + 1 ] [
      ;; diff represents the difference between the turtle's interest category and the category of the trend.
      ;; the smaller the difference, the higher the probability that the trend will be passed to that turtle.
      ;; (i.e. if difference = 0, random number is chosen between 0 and 9. if difference = 9, random number is chosen between 0 and 99
      let diff (interest-category - [trend-category] of myself)
        if 0 = random (10 * (1 + (abs diff))) [
          set color [color] of myself
          set trendy? true
          ;; if the turtle has already adopted the trend from media,
          ;; leave it be. otherwise, set its source to "friend"
          if trend-source != "media" [
            set trend-source "friend"
          ]
          set trend-category [trend-category] of myself
        ]
        set times-heard times-heard + 1
      ]
    ]
    ;; if a trend spreads between 2 turtles, turn the link between them red
    ;; (or blue or green-83 depending on the color-mode)
    ask links [
      if all? both-ends [trendy? = true]
        [ ifelse color-mode = 0 or color-mode = 1
          [set color red]
          [ifelse color-mode = 2
            [set color blue]
            [set color 83]
          ]
        ]
    ]
  ]
end 

;; when media? is true, patches run this procedure, representing TV-watching.
;; assume that a turtle will accept a trend regardless of category with media exposure

to media-trend
  set pcolor white ;; the turtle watches TV
  ;; the TV broadcasts the current trend
  set category [trend-category] of one-of turtles with [trend-setter? = true]
  ;; the media will try to influence one of the turtles on the TV patch
  let watcher one-of turtles-here
  if watcher != nobody [
    ask watcher[
      set times-heard times-heard + 1
      if random 10 <= media-influence [
      set color item ([category] of myself + 1) base-colors
      set trendy? true
      ;; if the turtle has already adopted the trend from a friend,
      ;; leave it be. otherwise, set its source to "media"
      if trend-source != "friend" [
        set trend-source "media"
      ]
      ;; they now follow the trend, therefore housing the same TREND-CATEGORY as every other TRENDY? turtle
      set trend-category [category] of myself
      ]
    ]
  ]
end 

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;;;Recoloring Procedures;;;
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;; procedure to recolor to the default scheme -- color-mode = 0
;; not blue = trendy, blue = not trendy

to recolor-default
  ask turtles [
    ifelse trendy? = true
      [set color item (trend-category + 1) base-colors]
      [set color gray]
  ]
  ask patches with [category = -1] [set pcolor black]
  ask links with [color = 83 or color = blue] [set color red]
end 

;; procedure to recolor to show source (friend vs media) -- color-mode = 1
;; "friend" = red, "media" = yellow, "not trendy" = blue

to recolor-by-source
  ask patches with [category = -1] [set pcolor black]
  ask turtles with [trend-source = "media"] [set color yellow]
  ask turtles with [trend-source = "friend"] [set color red]
  ask turtles with [trend-source = 0] [set color blue]
  ask links with [color = 83 or color = blue] [set color red]
end 

;; procedure to recolor to display the number of times heard -- color-mode = 2
;; lighter = more times heard, darker = fewer times heard

to recolor-by-times-heard
  ask patches with [category = -1] [set pcolor 3]
  ask turtles [set color scale-color green times-heard 0 world-width * 2]
  ask links with [color = red or color = 83] [set color blue]
end 

;; procedure to recolor to show popularity levels -- color-mode = 3
;; lighter = higher popularity (i.e. degree), darker = lower popularity

to recolor-by-popularity
  ask patches with [category = -1] [set pcolor 3]
  ask turtles [set color scale-color violet popularity 0 world-width * 2]
  ask links with [color = red or color = blue] [set color 83]
end 

;; procedure to recolor according to interest-category of meme

to recolor-by-trend
end 

;; procedure to recolor while the "go" function is running

to recolor
  ifelse color-mode = 0
    [recolor-default]
    [ ifelse color-mode = 1
      [recolor-by-source]
      [ifelse color-mode = 2
        [recolor-by-times-heard]
        [recolor-by-popularity]
      ]
    ]
end 

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;;;   Plot Reporters    ;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;

to-report current-trends
  show [trend-category] of n-of meme-count turtles with [trend-setter? = true]
end 

to-report fads
  report n-values meme-count [ i -> i = [trend-category] of turtles with [trend-setter? = true] ]
end