Superstition

 breed [cats cat]
breed [humans human]

globals [number-superstitous probability-list number-of-switches human-influence-range belief-influence]
humans-own [alpha superstitious? red-count cat-sighting-memory introduced?]

to setup
  clear-all
  reset-ticks
  set human-influence-range 5
  set number-of-switches 0
  set belief-influence 24
  set-default-shape humans "person"
  set-default-shape cats "wolf"
  setup-consideration-math
  create-cats number-of-cats
  [
    set color gray
    setxy random-xcor random-ycor
  ]
  create-humans 75
  [
    set color blue
    set introduced? false
    set cat-sighting-memory n-values memory-length [0] ;; Start by remembering no red patches under cats
    setxy random-xcor random-ycor
    set alpha random-normal initial-average-alpha 5
    set superstitious? false
    set red-count 1 ;; Avoids starting out with unrealistic probabilities, defaults to .33 or .66 for red-probability
  ]
end 

to go
  color-patches
  ask cats [
    cat-wiggle
  ]
  ask humans [
    wiggle
    adjust-alpha
    look
  ]
  tick

  ;set c c + count patches with [pcolor = red and any? cats-here] / count patches with [pcolor = red]
  ;set true-p c / ticks
  ;;set avg-alpha (sum [alpha] of n-of 20 humans) / 20

  set number-superstitous count humans with [superstitious?]
end 

to cat-wiggle ;;cat procedure
   ;;cats move more slowly than humans, so that humans probably don't see the same cat twice
  rt 30
  lt 30
  fd .1
end 

to color-patches
  if ticks mod 50 = 0 [
    ask patches [
      ifelse random 100 < red-patch-percentage
      [set pcolor red]
      [set pcolor black]
    ]
  ]
end 

to adjust-alpha ; human procedure
  if any? humans in-radius human-influence-range with [superstitious?]
  [
    set alpha alpha + other-human-influence
    set introduced? true
  ]
  if introduced? and not any? humans in-radius human-influence-range with [superstitious?]
  [
    set alpha alpha - other-human-influence / superstition-influence-bias
  ]

  if alpha < 0 [set alpha 0]
  if alpha > 100 [set alpha 100]
end 

to wiggle ; human procedure
  ifelse superstitious? and danger?
  [face max-one-of cats [distance self]
    rt 180
    rt random 45
    lt random 45
    fd 3]
  [
  rt random 90
  lt random 90
  fd 3]
end 

to look
  if any? neighbors with [pcolor = red] [set red-count red-count + 1]
  if any? neighbors with [any? cats-here] [
    let patches-sighted count neighbors with [pcolor = red and any? cats-here]
    ifelse patches-sighted = 0 and superstitious?
    [ if random 100 > alpha [
      set cat-sighting-memory bl fput count neighbors with [pcolor = red and any? cats-here] cat-sighting-memory
    ]]
    [set cat-sighting-memory bl fput count neighbors with [pcolor = red and any? cats-here] cat-sighting-memory] ;;Remembers the danger of the patch, or 0 if there aren't any red patches under cats
    consider
  ]
end 


;; Calculates the probability of having seen n or more red patches out of memory-length viewings by starting with the probability of 0 or more and removing the probability of 0-(n-1) using a binomial distribution.

to consider ;human procedure
  let p 1.0   ;Represents probability 0 or more
  let n 0
  let danger-impression 0
  let red-probability red-count / (ticks + 3 )
  foreach cat-sighting-memory [   ; Subtracts probability of seeing n patches when memory contains n+1 cases of seeing a patch
    if ( ? >= 1)
    [ set p p - ((item n probability-list) * (1 - red-probability) ^ (memory-length - n) * (red-probability) ^ n )
      set n n + 1
    ]
    set danger-impression danger-impression + ? - 1
  ]

  ifelse p * 100 <= alpha + danger-impression / memory-length
    [
      if not superstitious? [
        set number-of-switches number-of-switches + 1
        set alpha alpha + belief-influence
        set cat-sighting-memory n-values memory-length [1]
        set superstitious? true
        set color orange
        ask humans in-radius human-influence-range [set alpha alpha + other-human-influence]
      ]

    ]
    [
      if superstitious? [
        set number-of-switches number-of-switches + 1
        set superstitious? false
        set color blue
        ask humans in-radius human-influence-range [set alpha alpha - other-human-influence]
        set alpha alpha - belief-influence]
      ]
end 

;; Creates a list where [(item n list) == (memory-length choose n)]
;; seperated to clean up setup code and remove complicated math from it

to setup-consideration-math ;observer procedure
  set probability-list n-values (memory-length + 1) [?]
  let factorial-list (list)
  let factorial 1
  foreach probability-list [
    if ? > 0 [
      set factorial factorial * ?
    ]
    set factorial-list lput factorial factorial-list
  ]
  set probability-list map [(item (memory-length) factorial-list)/((item ? factorial-list) * (item ((memory-length) - ?) factorial-list))] probability-list
end