Monte Carlo Pi Model

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Firat Soylu (Author)

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Click to Run Model

globals [estimated-pi error-rate real-pi avg-pi circle-radius]

to setup 
  clear-all
  ;set real-pi 3.1415926535897
  set real-pi 4 * (count patches with [pcolor = yellow] / count patches)
  set circle-radius 200
  ask patches [
    if abs(pxcor) < circle-radius and abs(pycor) < circle-radius [set pcolor red]
    if distance patch 0 0 < circle-radius [set pcolor yellow]
  ]
  set sand-number 100
  reset-ticks
  set real-pi 4 * (count patches with [pcolor = yellow] / count patches)
end 

to incremental-go
  ifelse sand-number < max-sand-number [set sand-number sand-number + increment-by][stop]
  let i  0
  set avg-pi 0
  let accumulated-values 0
  while [i < sample-size] [
    ask turtles [die]
    throw-sand
    calculate-pi
    set accumulated-values accumulated-values + estimated-pi 
    set i (i + 1)
  ]
  set avg-pi  accumulated-values / sample-size
  show avg-pi
  tick
end 

to-report random-one ;reports 1 or -1
  report ifelse-value (random 2 = 0) [-1][1]
end 

to throw-sand
  set-default-shape turtles "circle"
  ifelse full-circle? = True 
  [
    ifelse grains-pile? = True
      [ create-turtles sand-number [set color black set size grain-size move-to one-of patches]]
      [create-turtles sand-number [set color black set size grain-size move-to one-of patches with [count turtles-here < 1]]]
  ]
  [
    ifelse grains-pile? = True
      [ create-turtles sand-number [set color black set size grain-size move-to one-of patches with [pxcor > 0 and pycor > 0]]]
      [create-turtles sand-number [set color black set size grain-size move-to one-of patches with [pxcor > 0 and pycor > 0 and count turtles-here < 1]]]
  ]   
end 

to calculate-pi
  let circle-turtles  turtle-set turtles with [[pcolor] of patch-here = yellow ]
  set estimated-pi 4 * count circle-turtles / count turtles
  set error-rate 100 * abs(estimated-pi - real-pi) / real-pi
end

There is only one version of this model, created over 12 years ago by Firat Soylu.

Attached files

File	Type	Description	Last updated
Monte Carlo Pi Model.png	preview	Preview for 'Monte Carlo Pi Model'	over 12 years ago, by Firat Soylu	Download

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