Monte Carlo Pi 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