Bifurcation diagram for the logistic map

 globals [     ;; setting the globals for the model functioning
  mylist-x
  mylist-r
  num-iterations
  axis
  F-const?
 ]

breed [ m-turtles m-turtle ]    ;; these are turtles to be ploted on
                                ;; on bifurcation diagram
patches-own [    ;; properties of the patches used
  alpha          ;; to set up X and Y axes
  omega
]

to setup   ;; general setup procedure
  ca
  set mylist-x  list (0) (0.5)     ;; setting the list for turtles x-coordinates
  set mylist-r list  (0) (0.95)    ;; setting the list for turtles y-coordinates
  create-axis                   ;; creating coordinates axes
  setup-alpha                   ;; and their components
  setup-beta-omega
  set num-iterations 20325    ;; this is the max number of iterates which
                              ;; "keeps" the results of iterations in the
                              ;; limits of the model world
  reset-ticks
end 

to create-axis
  ask patches with [ pxcor = 0 ] [ set pcolor white ]
  ask patches with [ pycor = 0 ] [ set pcolor white ]
end 

to setup-alpha
  ask patch -4 -4
  [ set plabel "0"
    set plabel-color white ]
  ask patch -4 190
  [ set plabel "f (x)"
    set plabel-color white
    ]
  ask patch 390 -7
  [ set plabel "r-parameter"
    set plabel-color white
   ]
end 

to setup-beta-omega
ask patch 105 5
[ set plabel "1.0"
set plabel-color white
  ]

  ask patch 205 5
[ set plabel "2.0"
set plabel-color white
  ]

  ask patch 255 5
[ set plabel "2.5"
set plabel-color white
  ]

  ask patch 305 5
[ set plabel "3.0"
set plabel-color white
  ]

  ask patch 355 5
[ set plabel "3.5"
set plabel-color white
  ]

  ask patch 395 5
[ set plabel "4.0"
set plabel-color white
  ]

  ask patch 10 100
[ set plabel "0.5"
set plabel-color white
  ]
    ask patch 10 195
[ set plabel "1.0"
set plabel-color white
  ]
end 

to go                                        ;; procedure of iteration

  set mylist-x lput result mylist-x               ;; generation of the list with
  repeat 50 [set mylist-x lput result mylist-x]   ;; x-coordinates of turtles

  set mylist-r lput result-r mylist-r         ;; generation of the list with
                                              ;; x-coordinates of turtles
  if ticks >= Num-iterations [ stop ]    ;; condition for stopping the model once
                                         ;; the preset number of iterations is reached
  create-m-turtles 1 [        ;; creating a turtle every iteration/tick
    set color green           ;; and ploting it according to the coordinates
    set shape "circle"        ;; as values in the respective lists
    set size 0.5
    set xcor (last mylist-r) * 100
    set ycor (last mylist-x) * 200
    ]
  tick
end 

to-report result                                               ;; reports the result of iterations
  report  last mylist-r * last mylist-x * (1 - last mylist-x)
end 

to-report result-r                  ;; reports the result of r-increments with every iteration/tick
  report last mylist-r + 0.00015
end 

to mark                       ;; marking the bifurcations by creating red color turtles
                              ;; in respective zones
  if ticks >= 20320 [         ;; condition that makes respective button active only after
                              ;; iterations are completed
  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 300
     set ycor 133
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 354
     set ycor 164
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 345
     set ycor 170
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 354
     set ycor 177
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 345
     set ycor 88
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 354
     set ycor 105
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 354
     set ycor 73
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 356.37
     set ycor 69.43
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 356.41
     set ycor 74.92
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 356.43
     set ycor 98.16
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 356.47
     set ycor 110.93
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 356.42
     set ycor 161.49
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 356.46
     set ycor 167.02
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 356.44
     set ycor 176.12
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 356.48
     set ycor 178.16
   ]
  ]
end 

to mark-pw                         ;; marking a periodic window

  if ticks >= 20320 [
  ask patches with [ pxcor = 380 ]
  [set pcolor red]
  ask patches with [ pxcor = 390 ]
  [set pcolor red]
  ]
end 

to calculate-feigenbaum-constant  ;; procedure ref. to Feigenbaum's constant: ploting
                                  ;; vertical lines aligned to bifurcations and marking
                                  ;; the distance between consecutive period-doublings with "L"
  if ticks >= 20320 [
                                    ;; condition that makes the procedure valid after the
  set F-const? true                 ;; preset number of iterations

  ask patches with [ pxcor = 300 ]
  [set pcolor white]
  ask patches with [ pxcor = 345 ]
  [set pcolor  white]
   ask patches with [ pxcor = 354 ]
  [set pcolor  white]
  ask patches with [ pxcor = 356 ]
  [set pcolor  white]

   ask patch 198 -7
  [ set plabel "L0"
    set plabel-color yellow
   ]

   ask patch 330 -7
  [ set plabel "L1"
    set plabel-color yellow
   ]

   ask patch 355 -7
  [ set plabel "L2/L3"
    set plabel-color yellow
   ]

   ask patch 100 155
   [ set plabel "Feigenbaum's constant = Li / Li+1"
    set plabel-color yellow
      ]
  ]
end 

to-report F-constant-1     ;; procedure for calculation of the 1st Feigenbaum's constant
  if F-const? = true       ;; based on x-coordinates of the turtles located in the bifurcations zones
  [                        ;; 'bifurcations zones'
  report (([xcor] of turtle 17294) - ([xcor] of turtle 16688)) /
         (([xcor] of turtle 17422) - ([xcor] of turtle 17292))
  ]
end