Bifurcation diagram for iterated sin_f

Bifurcation diagram for iterated sin_f preview image

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 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
  ca
  set mylist-x  list (0) (0.5)     ;; setting the list for turtles x-coordinates
  set mylist-r list  (0) (30)      ;; setting the list for turtles y-coordinates
  set num-iterations 16900         ;; setting the number of iterations
  create-axis                      ;; creating coordinates axes
  setup-coordinates                ;; and their components
  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-coordinates
  ask patch 5 5
  [ set plabel "0"
    set plabel-color white ]

   ask patch 10 345
  [ set plabel "1.0"
    set plabel-color white ]

   ask patch -10 200
  [ set plabel "f (x)"
    set plabel-color white ]

   ask patch 150 -14
  [ set plabel "r-parameter"
    set plabel-color white ]

  ask patch -19 -5
  [ set plabel "30"
    set plabel-color white ]

   ask patch 7 -5
  [ set plabel "40"
    set plabel-color white ]

   ask patch 35 -5
  [ set plabel "50"
    set plabel-color white ]

   ask patch 65 -5
  [ set plabel "60"
    set plabel-color white ]

   ask patch 100 -5
  [ set plabel "70"
    set plabel-color white ]

   ask patch 135 -5
  [ set plabel "80"
    set plabel-color white ]

   ask patch 170 -5
  [ set plabel "90"
    set plabel-color white ]

  ask patch 205 -5
  [ set plabel "100"
    set plabel-color white ]

   ask patch 232 -5
  [ set plabel "110"
    set plabel-color white ]

  ask patch 234 5
  [ set plabel "114"
    set plabel-color red ]
end 

to go                       ;; procedure of iteration

  set mylist-x lput result mylist-x             ;; generation of the list with
  repeat 20 [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 after
                                         ;; the preset number of iterations
    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) * 2
    set ycor (last mylist-x) * 3
   ]

  tick
end 

to-report result             ;; reports the result of iterations
   report  last mylist-r * sin( pi * last mylist-x / 2)
end 

to-report result-r             ;; reports the result of r-increments with every iteration/tick
  report last mylist-r + 0.005
end 

to mark                    ;; marking the bifurcations by creating red color turtles
                           ;; in respective zones
  if ticks >= 16900 [   ;; condition that makes respective button active only after
                        ;; iterations are completed
  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 166
     set ycor 223
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 192
     set ycor 283
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 198
     set ycor 268
   ]


  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 197
     set ycor 272
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 192
     set ycor 152
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 198
     set ycor 124
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 197
     set ycor 180
   ]

  crt 1 [
    set color red
    set shape "circle"
     set size 2
     set xcor 196.88
     set ycor 294.58
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 197.99
     set ycor 293.4
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 197.94
     set ycor 277.31
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 197.12
     set ycor 127.85
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 198.04
     set ycor 131.96
   ]

  crt 1 [
     set color red
    set shape "circle"
     set size 2
     set xcor 197.96
     set ycor 296.84
   ]

  crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 198.07
     set ycor 168.56
   ]

    crt 1 [
     set color red
     set shape "circle"
     set size 2
     set xcor 198.11
     set ycor 189.32
   ]

  ]
end 

to mark-pw                          ;; marking a periodic window

  if ticks >= 16900 [
  ask patches with [ pxcor = 212 ]
  [set pcolor red]
  ask patches with [ pxcor = 222 ]
  [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 >= 16890 [
                              ;; condition that makes the procedure valid after the
    set F-const? true         ;; preset number of iterations

    ask patches with [ pxcor = 166 ]
  [set pcolor white]
    ask patches with [ pxcor = 192 ]
  [set pcolor  white]
    ask patches with [ pxcor = 197 ]
  [set pcolor  white]
    ask patches with [ pxcor = 199 ]
  [set pcolor  white]

   ask patch 116 10
  [ set plabel "L0"
    set plabel-color yellow
   ]

   ask patch 180 10
  [ set plabel "L1"
    set plabel-color yellow
   ]

   ask patch 205 10
  [ set plabel "L2/L3"
    set plabel-color yellow
   ]

   ask patch 130 300
   [ 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'
  report (([xcor] of turtle 13701) - ([xcor] of turtle 13215)) /
         (([xcor] of turtle 13806) - ([xcor] of turtle 13701))
  ]
end 

There is only one version of this model, created over 1 year ago by Victor Iapascurta.

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Bifurcation diagram for iterated sin_f.png preview Preview for 'Bifurcation diagram for iterated sin_f' over 1 year ago, by Victor Iapascurta Download

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