Bifurcation diagram for iterated sin_f

Bifurcation diagram for iterated sin_f preview image

1 collaborator

Tags

Visible to everyone | Changeable by everyone
Model was written in NetLogo 6.0.1 • Viewed 459 times • Downloaded 22 times • Run 0 times
Download the 'Bifurcation diagram for iterated sin_f' modelDownload this modelEmbed this model

Do you have questions or comments about this model? Ask them here! (You'll first need to log in.)


Info tab cannot be displayed because of an encoding error

Comments and Questions

Please start the discussion about this model! (You'll first need to log in.)

Click to Run Model

 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 almost 7 years ago by Victor Iapascurta.

Attached files

File Type Description Last updated
Bifurcation diagram for iterated sin_f.png preview Preview for 'Bifurcation diagram for iterated sin_f' almost 7 years ago, by Victor Iapascurta Download

This model does not have any ancestors.

This model does not have any descendants.