Chaos Game Regular polygon of any size

1 collaborator

WHAT IS IT?

Thhis is using NetLogo to play the Chaos Game. In the Game, using two very simple rules, beautiful fractal pictures are generated. The rules are: In a regula polygon of n number of side, it has n number of apices. Into that space, a random spot is chosen as the starting point. Throw a die, and depending on the result of the throw, the next point chosen will be along the line that leads from that point to the indicated apex. How far along that line is the point going to be placed? In the original Chaos Game with the triangle, the point is midway along that ine, or r = 0.5. But that could be changed.

HOW IT WORKS

This program allows one to experiment with regular polygons of virtually any number of sides up to 360.

HOW TO USE IT

Select the number of sides you want the polygon to be by using the slider number-of-sides.Then choose "r" as mentioned above by using the slider "factor"

THINGS TO NOTICE

The classical Chaos Game was done on a triangle with r = 0,5 and it results in the Sierpenski triangle. Try the other polygons, and vary the "factor"

THINGS TO TRY

Try the other polygons and vary the "factor"

EXTENDING THE MODEL

what if the "factor" itself is a random number during the run. Try changing the code and see.

NETLOGO FEATURES

(interesting or unusual features of NetLogo that the model uses, particularly in the Code tab; or where workarounds were needed for missing features)

RELATED MODELS

(models in the NetLogo Models Library and elsewhere which are of related interest)

CREDITS AND REFERENCES

Written by Dr. Ronald P. Ng Singapore (e-mail address: ronaldpaul.ng@gmail.com

Comments and Questions

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Click to Run Model

globals [turtleX
         turtleY
         newXcor  ; the new xcor which the turtle will go to
         newYcor  ; the new ycor which the turtle will go to
         turtleDistance ; thd distance the turtle has to travel
         worldLength
        ]

to setup
  ca
  ;; with the worldLength, excessLength and octogonSide length set up, these data will be used
  ;; in defining the points of the octogon

  set worldLength max-pxcor  ;; that being the size of the world



  crt 2 [
          set color white
          set size 10]
  ask turtle 0 [setxy random-xcor random-ycor
                hide-turtle]
  ask turtle 1 [setxy 0 0
                face patch 0 160
                hide-turtle
                ]

  reset-ticks
end 

to go

  find-new-position ;use tutle 1
  set turtlex  [xcor] of  turtle 0
  set turtley [ycor] of turtle 0
  ask patch turtlex turtley [set pcolor green]
  move-new-position
  if ticks > max-ticks [stop]

  tick
end 

to move-new-position

  ask turtle 0 [set turtleDistance distancexy newXcor newYcor
                             face patch newXcor newYcor
                             fd turtleDistance * factor ]
  ask patch newXcor newYcor [set pcolor green]
end 

to find-new-position
  let random-turn random number-of-sides * (360 / number-of-sides)
  ask turtle 1 [rt (random-turn)
                fd 380]
    set newXcor  [xcor] of turtle 1
    set newYcor  [ycor] of turtle 1
  ask turtle 1 [setxy 0 0
                face patch 0 380]
end

There is only one version of this model, created over 2 years ago by Ronald Paul Ng.

Attached files

File	Type	Description	Last updated
Chaos Game Regular polygon of any size.png	preview	Preview for 'Chaos Game Regular polygon of any size'	over 2 years ago, by Ronald Paul Ng	Download

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