Chaos-game

Chaos-game preview image

1 collaborator

Jesus_marcano Jesus Marcano (Author)

Tags

(This model has yet to be categorized with any tags)
Visible to everyone | Changeable by everyone
Model was written in NetLogo 6.2.1-beta1 • Viewed 267 times • Downloaded 15 times • Run 0 times
Download the 'Chaos-game' modelDownload this modelEmbed this model

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


WHAT IS IT?

The chaos game is an algorithm first described by Michael Barnsley in 1988. Here's a YouTube video of him describing this game. http://youtu.be/MBhx4XXJOH8

HOW IT WORKS

Start with a triangle and many dots, then each dot ramdonly chooses a random vertex of the triangle and moves half the distance towards it in every time step. Note, the topology of the world is flat, not a donut.

HOW TO USE IT

"setup" places the vetices of the triangle and creates many dots all over the world. "go" starts the simulation.

THINGS TO NOTICE

The emergence of the Sierpinski triangle.

THINGS TO TRY

Try "watch one-of dots" button.

EXTENDING THE MODEL

Each dot jumps half the distance to a vertex. We could change that to 1/3 the distance for example.

NETLOGO FEATURES

I'm using a beta version of NetLogo and it's not breaking! (version 6.2.1-beta1)

RELATED MODELS

Example of other variations in Mathematica: http://mathworld.wolfram.com/ChaosGame.html

CREDITS AND REFERENCES

This program uploaded to Modeling Commons.

Comments and Questions

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

Click to Run Model

;; The chaos game
;; j.marcano Oct 8 2021

breed [vertices vertex] ;; these turtles are the vertices of the triangle
breed [dots dot] ;; these are dots that jump around following the game rules

to setup
  clear-all
  setup-vertices
  setup-dots
  reset-ticks
end 

to go
  ask dots [
    let this-vertex one-of vertices
    face this-vertex
    jump (distance this-vertex) / 2]
  tick
end 

to setup-vertices
  set-default-shape vertices "target"
  ;; ask the patches at the vertices of the triangle to each produce one vertex
  ask (patch-set patch -14 14 patch 14 14 patch 0 -14) [sprout-vertices 1]
end 

to setup-dots
  set-default-shape dots "dot"
  ;; create a bunch of dots
  create-dots 5500 [
    setxy random-xcor random-ycor
    set size 0.3] ; change the size value here if you can't see them
end 

There are 2 versions of this model.

Uploaded by When Description Download
Jesus Marcano over 2 years ago Chaos game first described by Michael Barnsley 1988 Download this version
Jesus Marcano over 2 years ago Initial upload Download this version

Attached files

File Type Description Last updated
Chaos-game.png preview Preview for 'Chaos-game' over 2 years ago, by Jesus Marcano Download

This model does not have any ancestors.

This model does not have any descendants.