Chaos game

1 collaborator

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

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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 is only one version of this model, created almost 3 years ago by Jesus Marcano.

Attached files

File	Type	Description	Last updated
Chaos game.png	preview	Preview for 'Chaos game'	almost 3 years ago, by Jesus Marcano	Download

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