Strange Attractors

This is an implementation of Numberphile’s ideas from their Chaos Game Video. Click on Run Simulation below to see the magic happen!

• Intro
• Tool
• Can you replicate these patterns?
  • Sierpinski Triangle
  • Sierpinski Tetrahedron
  • Sudoku
  • Big Sudoku
  • Octogon
  • Cursor
  • Falcon
  • Perspective
  • Tic Tac Toe
  • Trapezoid

Intro

In the plot you will see the latest point (orange) and a set of attractors. At every iteration, a random attractor is selected and the latest point becomes the midpoint between the attractor and the orange point. Repeat this thousands of times and fractals start to emerge.

You can play around with the list of attractors, number of iterations per simulation and the strength of the pull towards the attractor.

Tool

Can you replicate these patterns?

Sierpinski Triangle

Sierpinski Tetrahedron

Sudoku

Big Sudoku

Octogon

Cursor

Falcon

Perspective

Tic Tac Toe

Trapezoid