The Chaos Game

Random moves, perfect fractals

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The chaos game: jump part of the way to a random corner, over and over.
• Random order, but always the same final fractal (Sierpinski for 3 corners, halfway).
• Copies must leave gaps: 4 corners at halfway just fill the square.
• Iterated function systems draw ferns and other natural shapes.

Steps

1. A random walk
2. Play the chaos game
3. Why the holes?
4. Other shapes
5. Four corners, halfway
6. Barnsley’s fern
7. A pentagonal fractal