Elementary Rules

256 tiny universes

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• An elementary cellular automaton updates each cell from its 3-cell neighbourhood.
• There are 256 rules, numbered by their binary output table.
• Rule 90 makes the Sierpiński triangle, using addition mod 2.

Steps

1. The setup
2. Counting rules
3. Name a rule
4. Watch them grow
5. A shifting rule
6. Rule 90