The Dragon Curve

Folding paper, recursively

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

• Unfolding a strip folded n times gives 2ⁿ − 1 right-angle turns.
• Next sequence = previous, R, previous reversed and flipped.
• The limit is the dragon curve, which never crosses itself and tiles the plane.

Steps

1. Fold, fold, fold
2. Counting creases
3. Grow the dragon
4. Unfolding the dragon
5. The next sequence
6. How long a list?
7. Any single turn