Interactive Lab / The Heighway Dragon Curve

Iterated Function System Discovered 1967 Dimension 2 (boundary)

The Heighway Dragon Curve

T0=(),Tn+1=Tn(+1)reverse(Tn)T_0 = (), \qquad T_{n+1} = T_n \frown (+1) \frown \mathrm{reverse}(-T_n)
Cool Fact
Fold a strip of paper in half repeatedly, always the same way, then unfold every crease to a right angle — the silhouette is a finite approximation of this exact curve. Like the Koch curve, it also has a well-known L-system encoding, even though this page draws it the paper-folding way.

Rendering…