Dragon curve fractal
Fold a strip of paper in half again and again, then open every fold to a right angle: the edge traces the dragon curve. Each step copies the whole curve, rotates the copy 90° about its end, and joins the two. Press Grow to watch the copy swing out.
Segments
Turns
End-to-end shrink per fold1/√2
Boundary dimension≈ 1.524
The curve never crosses itself, and four copies rotated about the start point tile the whole plane. Its turn sequence is the “regular paperfolding sequence”: the k-th turn is R or L depending on the bit just above the lowest 1-bit of k.