Dragon Curve Generator

The Heighway dragon curve was first described by NASA physicists John Heighway, Bruce Banks, and William Harter. It can be created by repeatedly folding a strip of paper in half in the same direction, then unfolding to 90-degree angles. Two dragon curves tile the plane when placed back-to-back. The Hausdorff dimension is 2. The boundary of the dragon curve is itself a fractal.

The algorithm works by iteratively building a sequence of turns. Start with a single right turn [R]. Each iteration takes the current sequence, appends R, then appends the reverse of the sequence with each turn flipped (R becomes L, L becomes R). To draw: start heading right, and for each turn in the sequence, rotate 90 degrees in that direction and draw a unit-length segment. The result is scaled and centered to fit the canvas.