Dragon Curve

The Dragon Curve (specifically, the Heighway dragon, named after physicist John Heighway) can be built physically: take a long strip of paper, fold it in half repeatedly always in the same direction, then unfold it so every crease opens to exactly 90°. The resulting zigzag path, in the limit of infinitely many folds, is this famous fractal — a curve that never crosses itself, yet fills a bounded, densely-textured region of the plane with an intricate self-similar boundary. It was studied by physicists in the 1960s (including Heighway) and later popularized by Martin Gardner's Scientific American column, and became especially well known for tiling the plane when four copies are fitted together. Each additional fold exactly doubles the number of straight segments in the curve, making it a natural fit for a simple recursive rule (an L-system) rather than a closed-form equation.