Yes — a space-filling curve maps a 1D line segment onto every point of a 2D region
In 1890, Giuseppe Peano showed that a continuous curve can visit every point inside a square. This is the curve's path (the image of a map from a line segment to the plane), not the graph of a single y = f(x), so it doesn't violate the vertical line test — the same point gets revisited, so the curve crosses itself rather than giving one output per x. It shocked mathematicians because a 1-dimensional line could fill a 2-dimensional area. The same space-filling idea now helps index geographic data so that nearby places stay close together in storage.
