The Dragon curve is a classic example of a recursively-generated fractal shape. Benoit Mandelbrot called it the "Harter-Heighway" dragon curve and it formed the subject of one of Martin Gardner's Mathematical Games columns in Scientific American in 1967.1 The Dragon curve fills out an "island" of positive area with a fractal boundary.
1. Gardner, Martin. Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleights-of-Mind from Scientific American. New York: Vintage, 1978.