Space filling curve: Mathematical Analysis, Curve, Unit Square, Hypercube, Plane, Dragon Gosper Moore Sierpi¿ski Curve

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an N-dimensional hypercube). Because Giuseppe Peano (1858-1932) was the first to discover one, space-filling curves in the 2-dimensional plane are commonly called Peano curves.Intuitively, a "continuous curve" in 2 or 3 (or higher) dimensions can be thought of as the "path of a continuously moving point". To eliminate the inherent vagueness of this notion, brought to light by Peano's discovery, Jordan in 1887 introduced the following rigorous definition, which has since been adopted as the precise description of the notion of a "continuous curve"