Peano BasinWritten by Paul Bourke
The Peano Basin fractal documented in the 1890s as one of a series of curves described by Giuseppe Peano, another more well known example is this. It is space filling with fractal dimension of 2.
The Peano basin has been proposed as a mathematical model for river basin networks.
Figure 2.24 on Page 124 of Fractal River Basins: Chance and Self-Organization by Ignacio Rodríguez-Iturbe, Andrea Rinaldo