Giuseppe Peano (1858–1932) discovered this space-filling curve in
1890. Each iteration subdivides the square into a 3 by 3 grid, and
placing a copy of the current curve in each smaller square. The
curve obtained in the limit of this process is called the Peano
curve. This function maps the unit interval onto the unit square.
Furthermore, the final curve is also continuous yet nowhere
differentiable.
Bridges Finland Art Exhibition Catalog, p. 111, Edited by Conan Chadbourne, Robert Fathauer, Katie McCallum, and Nathan Selikoff, ISBN: 978-1-938664-20-5, Tessellations Publishing, 2016.
