Peano Curve

A number of fractal curves are associated with Peano.

The Peano curve is the fractal curve illustrated above which can be written as a Lindenmayer system.

The th iteration of the Peano curve illustrated above curve is implemented in the Wolfram Language as PeanoCurve[n].

REFERENCES:

Dickau, R. M. "Two-Dimensional L-Systems." http://mathforum.org/advanced/robertd/lsys2d.html.

Hilbert, D. "Über die stetige Abbildung einer Linie auf ein Flachenstück." Math. Ann. 38, 459-460, 1891.

Mandelbrot, B. B. The Fractal Geometry of Nature. New York: W. H. Freeman, pp. 62-63, 1983.

Peano, G. "Sur une courbe, qui remplit une aire plane." Math. Ann. 36, 157-160, 1890.

Wagon, S. Mathematica in Action. New York: W. H. Freeman, p. 207, 1991.