Moore curve

A Moore curve (after E. H. Moore) is a continuous fractal space-filling curve with a construction similar to the Hilbert curve.

Because the Moore curve is plane-filling, its Hausdorff dimension is 2.

The following figure shows the initial stages of the Moore curve.

Representation as Lindenmayer system

The Moore curve can be expressed by a rewrite system (L-system).

Alphabet: L, R

Constants: F, +, −

Axiom: LFL+F+LFL

Production rules:

L → −RF+LFL+FR−

R → +LF−RFR−FL+

Here, F means "draw forward", + means "turn left 90°", and − means "turn right 90°" (see turtle graphics).

Like the Hilbert curve, the Moore curve can be extended to three dimensions:

External links

• A. Bogomolny, Plane Filling Curves from Interactive Mathematics Miscellany and Puzzles

http://www.cut-the-knot.org/do_you_know/hilbert.shtml, Accessed 07 May 2008.

See also

• Hilbert curve
• Sierpiński curve
• z-order (curve)
• List of fractals by Hausdorff dimension