Sierpiński arrowhead curve

The Sierpiński arrowhead curve is a fractal curve similar in appearance and identical in limit to the Sierpiński triangle.

Evolution of Sierpiński arrowhead curve

Representation as Lindenmayer system

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

Alphabet: X, Y

Constants: F, +, −

Axiom: XF

Production rules:

X → YF + XF + Y

Y → XF − YF − X

Here, F means “draw forward”, + means “turn left 60°”, and − means “turn right 60°” (see turtle graphics).

Like many two-dimensional fractal curves, the Sierpiński arrowhead curve can be extended to three dimensions:

Literature

• Peitgen et al., Chaos and Fractals, Springer-Verlag, 1992.
• Roger T. Stevens, Fractal Programming in C, M&T Books, 1989.

See also

• List of fractals by Hausdorff dimension
• Sierpiński curve