Sierpiński arrowhead curve
- Sierpiński arrowhead curve
The Sierpiński arrowhead curve is a fractal curve similar in appearance and identical in limit to the Sierpiński triangle.
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.
ee also
* List of fractals by Hausdorff dimension
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