Does there exist an L-system for the sierpiński curve I was going through a list of space-filling fractals and their L-systems. Even though there is an L-system for the sierpiński arrowhead curve, I am unable to find an L-system for the sierpiński curve. Is there any L-system for this? The curve I am referring to is this: 
edit: 
An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures.
For example, Each order of Hilbert curve can be obtained using the L-system as given below
Alphabet : A, B
Constants : F + −
Axiom : A
Production rules:
A → − B F + A F A + F B −
B → + A F − B F B − F A +
"F" means "draw forward", "−" means "turn left 90°", "+" means "turn right 90°" and "A" and "B" are ignored during drawing. Commonly Turtle graphics is used to draw the curve

Axiom : F--XF--F--XF
Rule : X -> XF+F+XF--F--XF+F+X
Angle : 45
I too was surprised not to be able to find an L-system encoding of this famous curve. I made this one by moding the code for the Square Sierpinski curve.
The curve is usually shown with 2 different edge lengths but I guess that's just aesthetics.  
