Generative Algorithms: Lindenmayer-System (L-System)

An L-system or Lindenmayer system is a parallel rewriting system, namely a variant of a formal grammar (a set of rules and symbols), most famously used to model the growth processes of plant development, but also able to model the morphology of a variety of organisms.
L-systems can also be used to generate self-similar fractals such as iterated function systems. L-systems were introduced and developed in 1968 by the Hungarian theoretical biologist and botanist from the University of Utrecht, Aristid Lindenmayer (1925–1989).
For details and samples, check wikipedia

Koch Curve. Implemented with Grasshopper and RhinoScript.
download koch Curve sample...

Penrose Tiling. Implemented with Grasshopper and RhinoScript.
download Penrose Tiling sample...

Sierpinski Triangle. Implemented with Grasshopper and RhinoScript.
download Sierpinski Triangle sample...

Fractal Plant. Implemented with Grasshopper and RhinoScript.
download Fractal Plant sample...
GH_FractalPlant_LSystem_DynamicAngle.zip

Dragon Curve. Implemented with Grasshopper and RhinoScript.
download Dragon Curve sample...

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Comment by Leonid Krykhtin on June 16, 2009 at 1:01am: What do you mean by algorithm? A mathematical expression?

Comment by Rajaa Issa on June 14, 2009 at 3:17pm: Hi Leonid,
If you have an algorithm for a 3d fractal example, I'll be happy to write the code. Some of them it is only a matter of having multiple iterations using different initial string or location.

Comment by Rajaa Issa on June 14, 2009 at 3:14pm: Hi h8cru,
I don't have it, but you probably can simply rotate the reference plane and have additional iterations.

Comment by h8cru on June 14, 2009 at 10:54am: That seems very interesting! Do you have a Fractal Plant Script which works in 3D and not 2D?
It would be really wonderful if you or anyone could share such an example...
Thanks anyway

Comment by Leonid Krykhtin on June 13, 2009 at 2:47am: Cool! I was looking for this. Can you upload some other fractals that would be useful for designers and architects who is keen on creating something nature-like.