More on Lindenmayer Systems
We briefly explored Lindenmayer systems (or L-systems) in an old post: Toying with Basic Fractals. We quickly reviewed this method for creation of an approximation to fractals, and displayed an example (the Koch snowflake) based on tikz libraries.
I would like to show a few more examples of beautiful curves generated with this technique, together with their generating axiom, rules and parameters. Feel free to click on each of the images below to download a larger version.
Note that any coding language with plotting capabilities should be able to tackle this project. I used once again tikz for , but this time with the tikzlibrary lindenmayersystems.
Would you like to experiment a little with axioms, rules and parameters, and obtain some new pleasant curves with this method? If the mathematical properties of the fractal that they approximate are interesting enough, I bet you could attach your name to them. Like the astronomer that finds through her telescope a new object in the sky, or the zoologist that discover a new species of spider in the forest.
Hi, what does F stand for? Would you mind providing the LaTeX code of these examples, please?
From the tikz manual: “F moves forward a certain distance, drawing a line.”
Look for example at the code of the Dragon curve:
%%%%%%%%% start of code %%%%%%%%%
\pgfdeclarelindenmayersystem{Dragon curve}{
\rule{X -> X+YF+}
\rule{Y -> -FX-Y}}
\begin{tikzpicture}[color=blue]
\draw [l-system={Dragon curve, axiom=X, order=11, step=5pt, angle=90}] lindenmayer system;
\end{tikzpicture}
%%%%%%%%% end of code %%%%%%%%%