I love L-Systems! Really simple concept and implementation, but a huge variety of results and extensions.
In parallel of my studies, I created some years ago on the side an interactive app for generating and coloring L-Systems : https://epholys.itch.io/lsys . It's a bit rough, but I created a lot of interesting trees (all here : https://imgur.com/a/0Rx7uln) and included them as a zip file alongside the app.
This has L-systems for filling the plane with hats and spectres. It's a little ugly and slow because it keeps redrawing tile edges but it does the trick; it's compact enough that I managed to get the bbc micro bot to draw the spectres with a toot's worth of code
And this one draws the self-avoiding curve made by the F-clusters in the hat monotiling. It works slightly differently using a stack, which avoids some of the overdrawing in the systems above.
order: 10
axiom: FX
angle: 90
X -> X+FYF-
Y -> +FXF-Y
This avoids the self-intersections (like a similar depiction of the Hilbert and Gosper curves), yet it remains relatively simple, and reveals more of the structure inside the bulk of the curve.
It's especially pretty when completed into a twin-dragon with the axiom: FX+F+FX+F+ and same rules as above.
