An L-system, or Lindenmayer system, is a parallel rewriting system and a type of formal grammar used to model the growth of biological organisms. L-systems can also be used to generate space-filling curves and to describe mathematical processes, such as fractals, through the iteration of production rules.
Here are some L-system rules I gathered from various sources. I apologize for missing attributions; some original sources are lost and I need to recover them. Each curve is interactive and can be modified as needed.
F: Move forward by line length drawing a line
-: Turn left by turning angle
+: Turn right by turning angle
A: An axiom
A => B: A rule
setting = value: A configuration setting
The intentional decision has been made not to support branching, usually represented by [ and ] symbols. I acknowledge that these are powerful operations, yet I prefer to implement them as a fork operation, and I didn't explore this space.
This is a single-file static website that implements an L-system fractal as a web component. CodeMirror is used as an external dependency for a code editor. To use the website, open index.html in a browser.
Web Component example:
<web-fractal
data-name="H-indexing"
data-creator="oneearedrabbit"
data-creation-date="2024-02-12"
data-description="A new two-dimensional (2-D) indexing scheme called H-indexing, which has superior (possibly optimal) locality in comparison with the well-known Hilbert indexings. H-indexings form a Hamiltonian cycle and we prove that they are optimally locality-preserving among all cyclic indexings."
>
order = 4
angle = 90
A => BF-F-BFFFC-F-FC+F+BF-F-BFFFC-F-FC
B => BFFFC-F-FC+F+B
C => C+F+BF-F-BFFFC
</web-fractal>
Found a typo or have an L-system to suggest? Noticed an attribution mistake or want to clarify something? Please file a ticket: https://github.com/oneearedrabbit/l-sys-playground/issues
