James Lemin

L-System Explorations

L-System Explorations

A couple of years ago, I briefly played with a Python script to generate svgs based on L-Systems. The code was crude, generated a worrying amount of swastika-like images but it was fun to play with. The initial script suffered some logical issues, such as miss-applying rules, not using the extended syntax, and having a crude method of image generation - calling the script would generate a pseudo-random result each time. At the time, these were shortcomings that, though mildly annoying, were easy enough to work around through brute-forcing the script; generating hundreds of images, and picking out the most interesting ones.

Last week, I returned to the idea, fixing logical bugs, and building out functionality to explore the idea more. Beyond fixing the logical issues, my boals were:

My implementation is available here.

The script still has randomness at its heart, but it's now possible to create fractal-like images with a greater degree of control:

fractal-like image

Similarly, more traditional "nature-like" images are possible:

fractal tree

Using the Script

Calling the script with no parameters retains the original behaviour; a random set of rules will be created. The rules are validated to ensure pushes and pops are matched, and opposing directives are not placed next to each other (e.g., + and -).

python3 lsys.py

There is a configuration file which sets defaults. You can either update these configuration items, or pass the parameters directly to the script. For instance

# Number of iterations to apply the L-System rules to the axiom tree
RECURSION_DEPTH = 13

in config.toml is equivalent to passing --recursion 13 to the script:

python3 lsys_main.py --recursion 13

The resulting file will have a comment describing the rules to generate it:

<!--
TITLE: LSYS PARAMS
PARADIGM: geometric
N: 13
AXIOM: F
RULES: {'F': 'FF+'}
INITIAL_ANGLE: 90
ROTATE_ANGLE: 120.0
LINE_LENGTH: 150
CREATED: 2026-07-17 18:51:54
-->

You could use these definitions to manually create a variation, but there is a --read option which'll do this for you:

❯ python3 lsys_main.py --read output/F→FF+.svg

which outputs the following:

--rules "'F': 'FF+'" --axiom F --recursion 13 --initial-angle 90 --rotation 120.0

which can then be tweaked to generate variations on the first image.

Perhaps more usefully, there is also a --variant flag which will generate a variant of the image, based on the original rules:

❯ python3 lsys_main.py --variant output/F→FF+.svg

there is also an --iterate flag which will generate a series of images, each one a variant of the previous one:

❯ # create five variants of the original image
❯ python3 lsys_main.py --iterate output/F→FF+.svg -n 5

All of these features and more can be explored using the script's --help flag:

L-System SVG Generator

options:
  -h, --help            show this help message and exit
  --rules RULES         User-defined L-System rules dictionary (or literal string)
  --axiom AXIOM         Axiom for the L-System
  --initial-angle INITIAL_ANGLE
                        Initial angle for the L-System
  --rotation ROTATION   Rotation angle for the L-System
  --recursion RECURSION
                        Recursion depth for the L-System (overrides config)
  --title TITLE         Title printed in logs
  --paradigm {geometric,stochastic,extended-geometric,extended-stochastic}
                        Rule generation mode
  --bleed BLEED         Margin padding (in mm)
  --options-per-rule OPTIONS_PER_RULE
                        Rule variations per char for stochastic
  --ppmm PPMM           Pixels per mm
  --paper-size PAPER_SIZE PAPER_SIZE
                        Paper size width and height (mm)
  --background-color BACKGROUND_COLOR
                        Background color
  --precision PRECISION
                        Decimal places to round geometry
  --angle-divisors ANGLE_DIVISORS [ANGLE_DIVISORS ...]
                        Acceptable divisors of 360
  --output-dir OUTPUT_DIR
                        Directory path for SVG files
  --scale SCALE         Scale multiplier for length (< >)
  --angle-increment ANGLE_INCREMENT
                        Angle increment for rotation ( ( ) )
  --weight-increment WEIGHT_INCREMENT
                        Weight increment for line thickness (# !)
  --read READ           Read an SVG file and output the command line arguments to recreate it
  --variant VARIANT     Generate a systematic variant of an existing SVG file
  --iterate ITERATE     Progressively generate iterations of an existing SVG file
  -n, --iterations ITERATIONS
                        Number of iterations to generate (used with --iterate)
  --filename {datetime,rules,unix}
                        Syntax for generating output filenames