Lindenmayer L-system + Turtle Rendering

Math essence

Each iteration replaces every symbol S in the string by rules[S] (or S unchanged). The turtle maintains (x, y, theta) plus a stack; F pushes a line segment, +/- rotate by angle_deg, [/] save/restore state. Rendering is an n-segment linspace per F step blended onto the canvas with a 3x3 ink stamp for thickness.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/reas_processing/lindenmayer/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


PRESETS: dict[str, dict] = {
    "bush": {
        "axiom": "F",
        "rules": {"F": "F[+F]F[-F]F"},
        "angle": 22.5,
        "iterations": 4,
        "start_step": 6.0,
    },
    "stochastic_tree": {
        "axiom": "F",
        "rules": {"F": "F[+F]F[-F][F]"},
        "angle": 25.0,
        "iterations": 5,
        "start_step": 8.0,
    },
    "fractal_weed": {
        "axiom": "X",
        "rules": {"X": "F+[[X]-X]-F[-FX]+X", "F": "FF"},
        "angle": 22.5,
        "iterations": 5,
        "start_step": 5.0,
    },
    "koch_snowflake": {
        "axiom": "F++F++F",
        "rules": {"F": "F-F++F-F"},
        "angle": 60.0,
        "iterations": 4,
        "start_step": 8.0,
    },
}


class Lindenmayer:
    """Lindenmayer L-system string rewriting with 2-D turtle rendering.

    An axiom is iteratively rewritten using stochastic or deterministic
    production rules, then interpreted by a turtle drawing primitive
    (``F`` = forward, ``+/-`` = turn, ``[`` / ``]`` = push / pop). The
    output is a graceful fractal curve grown once and rendered onto the
    canvas. This is the canonical L-system + turtle pipeline featured in
    Aristid Lindenmayer's biological models and in Casey Reas's
    ``Form+Code`` chapter on recursive growth.
    """

    family: ClassVar[str] = "reas_processing"
    sketch: ClassVar[str] = "lindenmayer"

    def __init__(
        self,
        dim: int = 600,
        preset: str = "bush",
        axiom: str | None = None,
        rules: dict[str, str] | None = None,