Floraform Growth

Math essence

Each tendril integrates x_{t+1} = x_t + L·cos(theta_t + eta_t) where eta_t ~ N(0, sigma^2) is a bending noise; remaining length decreases by L each step. Once length falls below a threshold the tendril spawns 1-2 children whose initial budget shrinks geometrically with depth (growth_decay^depth). A hard cap on the branch population plus a growth-decay with depth keeps the figure bounded and fractal-like.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/nervous_system_hansmeyer/FloraformGrowth/reference.py

from __future__ import annotations

from typing import ClassVar

import imageio.v2 as imageio
import numpy as np


class FloraformGrowth:
    family: ClassVar[str] = "nervous_system_hansmeyer"
    sketch: ClassVar[str] = "FloraformGrowth"

    def __init__(
        self,
        dim: int = 600,
        n_initial_branches: int = 6,
        init_length: float = 0.35,
        extension_step: float = 0.006,
        split_length: float = 0.12,
        split_curvature_min: float = 0.55,
        branch_prob: float = 0.25,
        branch_jitter: float = 0.85,
        bend_noise: float = 0.13,
        growth_decay: float = 0.88,
        max_branches: int = 4000,
        max_steps: int = 600,
        bg_color: tuple[int, int, int] = (10, 14, 18),
        vein_color: tuple[int, int, int] = (190, 220, 240),
        accent_color: tuple[int, int, int] = (255, 170, 110),
        seed: int | None = None,
    ) -> None:
        self.dim = dim
        self.n_initial_branches = n_initial_branches
        self.init_length = init_length
        self.extension_step = extension_step
        self.split_length = split_length
        self.split_curvature_min = split_curvature_min
        self.branch_prob = branch_prob
        self.branch_jitter = branch_jitter
        self.bend_noise = bend_noise
        self.growth_decay = growth_decay
        self.max_branches = max_branches
        self.max_steps = max_steps
        self.bg_color = np.array(bg_color, dtype=np.uint8)
        self.vein_color = np.array(vein_color, dtype=np.uint8)
        self.accent_color = np.array(accent_color, dtype=np.uint8)
        self._seed = seed
        self.rng = np.random.default_rng(seed)
        self.canvas = np.full((dim, dim, 3), self.bg_color, dtype=np.uint8)
        self._branches: list[dict] = []
        self._stage = 0
        self.time = 0
        self.reset()

    def reset(self, seed: int | None = None) -> None:
        if seed is not None:
            self._seed = seed
        self.rng = np.random.default_rng(self._seed)
        self.canvas = np.full((self.dim, self.dim, 3), self.bg_color, dtype=np.uint8)
        cx = self.dim / 2.0