Main Vein

Math essence

The main vein integrates x_{t+1} = x_t + L·cos(theta_t), y_{t+1} = y_t + L·sin(theta_t), with theta_{t+1} = theta_t + A·sin(omega·t). At each step it spawns up to 3 offshoots with Bernoulli probability p; each offshoot runs the same dynamics for a finite life span with smaller amplitude. Stage progress is tracked so growth stops after max_stage steps regardless of vein position.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/complexification_net/mainVein/reference.py

from __future__ import annotations

from typing import ClassVar

import imageio.v2 as imageio
import numpy as np


class MainVein:
    family: ClassVar[str] = "complexification_net"
    sketch: ClassVar[str] = "mainVein"

    def __init__(
        self,
        dim: int = 500,
        max_segments: int = 240,
        segment_length: float = 4.0,
        meander_amp: float = 0.5,
        meander_freq_min: float = 0.005,
        meander_freq_max: float = 0.04,
        branch_prob: float = 0.03,
        branch_life_min: int = 18,
        branch_life_max: int = 70,
        max_stage: int = 240,
        bg_color: tuple[int, int, int] = (15, 18, 22),
        vein_color: tuple[int, int, int] = (180, 200, 220),
        seed: int | None = None,
    ) -> None:
        self.dim = dim
        self.max_segments = max_segments
        self.segment_length = segment_length
        self.meander_amp = meander_amp
        self.meander_freq_min = meander_freq_min
        self.meander_freq_max = meander_freq_max
        self.branch_prob = branch_prob
        self.branch_life_min = branch_life_min
        self.branch_life_max = branch_life_max
        self.max_stage = max_stage
        self.bg_color = np.array(bg_color, dtype=np.uint8)
        self.vein_color = np.array(vein_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._segments: list[dict] = []
        self._stage = 0
        self._main_vein: dict | None = None
        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)
        self._segments = []
        self._stage = 0
        cx = self.dim / 2.0
        cy = self.dim / 2.0
        angle = float(self.rng.uniform(0, 2 * np.pi))
        self._main_vein = self._make_segment(