Fibers (curling brush)

Math essence

Each fiber integrates position via x_{t+1} = x_t + v·cos(theta_t), y_{t+1} = y_t + v·sin(theta_t), with theta_{t+1} = theta_t + k·sin(omega·t + phi). At each step there is a small Bernoulli probability of spawning `branch_max` children with mutated curvature and reduced lifetime, so the field self-similar up to its lifetime budget.

Parameters

Reference

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

from __future__ import annotations

from dataclasses import dataclass, field

from typing import ClassVar

import imageio.v2 as imageio
import numpy as np


PALETTE: np.ndarray = np.array(
    [
        [12, 18, 30],
        [28, 36, 56],
        [48, 60, 90],
        [78, 92, 130],
        [110, 122, 162],
        [148, 152, 188],
        [188, 178, 200],
        [220, 200, 205],
        [240, 220, 200],
        [250, 232, 188],
        [255, 222, 152],
        [248, 200, 110],
        [232, 168, 80],
        [205, 130, 60],
        [170, 95, 50],
        [130, 70, 45],
        [95, 55, 40],
        [70, 42, 32],
        [50, 32, 24],
        [32, 22, 18],
    ],
    dtype=np.uint8,
)


@dataclass
class _Fiber:
    x: float
    y: float
    angle: float
    curvature: float
    curvature_phase: float
    curvature_speed: float
    speed: float
    age: int = 0
    life: int = 0
    alive: bool = True
    color: np.ndarray = field(default_factory=lambda: np.array([255, 255, 255], dtype=np.uint8))
    thickness: float = 1.0
    trail: list[tuple[float, float]] = field(default_factory=list)


class Fibers:
    family: ClassVar[str] = "complexification_net"
    sketch: ClassVar[str] = "fibers"

    def __init__(
        self,