Mechanical Flower Spline

Math essence

Spline: r(θ) = r0 + A*cos(p_d*θ + δ_d) + B*cos(q_d*θ), then sweep phi = 0..2π around Y: (x3, y3, z3) = (cos(phi)*r*cos(θ), r*sin(θ), sin(phi)*r*cos(θ)). Project with tilt mixing of (1-y) and (1-z). p_d, q_d, A_d, B_d, δ_d each step by drift*N(0, 1). Render painter-sorted by iy*w + ix.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/akten_quayola/MechanicalFlowerSpline/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


class MechanicalFlowerSpline:
    """Mechanical Flower Spline — Quayola, *Sculpture Factory* lineage.

    Quayola's Sculpture Factory uses industrial robots to carve
    classical sculptures block-by-block from a single block of matter.
    The flowers produced along the way are not floral in any natural
    sense; they are rotational splines swept around a vertical axis,
    emerging from an algorithmic gesture rather than from botany.

    Here the kernel is a parametric 2D spline
    ``r(θ) = r0 + A * cos(p θ + δ) + B * cos(q θ)``
    swept around Y into a flower-like 3D surface, projected orthographically.
    The petal count and petal geometry drift over time, the way
    Quayola's robots are "instructed by the algorithms" rather than by
    direct human design.
    """

    family: ClassVar[str] = "akten_quayola"
    sketch: ClassVar[str] = "MechanicalFlowerSpline"

    def __init__(
        self,
        num_rot: int = 96,
        num_theta: int = 360,
        dim: int = 512,
        r0: float = 0.5,
        A: float = 0.25,
        B: float = 0.12,
        p: int = 5,
        q: int = 3,
        delta: float = 0.0,
        tilt: float = 0.65,
        drift: float = 0.004,
        seed: int | None = None,
        background: tuple[int, int, int] = (16, 14, 26),
        **_,
    ) -> None:
        self.num_rot = int(num_rot)
        self.num_theta = int(num_theta)
        self.dim = int(dim)
        self.r0 = float(r0)
        self.A = float(A)
        self.B = float(B)
        self.p = int(p)
        self.q = int(q)
        self.delta = float(delta)
        self.tilt = float(tilt)
        self.drift = float(drift)
        self.bg_color = np.array(background, dtype=np.float32)
        self.reset(seed=seed)

    def reset(self, seed: int | None = None) -> None:
        self.rng = np.random.default_rng(seed)