Daily Sketch Curve Morph (Synthetic Gesture)

Math essence

theta = linspace(0, 12π, N). R, r, d each = base + Σ amp_k * sin(2π freq_k * t + phase_k) for their own chain. x = (R + r*cos(3θ))*cos(θ); y = (R + r*cos(3θ))*sin(θ) + d*sin(7θ + 0.7). Rotate (x, y) by _rot about centre, rasterize to canvas. canvas *= trail_decay each step; ink = line_color * stroke_alpha, with 1-pixel halo to either side.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/audio_reactive/LiebermanDailySketch/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


class LiebermanDailySketch:
    """Lieberman-style daily-sketch aesthetic: a parametric curve
    whose parameters morph continuously under a synthetic "gesture"
    signal (a chain of sin waves at different frequencies, mimicking
    mouse / pen motion).

    Implements a polar-rose / hypotrochoid family whose radii
    (R, r, d) and phase offsets are driven by independent sin
    chains. Each chain has its own frequency band — so the curve
    "wiggles in three different ways at once" (one of Zach
    Lieberman's signature rules from his *Daily Sketches* project:
    "use mathematical functions like sin() and tan() in place of
    randomness"). The trail canvas rotates the line each step to
    evoke the AR / rotation experiments from his openFrameworks
    sketches (notably the *Audio in Space* ARKit series).
    """

    family: ClassVar[str] = "audio_reactive"
    sketch: ClassVar[str] = "liebermandailysketch"

    def __init__(
        self,
        dim: int = 400,
        num_points: int = 600,
        base_R: float = 0.42,
        base_r: float = 0.18,
        base_d: float = 0.32,
        R_freq: tuple[float, ...] = (0.21, 0.43, 0.91),
        r_freq: tuple[float, ...] = (0.31, 0.83, 1.7),
        d_freq: tuple[float, ...] = (0.11, 0.67, 2.3),
        R_amp: tuple[float, ...] = (0.05, 0.04, 0.03),
        r_amp: tuple[float, ...] = (0.06, 0.05, 0.04),
        d_amp: tuple[float, ...] = (0.08, 0.06, 0.05),
        morph_speed: float = 1.0,
        rotation_speed: float = 0.18,
        line_color: tuple[int, int, int] = (245, 240, 230),
        bg_color: tuple[int, int, int] = (12, 12, 18),
        trail_decay: float = 0.96,
        stroke_alpha: float = 0.65,
        seed: int | None = None,
    ) -> None:
        self.dim = dim
        self.num_points = num_points
        self.base_R = base_R
        self.base_r = base_r
        self.base_d = base_d
        self.R_freq = np.array(R_freq, dtype=np.float32)
        self.r_freq = np.array(r_freq, dtype=np.float32)
        self.d_freq = np.array(d_freq, dtype=np.float32)
        self.R_amp = np.array(R_amp, dtype=np.float32)
        self.r_amp = np.array(r_amp, dtype=np.float32)
        self.d_amp = np.array(d_amp, dtype=np.float32)
        self.morph_speed = morph_speed