FFT-Spectrum Particle Field (Synthetic Audio)

Math essence

audio(t) = Σ amp_i * sin(2π freq_i t + phase_i) + Σ impulse_kick * δ(t mod 1). Each step the latest 256 samples (window_size) are Hann-windowed and FFT'd: bands = [|FFT(low_freq)|, |FFT(mid_freq)|, |FFT(high_freq)|]. fx, fy = field_gain * (band_diff_low_mid + 0.4, band_diff_mid_high + 0.4) + swirl * (ny, -nx). v *= 0.985. canvas *= trail_decay; canvas[p.y, p.x] += ink * (0.08 + 0.18 * high_band).

Parameters

Reference

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

from __future__ import annotations

from typing import ClassVar

import numpy as np


class PasmaFFTSpectrum:
    """FFT-spectrum particle field inspired by Piter Pasma's algorithmic
    animation work.

    A synthetic "audio" signal is generated each frame as a chain of
    sinusoids across low / mid / high bands, plus a 1 Hz impulse
    train (kick). A sliding window of the most recent samples is
    Hann-windowed and run through a real FFT; the magnitudes at the
    three band centres (low / mid / high) drive particle velocities
    along the x / y axes and a radial "pressure" pulse.

    Particles leave low-alpha strokes on a fading canvas (the
    classic "FFT visualizer" look), colour-cycled with the band's
    spectral centroid. This mirrors the way Pasma's pieces use
    magnitude bands (low / mid / high) to drive multiple visual
    parameters at once — one of his signature moves across the
    4 kB demos, *Skulptuur*, and the *Genuary* prompts.
    """

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

    def __init__(
        self,
        dim: int = 400,
        num_particles: int = 1400,
        window_size: int = 256,
        sample_rate: float = 256.0,
        low_freq: tuple[float, ...] = (0.7, 1.6, 3.0),
        mid_freq: tuple[float, ...] = (8.0, 14.0, 22.0),
        high_freq: tuple[float, ...] = (40.0, 64.0, 96.0),
        low_amp: tuple[float, ...] = (0.55, 0.40, 0.30),
        mid_amp: tuple[float, ...] = (0.35, 0.28, 0.20),
        high_amp: tuple[float, ...] = (0.20, 0.15, 0.10),
        kick_freq: float = 1.0,
        kick_strength: float = 1.6,
        field_gain: float = 6.0,
        max_speed: float = 5.5,
        trail_decay: float = 0.94,
        hue_drift: float = 0.004,
        bg_color: tuple[int, int, int] = (4, 6, 14),
        seed: int | None = None,
    ) -> None:
        self.dim = dim
        self.num_particles = num_particles
        self.window_size = window_size
        self.sample_rate = sample_rate
        self.low_freq = np.array(low_freq, dtype=np.float32)
        self.mid_freq = np.array(mid_freq, dtype=np.float32)
        self.high_freq = np.array(high_freq, dtype=np.float32)
        self.low_amp = np.array(low_amp, dtype=np.float32)
        self.mid_amp = np.array(mid_amp, dtype=np.float32)
        self.high_amp = np.array(high_amp, dtype=np.float32)