Gesture Driven Field

Math essence

Synthetic gesture g(x, y, t) = sum_k a_k * cos/sin(f_k * x ± f_k * y + phase_k + omega_k * t). Velocity = curl_mix * curl(g) + (1 - curl_mix) * grad(g). Each particle position is updated modulo canvas size and its colour is painted with a 12% alpha and the canvas is decayed towards the background by (1 - decay) per step.

Parameters

Reference

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

from __future__ import annotations

from typing import ClassVar

import numpy as np


class GestureDrivenField:
    """Gesture Driven Field — Memo Akten, *Body Paint* / *Forms* lineage.

    Akten's Body Paint (2009) interprets audience movement into fluid
    velocity; his collaboration with Quayola, *Forms* (2011), generalises
    the gesture → vector field coupling.  Here the gesture signal is
    synthetic:  a sum of sinusoids at small-integer frequencies, exactly
    the kind of "complex signal broken down into its basic elements at
    different frequencies" Akten describes in his SHM writings.  The
    field is the spatial gradient of that scalar gesture field, and
    particles are advected by it, leaving long-lived streaks.

    The result is a swirling, ribboned field reminiscent of Akten's
    interactive painting installations.
    """

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

    def __init__(
        self,
        num_particles: int = 1500,
        dim: int = 512,
        num_chains: int = 6,
        gesture_amp: float = 2.5,
        curl_mix: float = 0.5,
        decay: float = 0.985,
        seed: int | None = None,
        background: tuple[int, int, int] = (10, 8, 18),
        **_,
    ) -> None:
        self.num_particles = int(num_particles)
        self.dim = int(dim)
        self.num_chains = int(num_chains)
        self.gesture_amp = float(gesture_amp)
        self.curl_mix = float(np.clip(curl_mix, 0.0, 1.0))
        self.decay = float(np.clip(decay, 0.8, 0.999))
        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)
        self.t = 0.0
        ratios = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=np.float32)
        idx = self.rng.integers(0, len(ratios), size=self.num_chains)
        self.freqs = ratios[idx]
        self.phases = self.rng.uniform(0.0, np.pi * 2.0, size=self.num_chains).astype(np.float32)
        self.amps = self.rng.uniform(0.4, 1.0, size=self.num_chains).astype(np.float32)
        self.positions = self.rng.uniform(0.0, 1.0, size=(self.num_particles, 2)).astype(np.float32)
        self.hues = self.rng.uniform(0.0, 1.0, size=self.num_particles).astype(np.float32)
        self.canvas = np.tile(self.bg_color, (self.dim, self.dim, 1))

    def step(self, n: int = 1) -> None: