Data Particle Field (Refik Anadol — Machine Hallucinations / AI Data Sculptures)

Math essence

Sample N particle positions from a K-component 2D Gaussian Mixture: x_i ~ Σ_k π_k N(μ_k, Σ_k). Each step, velocity is updated by outward drift from μ_{c_i}, low-amplitude Gaussian kick, and damping (v *= 0.92); positions are integrated and wrapped on a torus. Each particle is additively splatted into a fading float canvas coloured by c_i ∈ {0..K-1}.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/anadol_webgpu/dataParticleField/reference.py

"""dataParticleField — Refik Anadol inspired data-particle field.

Inspired by Refik Anadol Studio's body of "AI Data Sculptures" and
"AI Data Paintings" (e.g. *Quantum Memories*, *Machine Hallucinations
— NYC*, *Coral Dreams*): a large cloud of data points, each positioned
and coloured according to an underlying dataset, on top of a faint
"data universe" canvas.

Here we synthesise the dataset as a 2D Gaussian Mixture Model (GMM)
with K clusters, then sample N particles from the mixture.  Each
particle carries (x, y, vx, vy, cluster_id, alpha); every step we
apply gentle outward drift from each cluster centre plus low-amplitude
noise so the field breathes, and we additively splat each particle
into a canvas coloured by its cluster (Anadol's "data pigments").
The result is a constellation of luminous blobs — a static "data
universe" portrait of the underlying mixture.

Reference:
- https://refikanadol.com/works/coraldreams/
  ("Machine Hallucinations — Coral Dreams", RAS, 2021)
- https://www.nvidia.com/en-us/research/ai-art-gallery/artists/refik-anadol/
"""
from __future__ import annotations

from typing import ClassVar

import numpy as np


# A palette inspired by Anadol's coral / cosmos pigments.
_PALETTE = np.array(
    [
        (255,  90, 110),  # 0 — coral
        (250, 150,  60),  # 1 — amber
        (255, 220,  90),  # 2 — gold
        ( 90, 230, 200),  # 3 — mint
        ( 60, 160, 255),  # 4 — azure
        (140, 100, 255),  # 5 — violet
        (240, 100, 220),  # 6 — magenta
        (255, 255, 255),  # 7 — accent white
    ],
    dtype=np.float32,
)


class DataParticleField:
    """Particles sampled from a 2D Gaussian Mixture Model.

    Parameters
    ----------
    dim : int
        Square canvas side length (px).
    num_particles : int
        Number of particles N to sample from the mixture.
    num_clusters : int
        Number K of Gaussian components in the mixture.
    palette_size : int
        Number of palette entries to cycle through cluster colours
        (``<= 8`` since the curated palette has 8 swatches).
    noise_scale : float