Cherniak Constellations (Dmitri Cherniak point-cloud + graph)

Math essence

Place N stars at positions drawn from N((dim/2, dim/2), (sigma*dim)^2). For each pair (i, j) with d = ||p_i - p_j||, if d < d_max then draw a line with alpha = alpha_max * (1 - (d/d_max)^falloff) and thickness = round(thickness_max * (1 - (d/d_max)^falloff)). For each star, draw a soft halo of radius halo_r and a small bright core of radius star_r, both with alpha proportional to the star's brightness.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/hobbs_cherniak_penne_deep/CherniakConstellations/reference.py

"""CherniakConstellations — Dmitri Cherniak pseudo-random constellations.

A homage to Dmitri Cherniak's *Constellations* series: a
pseudo-random point cloud with connecting lines filtered by
distance, producing graph-like emergent forms.

The kernel we implement:

    1. Place N "stars" at random positions on the canvas, with
       a slight bias towards the centre (a Gaussian falloff
       that gives a denser, more constellation-like cluster).
    2. For each pair of stars (i, j), if `||p_i - p_j|| < d_max`,
       draw a line from i to j.  The line's alpha and thickness
       decrease with distance (close pairs: bright + thick;
       distant pairs: faint + thin).
    3. Each star is drawn as a small filled disc with a
       bright centre and a soft halo (the "star" aesthetic).
    4. Lines that pass near a star get a slight brightness boost
       (the "halo" effect that makes the constellation feel
       connected).

Cherniak describes his *Constellations* work as exploring the
"possibilities of automated art" (LACMA, 2021) — a small set
of simple rules producing emergent graph-like forms.  The
key visual signature is the *sparse* connectivity: most pairs
of stars are NOT connected (because their distance exceeds
d_max), so the result is a graph of clusters and chains rather
than a fully connected mesh.

Reference:
- https://www.dmitricherniak.com
- https://www.youtube.com/watch?v=HoMt5vXmtP0
"""
from __future__ import annotations

from typing import ClassVar

import numpy as np


# ---------------------------------------------------------------------------
class CherniakConstellations:
    """Cherniak-style point-cloud + distance-filtered graph.

    Parameters
    ----------
    dim : int
        Square canvas side length (px).
    num_stars : int
        Number of stars N in the cloud.
    dist_max_frac : float
        Maximum connection distance as a fraction of dim.
    dist_falloff : float
        Power on the distance falloff. Higher = sharper cutoff.
    center_bias : float
        Gaussian sigma (as fraction of dim) for the centre bias.
        0 = uniform, 0.4 = strong centre clustering.
    star_radius_frac : float
        Star radius as a fraction of dim.
    star_halo_frac : float