Cherniak Ringers (Dmitri Cherniak — Ringers)

Math essence

For each wrap w in [0, num_wraps): pick anchor a_w = centroid_or_offset + drift(w); compute angles[i] = atan2(peg[i].y - a_w.y, peg[i].x - a_w.x); sort pegs by angle; for each adjacent pair (peg[order[k]], peg[order[k+1]]) draw a line whose endpoints are offset by tangent_drift * peg_radius perpendicular to the segment. With num_wraps = 512 and 22 pegs, the canvas is crossed by 22 * 512 = 11,264 segments with thousands of intersection points.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/art_blocks/CherniakRingers/reference.py

"""CherniakRingers — Dmitri Cherniak's "Ringers" string-on-pegs algorithm.

Inspired by Dmitri Cherniak's *Ringers* (Art Blocks Curated, January
2021) — 1,000 generative artworks that "explore all the ways a string
can wrap around a set of pegs."  It is one of the defining generative-
art projects of the NFT era and produced the iconic *Ringers #879*
("The Goose"), one of the most recognisable generative artworks ever
made.  Ringers was acquired by LACMA (*Ringers #962*) and Sotheby's
auctioned *#879* for $6.2 million in 2023.

Cherniak describes the algorithm in his own words (Bankless interview,
2021):

    "There are an almost infinite number of ways to wrap a string
    around a set of pegs. ... Each output from 'Ringers' is derived
    from a unique transaction hash and generated in Javascript in
    the browser. Feature variations include peg count, sizing, layout,
    wrap orientation, and a few colourful flourishes for good measure."

In a later After-Dinner-Mints podcast (May 2021) he gave the
algorithmic kernel:

    "Essentially it looks for the centroid for the balanced ringer.
    It looks for the centroid. So it kind of averages all the pegs
    and then it tries to loop a string around each of the pegs based
    on kind of it sorts all the pegs from the angle it forms with the
    centroid."

The algorithm we implement:

    1. Lay out N pegs on the canvas.  Three layouts are typical of
       Ringers: a circle (the canonical 'balanced' layout), a 3x3 grid
       (the famous "3x3 grid" trait), and a random constellation.
    2. Pick an "anchor" point — the centroid of the pegs, or an
       arbitrary off-centre point (Cherniak's "arbitrary point" bug
       that he kept because it made for interesting looks).
    3. Sort the pegs by angle from the anchor.
    4. Draw the string as a closed loop: from peg i, draw a straight
       line to peg i+1, and so on around the sorted order.  Each line
       either stays in front of (covering) or behind (occluded by) the
       peg, depending on the wrap orientation.
    5. After K wraps (default 512), the canvas is densely threaded
       with string intersections — the canonical Ringers look.
    6. Each peg is filled with its assigned colour (the rare
       "bullseye" trait gives a concentric ring instead).

Reference:
- https://www.artblocks.io/collection/ringers-by-dmitri-cherniak
- https://www.curated.xyz/editorial/collecting-ringers
- https://www.bankless.com/talking-ringers-with-dmitri-cherniak
- "Art Blocks After Dinner Mints w/ Dmitri Cherniak" podcast, May 2021.
"""
from __future__ import annotations

from typing import ClassVar

import numpy as np


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