Penne Bones of the Earth (Aaron Penne — Apparitions)

Math essence

For each band b in [0, num_bands): x_b[i] = lerp(0.04*dim, 0.96*dim, i/nodes); y_b[i] = baseline_b + reach * (0.7*value_noise_1d(i, grid_size) + 0.3*value_noise_1d(i, 2*grid_size)). baseline_b = (b+1) * dim/(num_bands+1) + altitude_drift * normal(0, 1). Each band is rasterised as a polyline of segment-to-segment lines with a per-band alpha.

Parameters

Reference

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

"""PenneBonesOfTheEarth — Aaron Penne noise-perturbed layered lines.

Inspired by Aaron Penne's *Apparitions* (Art Blocks Curated, March
2021) and his broader body of generative work (*Return*, *Catalina*,
*East/West Street*, *Saying The Same Thing*).  Penne is the
Director of Engineering at Art Blocks, was one of the top-50 NFT
artists globally in 2021, and won the inaugural Lumen Prize for Art
and Technology in 2022 (with Boreta, for *Rituals — Venice*).

Penne describes his core algorithm in his 2021 ARTXCODE essay on
Apparitions:

    "The initial inspiration for this algorithm was a visualization
    published in 1893 by Levi Walter Yaggy. ... I approached this by
    drawing multiple straight lines across the screen, and
    perturbing them according to an underlying noise field. Each
    line is actually hundreds of connected points, offset according
    to various rules."

The key DNA of Penne's work, named here PenneBonesOfTheEarth (after
the conceptual *bones-of-the-earth* geological visual language that
runs through his 2019 *Bones of the Earth* series):

    1. Draw N horizontal "bands" (long lines stretching across the
       canvas, the canonical "stretched sheet" feature of Apparitions
       and Bones of the Earth).
    2. Each band is parameterised by 100–300 nodes (the Stretch
       feature: "The more nodes, the higher the detail, and the more
       compressed the form").  The band has a baseline y-position
       and a per-node vertical offset.
    3. The per-node vertical offset is sampled from a noise field —
       "the size of the step taken in the noise domain ... used to
       determine the variability within the form" (Penne's "Spook"
       feature).
    4. Bands stack up like geological strata, each with its own
       colour drawn from a hand-curated palette (the "Zephyr" colour
       picker picks "a new random color with every band").
    5. Lines are drawn solid or blended (the "Brush Style" feature
       controls whether lines are crisp or feathered).

The implementation here draws N bands, each with a noise-perturbed
baseline y-coordinate and an optional per-band colour from the
palette, with two Brush Styles (solid and feathered alpha-blend).

Reference:
- https://www.artxcode.io/journal/aaron-penne-apparitions-on-art-blocks
- https://www.aaronpenne.io/about
"""
from __future__ import annotations

from typing import ClassVar

import numpy as np


def _smoothstep(t: np.ndarray) -> np.ndarray:
    return t * t * (3.0 - 2.0 * t)


def _value_noise_1d(