Shane Organic Noise — layered Perlin with rotation and twist

Math essence

Per layer k: rotate (x, y) by angle k*twist_per_layer, displace by sin/cos of the polar angle for an organic warp, then sample Perlin gradient noise at scale*(x', y') + offset_k. Layers are summed with amp = 0.62^k. A radial vignette (1 - r*0.85) dampens the field near the edges. The final scalar is fed through the IQ cosine palette a + b*cos(2π*(c*t + d)) with offset drift over time.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/shader_legends/ShaneOrganicNoise/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


_PERMUTATION = (
    151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225,
    140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148,
    247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32,
    57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175,
    74, 165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122,
    60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54,
    65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200,
    196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52,
    217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207,
    206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213, 119,
    248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9, 129,
    22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218,
    246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241,
    81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157,
    184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93,
    222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180,
)
_P = np.zeros(512, dtype=np.int32)
for _i in range(256):
    _P[_i] = _PERMUTATION[_i]
    _P[256 + _i] = _PERMUTATION[_i]


def _fade(t: np.ndarray) -> np.ndarray:
    return t * t * t * (t * (t * 6.0 - 15.0) + 10.0)


def _lerp(t: np.ndarray, a: np.ndarray, b: np.ndarray) -> np.ndarray:
    return a + t * (b - a)


def _grad2(hash_idx: np.ndarray, x: np.ndarray, y: np.ndarray) -> np.ndarray:
    h = hash_idx & 7
    u = np.where(h < 4, x, y)
    v = np.where(h < 4, y, x)
    sign_u = np.where((h & 1) == 0, 1.0, -1.0)
    sign_v = np.where((h & 2) == 0, 1.0, -1.0)
    return sign_u * u + sign_v * v


def _perlin2(x: np.ndarray, y: np.ndarray, seed: int) -> np.ndarray:
    """Vectorised Ken-Perlin improved noise in 2D (z=0)."""
    xi = np.floor(x).astype(np.int32) & 255
    yi = np.floor(y).astype(np.int32) & 255
    xf = x - np.floor(x)
    yf = y - np.floor(y)
    u = _fade(xf)
    v = _fade(yf)

    perm = _P if seed == 0 else np.roll(_P, seed & 255)

    A = (perm[xi] + yi) & 255