Menger Sponge, 2D Carpet edition — recursive 3x3 / centre-removal

Math essence

Iterate levels times: subdivide p into 3x3 sub-cells; mark (sub_x == 1 && sub_y == 1) as killed at this level. Survivors (kill == levels) are kept; killed pixels are recorded with the level that cut them. The render maps each kill level to a different hue band via level_hue[level] * hue_shift, modulated by an IQ cosine palette. A per-cell hash tints survivors; the sub-square boundary distance is multiplied by edge_softness to mark outlines.

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/shader_legends_2/MengerSponge2D/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


def _hash11(x: np.ndarray) -> np.ndarray:
    p = 127.1 * x
    return (np.sin(p) * 43758.5453123 - np.floor(np.sin(p) * 43758.5453123)).astype(np.float32)


def _hash12(x: np.ndarray, y: np.ndarray) -> np.ndarray:
    p = 127.1 * x + 311.7 * y
    return (np.sin(p) * 43758.5453123 - np.floor(np.sin(p) * 43758.5453123)).astype(np.float32)


def _depth_levels(
    xv: np.ndarray,
    yv: np.ndarray,
    levels: int,
) -> np.ndarray:
    """Per-pixel *kill depth* of the 2D Menger sponge (carpet).

    Returns the integer level at which the pixel gets cut.  Pixels
    outside any cut are capped at `levels` (survivors).
    """
    kill = np.full(xv.shape, levels, dtype=np.int32)
    size = 1.0
    cx = 0.0
    cy = 0.0
    s = 1.0
    for lev in range(levels):
        x = xv * s + cx
        y = yv * s + cy
        ix = np.floor(x / size).astype(np.int64)
        iy = np.floor(y / size).astype(np.int64)
        fx = (x / size) - ix.astype(np.float32)
        fy = (y / size) - iy.astype(np.float32)
        sub_x = np.floor(fx * 3.0).astype(np.int64)
        sub_y = np.floor(fy * 3.0).astype(np.int64)
        centre_hit = (sub_x == 1) & (sub_y == 1)
        # Update: pixels that get hit at this level and haven't
        # been assigned an earlier kill level get lev.
        first_hit = centre_hit & (kill == levels)
        kill = np.where(first_hit, lev, kill)
        s *= 0.3333333
        cx = cx * 0.3333333
        cy = cy * 0.3333333
    return kill


def _sponge_mask(
    xv: np.ndarray,
    yv: np.ndarray,
    levels: int,
) -> np.ndarray:
    """Boolean survival mask for the Menger carpet: True => pixel
    is *in* the fractal (survives all levels)."""
    kill = _depth_levels(xv, yv, levels)