Menger sponge

References

• voxels

• plot

import k3d
import numpy as np

def iterate(length, x, y, z):
    nl = length // 3

    if nl < 1:
        return

    margin = (nl - 1) // 2

    voxels[z - margin:z + margin + 1, y - margin:y + margin + 1, :] = 0
    voxels[z - margin:z + margin + 1, :, x - margin:x + margin + 1] = 0
    voxels[:, y - margin:y + margin + 1, x - margin:x + margin + 1] = 0

    for ix, iy, iz in np.ndindex((3, 3, 3)):
        if (1 if ix != 1 else 0) + (1 if iy != 1 else 0) + (1 if iz != 1 else 0) != 2:
            iterate(nl, x + (ix - 1) * nl, y + (iy - 1) * nl, z + (iz - 1) * nl)

iteration = 4
size = 3 ** iteration

voxels = np.ones((size, size, size))

iterate(size, size // 2, size // 2, size // 2)

plt_voxels = k3d.voxels(voxels.astype(np.uint8),
                        color_map=(0xfdfe03), outlines=True)

plot = k3d.plot(grid_visible=False,
                camera_auto_fit=False)
plot += plt_voxels
plot.display()

plot.camera = [98.5152, -60.0912, 88.9902,
               43.4731, 37.6014, 31.5219,
               -0.2226, 0.3405, 0.9135]