Tool

Sierpinski carpet playground

Subdivide a square into a 3 × 3 grid and pick which sub-squares survive. The classic Sierpinski carpet keeps 8 of 9; the two Vicsek variants keep 5 of 9.

step 0: filled unit square
step n: subdivide each surviving square into 3×3 = 9 sub-squares,
        keep all EXCEPT the centre. (kept: 8 of 9)

Hausdorff dim: log 8 / log 3 ≈ 1.8928

Background at /fractals/sierpinski-carpet and /fractals/vicsek-fractal.