Sierpiński Carpet

Self-similar fractal constructed by iterative hole-punching — dim = log 8 / log 3 ≈ 1.893

Level: 1 | Filled squares: 8¹ = 8 | Dimension: log(8)/log(3) ≈ 1.8928

At each step, divide each square into a 3×3 grid and remove the central cell. After n steps, 8ⁿ squares remain of side 3⁻ⁿ. Total area → 0 but the fractal is uncountably infinite. The 3D analog — the Menger sponge — has dimension log(20)/log(3) ≈ 2.727.