The 2D Cantor set — remove the middle third in both x and y directions repeatedly. The resulting fractal has Hausdorff dimension log(4)/log(3) ≈ 1.261.
2D Cantor Dust
1D Cantor Set
Devil's Staircase
5
33%
At 5 iterations: 1024 squares remain out of 3125.
Hausdorff dim ≈ 1.261.