Fractal construction by infinite removal — measure zero, uncountably infinite
Depth: 6 |
Intervals: 64 |
Total length: 0.0878 |
Dim = log(2)/log(3) ≈ 0.6309
Classic Cantor set: remove the middle third at each step. After n steps: 2ⁿ intervals each of length (1/3)ⁿ.
Total measure → 0 as n→∞, yet the set is uncountable (it bijects with ℝ).
Hausdorff dimension = log(2)/log(3) ≈ 0.6309 — strictly between 0 and 1.
Changing remove ratio gives a different "fat" or "thin" Cantor set.