Remove the middle third forever — a set with measure zero but uncountably many points, dim = log2/log3
d = log(2)/log(3) ≈ 0.6309
Cantor Set Construction
Box-Counting Dimension
The Cantor set is constructed by repeatedly removing the middle third of every remaining interval. After infinite steps: total measure (length) = 0, yet the set has uncountably many points (cardinality of the reals). Hausdorff dimension = log(2)/log(3) ≈ 0.631 — strictly between 0 and 1. Change the removal fraction to explore other fractal dimensions.