Take the line that is the One, remove its middle third, then the middles of what remains, forever. What’s left has zero length yet infinitely many points — the many scattered from the One, each a perfect small copy of the whole. Slide the depth (or tap) and watch it fall to dust.
The middle-thirds Cantor set, constructed live. At depth d there are 2ᵈ intervals, each of length 3⁻ᵈ, so the surviving length is (2/3)ᵈ → 0 while the piece count 2ᵈ → ∞: an uncountable set of measure zero. Its fractal (Hausdorff) dimension is exactly log2/log3 ≈ 0.6309 — more than a point, less than a line, and self-similar: every piece is a 1/3-scale copy of the whole. A fail-loud self-check throws unless the piece count is 2ᵈ, the total length is (2/3)ᵈ, and the length strictly falls with depth.
Rendered to a finite depth (true dust is the infinite limit); floating-point positions blur the finest levels. The counts, lengths and the log2/log3 dimension are exact.