Nearest-neighbour projection ratio ℓ_3D/ℓ_2D versus sample size N for fractal ensembles. For each N, we averaged 100 realisations per configuration and then combined across nine fractal setups (D ∈ {1.7, 2.0, 2.5}, n_div ∈ {2, 3, 4}) with jitter=True and prune=True. The solid curve shows the cross-configuration mean, and the dashed curves indicate ±1σ across configurations (not the run-to-run uncertainty). The dashed horizontal line marks the geometric fixed-pair baseline 4/π ≃ 1.27. Projection bias is present at all N, with ℓ_3D/ℓ_2D increasing sub-linearly with N and reaching ~2.0–2.3 by N = 200, depending on fractal parameters. A higher D (less clumpy) yields larger ratios at a fixed N, indicating that beyond geometric compression, crowding and neighbour reassignment drive additional shortening in projection.