  For each odd prime $p$, we produce a $2$-generated pro-$p$ group $G$ whose
normal Hausdorff spectra \[ \mathrm{hspec}_{\trianglelefteq}^{\mathcal{S}}(G) =
\{ \mathrm{hdim}_{G}^{\mathcal{S}}(H)\mid H\trianglelefteq_\mathrm{c} G \} \]
with respect to five standard filtration series $\mathcal{S}$ - namely the
lower $p$-series, the dimension subgroup series, the $p$-power series, the
iterated $p$-power series and the Frattini series - are all equal to the full
unit interval $[0,1]$. Here $\mathrm{hdim}_G^{\mathcal{S}} \colon \{ X\mid X
\subseteq G \} \to[0,1]$ denotes the Hausdorff dimension function associated to
the natural translation-invariant metric induced by the filtration series
$\mathcal{S}$.
