world dictionary, or, (d) discovery in random-order. The two sets of results here span a range of symbol list and dictionary sizes. We see that for randomly chosen discovery order, $\delta_r \sim \SySize$ within random error, as expected. The values for $\delta_\omega$ and $\delta_\chi$ are somewhat suppressed below the $\SySize$ value, as expected since it is very unlikely that any two subsequent interrogations will be as different as assumed by the normalization. As should be expected, the two discovery orders give results that differ only due to sampling error, since the “frequency-order” is randomly re-set by the algorithm at each subdictionary interrogation.

![Scaling of innovation in ${\mathsf{N}}^{\DcSize}_{\SySize}$ null random dictionaries, with symbol number $\SySize$ varying on a log scale from $2$ to $32$, and dictionary size $\DcSize$ on a log scale from $45$ to $1024$.\
[]{data-label="fig-null-scaling"}](Null00000-Rank "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{N}}^{\DcSize}_{\SySize}$ null random dictionaries, with symbol number $\SySize$ varying on a log scale from $2$ to $32$, and dictionary size $\DcSize$ on a log scale from $45$ to $1024$.\
[]{data-label="fig-null-scaling"}](Null00000-Freq "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{N}}^{\DcSize}_{\SySize}$ null random dictionaries, with symbol number $\SySize$ varying on a log scale from $2$ to $32$, and dictionary size $\DcSize$ on a log 