with symbol number $\SySize$ varying on a log scale from $2$ to $32$, and word length $\pWordLen$ from $2$ to $11$.\
[]{data-label="fig-fixed-parscaling"}](Fixed00000-Rank-par "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{F}}^{1024}_{\SySize,\pWordLen}$ fixed random dictionaries, with symbol number $\SySize$ varying on a log scale from $2$ to $32$, and word length $\pWordLen$ from $2$ to $11$.\
[]{data-label="fig-fixed-parscaling"}](Fixed00000-Freq-par "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{F}}^{1024}_{\SySize,\pWordLen}$ fixed random dictionaries, with symbol number $\SySize$ varying on a log scale from $2$ to $32$, and word length $\pWordLen$ from $2$ to $11$.\
[]{data-label="fig-fixed-parscaling"}](Fixed00000-Nonl-par "fig:"){width="\plotthreewidth"}

Fig. \[fig-fixed-scaling\] compares the innovation measures for two symbol discovery possibilities: (a) discovery the frequency-order of symbols in the world dictionary, or, (b) discovery in random-order. The two sets of results here span a range of symbol list and dictionary sizes, but are constrained by a fixed word length $\pWordLen=8$. Since the dictionary parameters do always not honour the sampling inequality above, particularly for the smallest symbol lists, we see a pronounced ‘knee’ in each of the $\delta$ measures below $\SySize=4$.

For large symbol lists and small dictionary sizes we see that the $\delta$ measures report higher innovation for frequency-order discovery, although the difference is not large. This occurs because as the most frequent symbols 