scale from $45$ to $1024$.\
[]{data-label="fig-null-scaling"}](Null00000-Nonl "fig:"){width="\plotthreewidth"}

Fixed length words: F-dictionaries
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A fixed length word dictionary ${\mathsf{F}}^{\DcSize}_{\SySize,\pWordLen}$ containing $\DcSize$ words can be straightforwardly generated using a symbol list of length $\SySize$, with $\pWordLen$ symbols per word, each symbol being chosen randomly. Words can contain any number (up to $\pWordLen$) of repeated symbols, and words may be repeated in the dictionary.

With this generator, we will want ${\DcSize} \ll {\SySize}^{\pWordLen}$ so that the random sampling of all possible words plays a strong role when populating the dictionary.

![Scaling of innovation in ${\mathsf{F}}^{\DcSize}_{\SySize,8}$ fixed 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-fixed-scaling"}](Fixed00000-Rank "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{F}}^{\DcSize}_{\SySize,8}$ fixed 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-fixed-scaling"}](Fixed00000-Freq "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{F}}^{\DcSize}_{\SySize,8}$ fixed 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-fixed-scaling"}](Fixed00000-Nonl "fig:"){width="\plotthreewidth"}

![Scaling of innovation in ${\mathsf{F}}^{1024}_{\SySize,\pWordLen}$ fixed random dictionaries, 