log scale from $45$ to $1024$.\
The floating contours that appear indicate the number of symbols that (on average) are not chosen to appear in the dictionaries. []{data-label="fig-chain-scaling"}](Chain00000-Rank "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{C}}^{\DcSize}_{\SySize,\pFfork}$ chain 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 $1024$.\
The floating contours that appear indicate the number of symbols that (on average) are not chosen to appear in the dictionaries. []{data-label="fig-chain-scaling"}](Chain00000-Freq "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{C}}^{\DcSize}_{\SySize,\pFfork}$ chain 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 $1024$.\
The floating contours that appear indicate the number of symbols that (on average) are not chosen to appear in the dictionaries. []{data-label="fig-chain-scaling"}](Chain00000-Nonl "fig:"){width="\plotthreewidth"}

![Scaling of innovation in ${\mathsf{C}}^{1024}_{\SySize,\pFfork}$ chain dictionaries, with symbol number $\SySize$ varying on a log scale from $2$ to $32$, and fork probability $\pFfork$ from $1/11$ to $10/11$.\
[]{data-label="fig-chain-parscaling"}](Chain00000-Rank-par "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{C}}^{1024}_{\SySize,\pFfork}$ chain dictionaries, with symbol number $\SySize$ varying on a log scale from $2$ to $32$, and fork probability $\pFfork$ from $1/11$ to $10/11$.\
[]{data-label="fig-chain-parscaling"}](Chain00000-Freq-par "fig:"){width="\plotthreewidth"} ![Scaling 