only kept if the result is not already present; or (ii) with probability $\pFfork$, another (single) random symbol is chosen to be the new word, but is only kept if the result is not already present.

In this way the fork-fraction $\pFfork$ determines how fast the dictionary accumulates words with different symbols. Although we should note that the starting symbol has no special role, a low $\pFfork$ means that the early-chosen symbols, and in particular $\alpha_\circ$, will dominate the symbol frequencies in the resulting dictionary.

![Scaling of innovation in ${\mathsf{B}}^{\DcSize}_{\SySize,\pFfork}$ blinkered 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-blinkered-scaling"}](Blinkered00000-Rank "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{B}}^{\DcSize}_{\SySize,\pFfork}$ blinkered 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-blinkered-scaling"}](Blinkered00000-Freq "fig:"){width="\plotthreewidth"} ![Scaling of innovation in ${\mathsf{B}}^{\DcSize}_{\SySize,\pFfork}$ 