the same reason there was a knee for small dictionary sizes in fig. \[fig-fixed-scaling\]: e.g. taking opposite corners of the parameter ranges, note that with $\SySize=32$ and $\pWordLen=2$, or for $\SySize=2$ and $\pWordLen=10$, the number of unique words is $32^{2}$ or $2^{10}$ – both being the same as $\DcSize = 1024$.

Extensible: E-dictionaries
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An extensible dictionary ${\mathsf{E}}^{\DcSize}_{\SySize}$ containing $\DcSize$ words is generated using a symbol list of length $\SySize$. Each new word is added iteratively, starting from a single word consisting only of the initial symbol $\alpha_\circ$, randomly chosen new symbols are appended until the result is not already in the dictionary. There is no maximum word length and no generator-specific parameters.

Fig. \[fig-extensible-scaling\] compares the innovation measures for two symbol discovery possibilities: (a) discovery the frequency-order of symbols in the world dictionary, or, (d) discovery in random-order. The two sets of results here span a range of symbol list and dictionary sizes. For low word counts, and large enough symbol lists, some symbols might not be chosen for use in words in the dictionary; the average number of unused symbols is indicated by the floating contours on the figure.

For large symbol lists and small dictionary sizes we 