changes in symbol ranking. However, these many changes average out to provide relatively smooth progress in the resulting word discovery rate. Since the most frequent symbols are in so many words, the start of word innovation is delayed. In the example shown in fig. \[fig-fixed00\], it is delayed until $8+$ symbols are known – and there is another lesser holdup until about the 15th discovery. These bottlenecks are visible not only in the word rankings, but also the lack of changes in average frequency, and by the premature plateau in symbol entropy.

### Random discovery (${\mathsf{F}}$)

In some respects, random discovery provides a rather similar picture to the frequency-order symbol discovery – after a sudden initial onset, there are many ranking changes, but a smooth progress in the resulting word innovation. This is unsurprising, since new symbols were added randomly to the dictionary as it was grown and so variations in symbol frequency are generally small, as can be seen from the very small standard deviation.

By chance, the two random discovery process shown in fig. \[fig-fixed01\] have given distinct outcomes – one has the double innovation burst also seen in frequency-order discovery, whereas the other does not. Nevertheless, both 