I'm looking for a simple rewrite system which displays high period.
In order to do that, I've ran a brute-force search on every elementary cellular automata, for a few fixed memory lengths
L. The result is that, when
L=7, there are rules with the max possible period (128). Yet, for
L=8, no matter which rule is used, I couldn't get a period > 180. For
L=9, the maximum period of 133.
I've, then, tried a few variations of the core idea. For example, I tried using 3 symbols instead of just
2 and do a similar brute-force search, but the results are similar.
Thus, I ask: is there any similar system with a rewrite rule which displays high period?