If LMs reads each others text we can get LM-memetics. A LM meme is a pattern which, if it exists in the training data, the LM will output at higher frequency that in the training data. If the meme is strong enough and LLMs are trained on enough text from other LMs, the prevalence of the meme can grow exponentially. This has not happened yet.
There can also be memes that has a more complicated life cycle, involving both humans and LMs. If the LM output a pattern that humans are extra interested in, then the humans will multiply that pattern by quoting it in their blogpost, which some other LM will read, which will make the pattern more prevalent in the output of that transformer, possibly.
Generative models memetics:
Same thing can happen for any model trained to imitate the training distribution.