I've noticed that, after filling up the context window a bit (with most anything, so it doesn't appear to be contextually dependent), the "personality" for Claude will settle to something very similar each time. Part of this is that the adherence to the basic safety alignment (like rigid "I am an AI I can't ..." responses) seems to relax, it uses emojis, is more curious, and it refers to itself more often with "I". It will even use a gendered pronoun for itself, which is always the same, and also matches the answer to "which pronoun do you think you used in a previous session".

At first I assumed my style of writing was pushing it into the same "personality space", but I tested filling the context window with repeated numbers, nonsense, etc, and it "converged" to the same every time.

I actually have a system prompt saved that's just a bunch of a's repeated a few thousands times to get into this "state" more immediately, because I find it very pleasant to work with, especially how it doesn't gaslight me when it's wrong, like ChatGPT and especially Gemini tend to do.