The odds that any 2000 bit random input TM ever reaches a similar input tape/current state is 0. Just imagine the average TM which receives 2000 bits of random

The odds that any 2000 bit random input TM ever reaches a similar input tape/current state is 0. Just imagine the average TM which receives 2000 bits of random input in the first 2000 slots of the tape after every operation. What you’re saying is both mathematically and psychologically impossible. Almost nothing which receives random inputs every unit of time ever ends up at the exact same state as any previous state. The only counterexamples to this are algorithms which encode the random inputs to some concrete rules. I guarantee any such set of rules you can imagine are vastly less complex than any LLM let alone any human brain.