Randomly initialized life quickly collapses into stable structures, most of the time. Modeling it as if it continually permuted randomly though possible states does not fit how it really tends to work in practice.
Randomly initialized life quickly collapses
into stable structures, most of the time.
Looking at a random game of life with 10^6 cells, I get the feeling that it will not loop for a long time.
Maybe it is a misunderstanding. I do not mean to find a self-replicator of size c in a field of size c. I would expect that the field is big. Very big. Let's say 10^80 cells. That is the estimate for the number of atoms in the universe. The self replicator would be way way smaller. One manually constructed replicator (Gemini) is just 10^7 cells. And that is certainly not the smallest replicator possible.