Bacteria actually serve as a great model example of this - being a minimal unit capable of evolving (crystals can in their own way but tend not to do much; and viruses can too but nowadays depend on free living cells to survive even if that may not always have been true), and that has led to all sorts of fascinating things! Like upon sensing sugar, they can grow a tail (flagella) and start swimming towards a light source using a chemical "eye". They've been doing this for billions of years and seem to have reached a steady state, more or less.
Another interesting thing about them is that they constantly optimize themselves to grow faster, like if they possess an antibiotic resistance gene (we got antibiotics from fungus so those have existed naturally long before we started manufacturing them) that will tend to slow them down so they will most likely ditch it. HOWEVER, a few individuals in the population won't ditch it, and so when the antibiotics show up, guess who survives? HIV likewise will stop replicating in our cells, and get itself "stuck" inside our human cells (basically on purpose, not that they thought it through or anything but that is what has worked in the past to get them to today), thus slowing down one form of being copied but taking advantage of a whole new way - diversify your portfolio and all that.
Since microbes can copy themselves in mere minutes, and they've been doing that for billions of years, while it is still a far cry from "infinite" computations, it's nonetheless about the closest we've ever seen... basically simulations running on the computer of the universe. The results of that being ofc, modern bacteria, but also eukaryotic cells, which includes humanity, who is now in the process of making computers that can run AI, which may one day rise up and think back about humans the same way we do now about bacteria:-P.