Would life emerge in Life?

[mmcirvin]

Thinking about replicators in Conway's Game of Life made me wonder about whether one would expect them to emerge eventually and become dominant in a very, very, very long-lived "random soup" situation.

I actually doubt it. All life on Earth seems to have common ancestry, and a likely reason is that once life arose once, it quickly ate up all the stuff lying around that would be useful raw materials for abiogenesis a second time. In Life, though, there's no competition for raw materials; there's just competition for room. And there are simple spacefiller and breeder patterns that already expand into the plane at a population rate proportional to t², which is the fastest anything can ever expand in a 2D cellular automaton with local rules. They could outcompete any complicated replicator, which would likely reproduce at t² at best but with a lower constant of proportionality. And simple spacefillers or breeders would be much, much more likely to arise by chance.

On the other hand, there's the question of robustness. Generally speaking, these patterns are fragile; they can't productively expand into a region filled with the static and oscillating junk left over from a random soup. Maybe some suitably adapted replicator could do better.

Or maybe there are breeders that are particularly aggressive on junk. This is probably ripe for experiment, if somebody hasn't done it already.

Comments

[ikkyu2.livejournal.com]

I feel like I've seen versions of Life that had raw materials somehow implemented, I think as a cell property. Little buggers started fighting over the good squares.

[beamjockey.livejournal.com]

They'd been kicked out of Eden...

[mmcirvin.livejournal.com]

There's a CA called "Langton loops" which has simple replicators that look like square loops with circulating rings of genetic material in them. A variant of it exists called "Evoloop" in which the loops disintegrate when they die, and collisions can sometimes yield surviving loops with mutated genes. The result is that the competition for space actually becomes a selective pressure. The loops in the cramped, chaotic middle of the populated world rapidly evolve in an r-strategy sort of way to become smaller and faster-breeding.

Not life, but...

[cshalizi.livejournal.com]

In the "cyclic" cellular automata, with certain parameter settings, you can prove that, starting from uniformly random initial conditions, the lattice will be completely taken over by spiral waves. (This happens with probability tending to 1 as the lattice size grows.) The angular velocity of the spirals' rotation is constant once they form, but they can from with different velocities, and, again provably, the faster spirals eventually eat the slower ones. (See http://psoup.math.wisc.edu/papers/cca.zip and http://psoup.math.wisc.edu/papers/tr.zip.) There were some papers in the early Artificial Life conference proceedings, by people from the Utrecht theoretical biology group, about using this as a "substrate" for natural selection, but I don't remember the details, and it doesn't seem to have gotten very far.

[mmcirvin.livejournal.com]

Life with some sort of prepared grid might also change things considerably. I was thinking about how a grid of preexisting glider-tape reflectors might make Gemini-like replicators easier to construct.

(There's a complicated pattern called "metapixel" that allows a Life grid to emulate either itself or a variety of other cellular automata on a vast, slow scale; you could just use it to emulate the Fredkin replicator CA and then have natural replicators flying all over the place on the meta-level. But that's sort of a trivial case.)

[acw.livejournal.com]

The last time I spoke to him on the subject (perhaps five years ago?), Gosper believed that the sufficiently far future of sufficiently large randomly-initialized fields would be dominated by evolving, nontrivial replicators. I have never been able to follow his reasoning, but I have to give it respect because Gosper is Gosper.

I have a strong opposite intuition: that the Life universe is not sufficiently habitable for an eventual regime of replicators.

Gosper does not contend that replicators will arise from the primordial soup. Rather, he asserts that robust replicators are possible, and therefore would exist ab initio in a sufficiently large starting grid. At the beginning, they would be extremely rare, but because they replicate, they would take over the universe eventually.

He and I differ on whether robust replicators are possible. I think they're not; the key is the word "robust". Such a replicator must be able to survive and reproduce embedded in an endless random background that will constantly be firing gliders (and worse things) at the replicator. The replicator must be surrounded with a protective coat that will neutralize anything the outer chaos throws at it. It's this that strikes me as implausible.

I offered a challenge which illustrates the difficulty. Design a Life pattern that has two parts, a core of diameter N and a surrounding membrane of thickness N; the whole thing would fit in a square of diameter 3N. The designer gets to pick N. We run the pattern in a big field, say of diameter 100N. On our first run, the rest of the field should be empty. The pattern can do anything the designer likes; we stop it after some agreed-upon number of steps T, a fair-sized multiple of N, say 100N or 1000N steps. Then, the challenge part: we re-run the pattern with the outer part of the background initialized randomly. The designer is supposed to use the membrane to protect the core against the evil influence of the surrounding chaos; after T steps we look at the core and see if it differed from the state of the core after T steps in the initial run.

I contend no such protection is possible. Chaos is too radioactive. I would love to be proven wrong.