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Replicator idea.

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Replicator idea.

Postby Keiji » August 4th, 2010, 4:56 pm

We already have Life meta-cells - large square Life patterns that can be put in grids to simulate any Life-like rule.

Is it possible to come up with a meta-cell whose population is zero if the state it is simulating is "dead"? If it were possible at all, I would imagine it would be done by having gliders or other spaceships from neighboring cells colliding in a "dead" meta-cell and thus forming whatever circuitry was required to recreate the meta-cell itself.

If this were possible, you could simply set it to simulate HighLife, with the HighLife replicator as the simulated pattern, and voila, you now have a Life replicator.

I'm sure that, if such a meta-cell were possible, it would be much larger than current meta-cells, but I had imagined it may be significantly smaller than a "universal computer-constructor"-based replicator.
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Re: Replicator idea.

Postby calcyman » August 5th, 2010, 3:41 am

If this were possible, you could simply set it to simulate HighLife, with the HighLife replicator as the simulated pattern, and voila, you now have a Life replicator.


I've considered this before.


but I had imagined it may be significantly smaller than a "universal computer-constructor"-based replicator.


No, each metacell would need eight universal construction arms, and the appropriate tape for directing them to construct another metacell.
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Re: Replicator idea.

Postby Keiji » August 5th, 2010, 6:52 am

That's if you rely on universal construction to make the meta-cell. There may be a more specialized way to do it.
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Re: Replicator idea.

Postby Macbi » August 5th, 2010, 7:31 am

There's no point in using meta-cells though. Just take whatever mechanism is used to make a new meta-cell when one is needed, and use it in a replicating spaceship instead.
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Re: Replicator idea.

Postby calcyman » August 6th, 2010, 6:24 am

That's if you rely on universal construction to make the meta-cell. There may be a more specialized way to do it.


Tape-directed universal construction is the only way to construct new metacells.


Furthermore, there are much simpler replicators than HighLife's replicator. A single cell in Rule 90 self-replicates, and requires only two inputs and outputs, as opposed to eight.
Last edited by calcyman on August 12th, 2010, 4:30 am, edited 1 time in total.
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Re: Replicator idea.

Postby Sam Alexander » August 11th, 2010, 11:31 pm

I'm kind of a newbie so I might not be understanding you right.

But it seems to me like if such metacells could be found where the "dead" metacell has population zero, and these metacells satisfied life-like rules where a spaceship can achieve diagonal speed c/3, then the corresponding metacell spaceship would have diagonal speed c/3 in Conway's Life, contradicting the fact that c/4 is the diagonal speed limit there.

EDIT: No, nevermind, I just realized, it must take many generations in the real game for one generation to occur in the meta game. This might lead to spaceships with interesting speeds, though: if some metacells satisfy life-like rules which permit a spaceship that goes speed x, and it takes n real generations for one meta generation to pass, and the meta cells are dimension k by k, then that yields a ship in Conway's Life which moves at speed xk/n... assuming of course that the "dead" metacells have pop 0
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Re: Replicator idea.

Postby Tropylium » February 14th, 2013, 10:14 pm

Revisiting this topic, I notice one argument had not been made. While this is certainly true…
calcyman wrote:Tape-directed universal construction is the only way to construct new metacells.

…this however need not be:
calcyman wrote:each metacell would need eight universal construction arms, and the appropriate tape for directing them to construct another metacell.

Under the "simulated replicator" approach, it's possible to consider equipping each metacell with only "half" a construction arm in each direction. This might simplify the actual job of construction quite a bit, eliminating the need for second-degree (elbow) advance/retract commands. In other words, new metacells would be constructed by input from two or more adjacent metacells. (Circuitry for metacells communicating their presence to each other would be required, of course.)

The same might be downgradeable to a simpler replicator mechanism just as well. At its simplest, a replicator unit would only need four half-constructor arms: forward, forward-right, backward, backward-right. Combined with a mirror image (or a near mirror image, to make sure they agree on which daughters get constructed first) this would suffice to emulate the "bare domino" replicator:
...O... → ..O.O.. → .O...O. → O.O.O.O → etc.
...O...   ..O.O..   .O...O.   O.O.O.O
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Re: Replicator idea.

Postby dvgrn » February 15th, 2013, 12:13 pm

Tropylium wrote:The same might be downgradeable to a simpler replicator mechanism just as well. At its simplest, a replicator unit would only need four half-constructor arms: forward, forward-right, backward, backward-right. Combined with a mirror image (or a near mirror image, to make sure they agree on which daughters get constructed first) this would suffice to emulate the "bare domino" replicator...

Seems like once you've given up the universal metacell capability by adding special-purpose circuitry to support particular rules or particular replicators, you can simplify a bit more than that. If I'm thinking about this right, you'd still need four "half-constructor arms" to emulate a Rule-90 1D rule, but you wouldn't need any near mirror images.

However, the idea of half a constructor arm isn't very clear to me. Should I be thinking about half of a Gemini-spaceship-style pair of 90-degree construction arms? I tend to think of that as one construction arm, not a half of anything.

It's certainly possible to have two replicators each supplying half of the data for a single replicator arm. This would be fairly trivial with a single-arm Geminoid design, in particular. This kind of arm can be programmed to build arbitrary constellations either leftward or rightward from the elbow, so there's quite a lot of construction flexibility. You can even have two or more elbows in series, to build things around multiple corners, if you don't mind exponentially longer recipes.

But I don't immediately see any advantages to dividing the work up between two replicators, instead of just sending everything from one place. Each replicator has to have a copy of all the construction information, anyway, and the communication problem (i.e., which neighbor gets the task of building a given new metacell) is fairly easy to solve in any case.

With single-arm construction, it would be possible to build a Rule 90 metacell/replicator with just two arms, let's say SW and SE... and some equivalent Sierpinski-type rules could be emulated with a metacell/replicator with just one arm, pointed SE let's say. You could get the usual sawtooth-population replication pattern by having each metacell send a self-destruct signal to its neighbor on the right, or build a copy of itself there if there is no right-hand neighbor. (Or what am I forgetting here?)

Edit: Looks like this is Wolfram's Rule 60. I'll have to think a bit more to see if a one-arm design can do something a little more interesting, along the lines of Rule 124 -- but Rule 124 has construction effects that would have to propagate leftward as well as rightward. Is there an interesting 1D automaton where the metacell would only have to send destruct signals leftward?
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