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?