dvgrn wrote:Use or non-use of the semi-Snark doesn't make any difference to the speed-limit calculation, because the limiting factor is the repeat rate slowest piece of necessary circuitry that will process the INC instructions.
As Calcyman mentioned, once we're rebuilding the Gemini anyway, there are various obvious ways to improve on that (1,1)c/579 speed limit. For starters, he suggested replacing the 575-tick Silver reflector/G-to-H converter in the Gemini -- I think there were only a few of them, anyway! -- with equivalent 497-tick-recovery G-to-H units, to bring the speed limit up to (1,1)c/501.
But that's just the tip of the iceberg. It's technically possible to overclock a Silver reflector to run at double speed. That might work for some Geminoid construction-arm designs where there's a single input channel decoded with semi-Snarks, but the coded stream of glider pairs will cut the elbow speed in half so you'd end up right back where you started. There are ways to avoid that problem, but it's a big headache.
A much better trick is to use tandem gliders as signals; with a decent dead spark coil recipe
, a Geminoid using Herschel transceivers could process INC instructions with 117-tick spacing, for a speed limit of (1,1)c/121.
The new 9hd and 10hd construction arms make things even more complicated, because there are multiple INC operations with different lengths and different costs. It's still unknown what the most efficient INC operation is for either 9hd or 10hd. However, there's a four-cycle 10hd INC10, and maybe a 5-cycle 9hd INC12 (can't find the reference right now). That would increase the speed limit to around (1/1)c/100.[Explanation of silly terminology: A "four-cycle INC10" just means there's a four-glider-pair recipe that can push an elbow block (10,10). If that could be done at 117-tick spacing, the elbow would move at about (1,1)c/87 -- 117*4/10, plus 40 ticks for the Doppler effect of the elbow moving away. But that doesn't work in practice because the four glider pairs aren't identical. You need to allow some extra ticks so that both channels can run at 117-tick spacing simultaneously.]
Spartan Herschel circuits can be made to work at 117-tick compression, and they are universal -- they can do any task that slower circuits can do, as long as space and absolute construction time are not limited. But they're very awkward to work with, so we're probably talking about stable circuitry an order of magnitude bigger than what's in the current linear replicator.
At some point, if you have to build lots of still lifes anyway, it makes more sense to go back to a minimal constructor arm, and use it to build and trigger a Cordership seed. Then you wait around a long time -- no trillions of gliders needed for INC operations in this case! -- send a glider or two to shoot down the Cordership, and build your next replicator unit out of the debris. That gives you a spaceship speed asymptotic to c/12. The equivalent for orthogonal construction arms would be a loafer followed by a *WSS, with a speed asymptotic to c/7.