triller wrote:Dave, your improved PD recipe would break down in my construction arm at glider 5...
Well, or perhaps my "improved" recipe just plain isn't an improvement for your purposes! I haven't done much with those original WHITE/BLACK/INC/DEC salvos for a while -- too many different input lanes. Newer Geminoid replicator units need just two input lanes to move the elbow and fire both colors of glider. You could actually do the trick with pairs of gliders on just one lane
, but that might be going a bit too far.
Anyway, you're absolutely right that my 19-glider recipe wouldn't work in the old 2003 prototype construction arm, which used those salvos. The original idea was to use only stable intermediate patterns, on the theory that not having to handle separate WHITE-ODD, WHITE-EVEN, BLACK-ODD, BLACK-EVEN salvos would make the circuitry enormously simpler. With stable intermediate patterns, the phases of the BLACK and WHITE gliders would never matter; construction options are much more limited, but it still appears to be a universal construction toolkit.
triller wrote:Perhaps I've overlooked a step in the evolution of elbow based slow salvo theory that it would behoove me to be aware of. If so, examples would be most appreciated.
The Gemini spaceship used the exact same salvos from your image -- but Andrew Wade's radical simplification was to remove all the complicated clock and tape-reading circuitry. He ran the construction arm completely asynchronously with twelve streams of gliders (he had to, to get the gliders from his two construction arms synchronized properly). With Gemini's asynchronous memory, it's trivial to produce any phase of BLACK or WHITE output glider just by changing the phase of the input gliders.
The newer Geminoid constructor arms shamelessly copy this innovation, but reduce the amount of circuitry by a couple more orders of magnitude by using just two channels instead of twelve -- removing one more layer of complexity by feeding each of the two lanes leading to the elbow directly with its own channel. In other words, the INC/DEC/BLACK/WHITE recipes are stored directly in glider-stream "memory", not encoded in any way.
As a handy side effect, it' now makes perfect sense to have dozens of INC, DEC, BLACK, and WHITE recipes instead of just one each. It makes slow-salvo construction a lot more efficient when you can do a one-step INC7 or DEC22
instead of seven or twenty-two separate operations...!
This also means that my 19-glider PD recipe works fine in a Geminoid replicator unit -- it can easily handle what I call "P2 slow salvo" constructions. Succeeding gliders from the elbow don't have to arrive at any particular time, but they do have to have the right phase mod 2 whenever they arrive, because intermediate patterns are allowed to be either period-2 or stable.
(Really in a Geminoid design it's perfectly possible to allow intermediates that are period-3 or higher, but there are relatively few easy-to-reach P3+ oscillators... including pulsars as targets doesn't really add much construction versatility, so it's simpler to exclude everything above P2.)
I think the first thread in this post has some P2-slow recipes, come to think of it. It might be possible to convert them to something usable by a construction arm with a period-120 clock, though... what should we call this kind of thing? P2 intermediate patterns, but you're only allowed to hit them with WHITE-ODD or BLACK-EVEN gliders. "Phase-limited P2", maybe?
It's still fairly likely that the 22-glider PD recipe could be improved a bit by tricks like the ones I used. You'd just have to use Paul Chapman's original P1 slow-salvo block-move table
instead of the new (more efficient) P2 one, and be careful that your initial junk includes a blinker in the right phase that doesn't have to be moved... and that last part is probably a good idea anyway!