simsim314 wrote:I've a small modification to the plan:
1. Use a thin universal constructor, that requires 3-4 different lanes for all operations.
2. Use unique A-B-C-D construction for each lane.
3. Using universal constructor, we can make dry salvo of the 9-glider combinations for the next step. This only requires about 40 dried gliders, which will be build with universal slow salvo thin constructor.
The current plan involves reducing the number of half-bakery trails to the bare minimum needed to build universal slow salvos (currently 11, including two "guard trails"). These NEward gliders will use adjustable elbows to fire gliders SE and NW to rebuild and trigger a freeze-dried 11-glider seed at the NE end of the ship.
Let's see if I understand this new proposal correctly. The idea is to increase the number of half-bakery trails until we can build synchronized
triplets or quadruplets of northeast-traveling gliders -- is that right?
The advantage of using synchronized gliders would be that you get exactly the combinations of gliders you want, as fast as you can build them; theoretically you could pack the rakes as tightly together as the half-bakery reaction allows.
Here are some notes on why I don't think this will work very well for a knightship using half-bakeries:
- Three synchronized gliders would need about 30 trails, and four would need 40 trails. (Please correct me if I go wrong here.) It might be hard to find a universal set of elbow operations with just three gliders, especially because the available ABCD recipes will restrict where we can build multiple gliders close to each other.
- Synchronized salvos will only work if the elbow is drifting 2hd south and east with every operation, because that's how these strange half-bakery rakes work! I don't know if even four synchronized gliders can manage to make an elbow do this 2hd drifting trick. The alternative would be to do a reset after every glider, same as in the 9-trail design, but that would almost certainly make up for any efficiency gains from the synchronized method.
- Another disadvantage of synchronized gliders is that elbow movement wouldn't be very efficient, due to the limited number of operations. The elbow would have to be constrained to stay on a particular line, diagonal or oblique, and each operation would have to restore the elbow to the same state to accept the next synchronized salvo. In practice an N-glider synchronized salvo would allow a lot less than 2^N-N working ops, I think -- you might just find INC1, DEC1, BLACK and WHITE... and for this knightship to work we'll really need separate operations to shoot each color of glider left and right from the elbow.
- By contrast, the "slow elbow" method can convert any random piece of junk into an elbow target, and the target can drift around anywhere inside the wide 79hd shooting range without causing any particular problems, and we can shoot gliders to the left and the right equally well. If we're hitting multiple slow targets simultaneously, each elbow might be constrained to drift around inside about a 30hd diagonal stripe.
- A major disadvantage of doubling or tripling the number of trails is that each ABCD set will need a different custom way of suppressing the synchronized gliders coming out at the SW end. There might end up being standard ways to clean up any SW-traveling gliders using a small set of dedicated rakes on the SE side... but for the moment it's looking a lot easier to solve one specific suppression problem that's as simple as we can make it, for one particular minimal set of nine trails.
- The more half-bakery trails we have, the bigger the freeze-dried salvos will be that we'll need to build and rebuild at the NE end. The increase in recipe size will be something-or-other bigger than O(N), where N is the number of trails, because all the glider seeds have to be triggered in precise synchrony with each other. This will tend to require more and more "one-time wiring" as N increases. Also seeds with a larger area take proportionally more work to construct.
Currently known recipes seem to indicate we can get a 90-degree glider out for about every 6 slow gliders that we shoot at a target -- three or four gliders to move the target to a good spot, and two or three more to extract a 90-degree glider. With the 9-trail system we can use only about one out of every 20 gliders that we could theoretically shoot, so that works out to about 100-150 half-bakeries in each trail for every 90-degree glider that we get from the elbows in the NE to do actual construction
(It would be more like 1:13 instead of 1:20 if we assume we're working with three elbows simultaneously and using P1 slow salvos -- but every now and then we'll have to skip taking a shot at one elbow or another, and reset to get the other phase of a glider on a particular lane.)
We might have to rebuild about a 50-still life seed to get our 9 synchronized gliders. Let's say 10 slow gliders are needed to build each still life, with 150 half-bakeries per still life. That give us 75,000 half-bakeries in each trail, more or less, and a bounding box of maybe 40x75K=3 million cells on a side.
That's going to be pretty big! So... have we missed anything? Or are my calculations badly off somehow? Is there another design that will allow for a significantly smaller knightship?
simsim314 wrote:I was trying to optimize universal construction lanes. The best I really came up with is (although I vaguely remember dvgrn had posted some improvement over it)...
The key improvement is the one I described above. With slow-elbow constructions, it's generally kind of a waste of gliders to move an elbow back to its exact original location -- or even to convert it back to the same type of object again. For the next sideways glider the elbow will have to move somewhere else anyway, and will go through all kinds of other object stages along the way. Might as well work directly from whatever junk is left over from the last sideways glider construction.
Each new output glider is buildable anywhere along its lane, so it will be a matter of hunting through lots of possible elbow moves to find the cheapest one. As we've discussed elsewhere, it will probably take some significant new search software to come up with longer slow-elbow salvos that are really optimal.