codeholic wrote:Do we actually need all possible equivalence classes? For the "classic" setup with 1 NW and 2 SE rakes we'd need just one of each type, if I get it right. If we are to build 1 NW reflector + 3 SE rakes then we'll need at most 2 same-color turners and 1 anti-color turner.
That seems mostly right. If I have all the math figured out right (and please don't assume that!) then we can perfectly well get away with just one same-color and one anti-color 180-turner no matter what the rake geometry is.
We can freely substitute any same-color rake for any other same-color rake, and the same with the anti-color ones. The only caveat is that we have to adjust the number of resets, to produce a glider with the right timing mod 8 so that the 180-turned glider goes to the correct spacetime location.
Our anti-color rake collection includes a 0-delay and a 4-delay rake. I believe this means that we can get away with no more than three resets before one of those two rakes will produce its output in the correct phase mod 8. If we had 2-delay and 6-delay anti-color rakes as well, then we'd need just one reset at most.
Depending on the timing, we might not need any resets at all -- I haven't tried building any of the actual HB-trail geometries yet to see how the current collection works out. A knightship might work out perfectly for some carefully chosen period P+8N, but you'd need seven resets if you wanted to build period P+8N+1 (or whatever).
So it seems to make sense to keep collecting and classifying 180-turners just until it gets too annoying to do any more -- and then we'll just pick a knightship period that works best for the equivalence classes we have available, to find a front end that needs only a reasonable number of resets.
I'm finding the new A1:BCDA2 design
to be a bit of a headache, in terms of figuring out how far away to put A2 at the northwest end so that it will end up at exactly the right place in the southeast
when it's time for the suppression reactions to happen.
It looks to me as if we'll have to send the C trigger gliders, and maybe the A2 ones also, to their 180-turners right away, and then wait for quite a few resets before we can send the B trigger gliders. The C gliders will get slowed down a lot by the very long string of half-bakeries they'll need to reach their initial diagonal -- but we need them to arrive a good while before
the B gliders, so we'll have to wait around before triggering the Bs.
(We can't just move the B 180-turners farther northeast in this case, because the trigger and return glider paths would cross the C gliders' half-bakery chains, and of course those aren't permeable.)
We can be building a superslow elbow on the A1 track in the NW while all these resets are going on, so we're not exactly wasting HBK length. But if lots of resets have to happen anyway, then we definitely don't need representatives of all 16 180-turner equivalence classes. The two that chris_c has already made into (-3,-6)-compatible recipes should be all we need...!
See any holes in my wild theories so far?