oblique wrote:My current - almost usable enough to run first tries - multi bakerake version of the search has a notion of "state" ... currently it's expressed in a lane offset between lane 0 of the pattern and lane 0 of the track. In other words: state = 0 means that a R1L0B rake will just hit the bottom left edge of the bounding box of the current target.

One of the unfinished problems is the value of this state at the start of the search.

Okay, so then state = 1 is the next lane, which will also hit the current target -- but state = -1 (or state = 30) would presumably miss it?

It should be easy to translate my current investigations into those terms. I'm working toward a simple parametrization of the possible locations of any constructed object, relative to the block trails, using collisions between gliders on backward lane B and forward lane F.

oblique wrote:If you would find out that there are only some possible values for this state after the creation of any of these targets that would greatly reduce the search space (currently I'm trying to allow any combination of state, rake and starting pattern at a fixed cost).

There are definitely initial targets that are more expensive and less expensive, depending on the exact location. But with twelve different fore+back rake combinations (even assuming nobody comes up with more variants) there will be relatively few targets that need more than (say) two dozen rephasers total to construct, and also relatively few that need less than half a dozen.

As an example, below I've attached a much smaller spaceship termination than

the one I posted earlier on the 31c/240 thread. It can still be tightened up a bit more, but this is pretty good. I've been looking at packing rephasers a little closer together -- it's certainly possible, especially for longer chains:

`#C 5 mutually suppressing rephasers, 3 shorter ones in the middle,`

#C using about as much space as 4 standard-height rephasers

x = 801, y = 2512, rule = B3/S23

126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b

2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o

114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o

108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o

88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o

108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o

114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$

126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o

114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o

108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o

88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o

108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o

114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$

126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b

2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o

114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o

108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o

88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o

108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o

114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$

126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o

114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o

108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o

88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o

108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o

114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$

126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b

2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o

114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o

108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o

88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o

108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o

114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$

126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o

114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o

108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o

88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o114b2o

108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$126b2o

114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o30$

126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b

2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o

114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o

108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o

88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o

108b2o88b2o108b2o114b2o30$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o

114b2o108b2o88b2o108b2o114b2o6$668b2o$667bo$127b3o537b3o$126bo3b2o520b

o13b3o7b3o$125b4ob2o3b2o514bo2bo10bo10b3o$124b2o2b3o3bo2bo517bo6bob2o

3bo4bo4bo$125bobo6bo2bo512bo4bo5bo7bo4bo3b2o$126b2o5b2ob2o516b2o5bo6bo

9bo$134b2o526bo11bo2bo$651b3o10b3o3b2o3bo$670b2o$670bo4$126b2o540b2o$

126b2o540b2o6$139bo$140bo$138b3o101b2o108b2o88b2o108b2o$242b2o108b2o

88b2o108b2o2$651bo$134b2o514bo9b2o$134b2o514b3o7b2o17$126b2o540b2o$

126b2o540b2o8$242b2o108b2o88b2o108b2o$242b2o108b2o88b2o108b2o3$134b2o

524b2o$134b2o524b2o17$126b2o540b2o$126b2o540b2o7$552b2o$352b2o88b2o

106bo$241bob2o107b2o88b2o104bo3bo$235b2o4bo2bo303bobo2bo$60bobo173bo4b

o310b2o$60b2o72b2o101b3obo305b2o111b2o$61bo72b2o101bo2b2ob3o301bo7bo2b

o101b2o$237bo3bob3o315bo$239b2o311bo8bo$548bobobo8bo176bobo$551b4o3bo

180b2o$548bo3bo186bo$224b5o320bobo$225b3o$226bo20b2o$246bo2bo6bo291b2o

$246bob2o4b2o292b2o$247bo3b5o$251bo2bo$248bob4o$249bo$248bo2$126b2o

114b2o22bo285b2o114b2o$126b2o114b2o23bo284b2o114b2o$265b3o3$199bo324bo

$200bo322bo$198b3o322b3o2$352b2o88b2o$352b2o88b2o147bo$590bo$590b3o$

134b2o98b2o324b2o98b2o$134b2o98b2o324b2o98b2o9$439bo$438b3o$213bo223b

2o2bo$211b2o228b2o$212b2o224b3ob2o$359b2o78bo2b2o$359b3o76b3o$358bo2bo

79b2o144bo$126b2o114b2o113b2ob2o79b2o109b2o34b2o78b2o$126b2o114b2o113b

2ob2o190b2o33b2o79b2o$358b2ob2o$361bo72bo$358b3o73bobo$359bo74b2o7$

350b2o$134b2o98b2o114b2o8b2o72b2o124b2o98b2o$134b2o98b2o124b2o72b2o

124b2o98b2o$349bo$348bobo$351bo$346bo3bo$345bo4bo$344bo2$349bo$346bo8$

126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b

2o9$obo$2o$bo$134b2o224b2o72b2o224b2o$134b2o224b2o72b2o224b2o$798bobo$

799b2o$799bo14$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o

88b2o108b2o114b2o12$134b2o224b2o72b2o224b2o$134b2o224b2o72b2o224b2o9$

153bo$151b2o$152b2o2$416bo$414bobo230bo$415b2o231b2o$647b2o$126b2o114b

2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o20bo67b2o108b2o114b2o$374b

obo421b2o$374b2o421bobo$799bo3$b2o$bobo$bo4$134b2o224b2o72b2o224b2o$

134b2o224b2o72b2o224b2o17$126b2o114b2o108b2o88b2o108b2o114b2o68b2o$

126b2o114b2o108b2o88b2o108b2o114b2o67bobo$739bo3$61b2o$61bobo$61bo22$

678b2o$677bobo$126b2o114b2o108b2o88b2o108bo115b2o9bo$126b2o114b2o108b

2o88b2o107bob2o113b2o$551bo3bo2b3o$121b2o428bo5bo$121bobo119bo307b2obo

bo$121bo115b2o3bob5o301bobobo4bo$236bo2b4o2b4ob2o298bobobob3o$235bobob

2o2b3o305bo3b2o$231b2ob2o431b2o$225bo4b4o3b3o329bo95b4o$225bo4bo8bo11b

3o314b3o94bo2bo$225bo5bobob2o13b2o3bo311bobobo87b2o3b2o4b2o$232bobo2b

4o7b2o3bobo311bobobo85b2o2bo3b3o3b2o$239b2o6bobo5bo291b2o19b3o86bo2b3o

2bob2ob2o$130bo105b3o7bo4b3o291bo3bo19bo87bo4bo4b4o$129b3o101b2o2b2o6b

o6bo290bo5bo108b5o$128bo2b2o102bobo8bo296bobob2o111b2o$127b2o106b3o9b

4o291bo4bo$126b2ob3o130bo279bo4bo$126b2o2bo129bobo279bo4bo$129b3o129b

2o281b3o$127b2o$127b2o113b2o308b2o114b2o$242b2o284bo23b2o114b2o$528bob

o$135bo392b2o$133bobo$134b2o482b2o$617bobo$619bo$655bo$352b2o88b2o211b

obo$181b2o169b2o88b2o211b2o$181bobo$181bo$134b2o98b2o324b2o98b2o$134b

2o98b2o324b2o98b2o7$216bobo$216b2o$217bo3$582bobo$583b2o$583bo$434bo2b

2o$438b2o$126b2o114b2o193b2o113b2o114b2o$126b2o114b2o308b2o114b2o$433b

2o2b2o$359b3o77bo118b2o$359bobo71b4o120bobo$358bo2bo73bo2bo120bo$358b

3o$358b3o$241b2o116bo2bo$241bobo115bo$241bo120bo2$350b2o8bo$134b2o98b

2o114b2o9bo72b2o9b3o112b2o98b2o$134b2o98b2o124b2o72b2o124b2o98b2o$445b

3o$445b2o3$349bo$348bobo$348bob2o$351bo$348bobo$349bo7$126b2o114b2o

108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o54b2o52b2o114b2o$497bob

o$499bo3$301b2o$66bo234bobo$64b2o235bo$65b2o3$734bo$134b2o98b2o124b2o

72b2o124b2o98b2o73b2o$134b2o98b2o124b2o72b2o124b2o98b2o72b2o17$126b2o

114b2o108b2o88b2o108b2o114b2o$126b2o67bo46b2o108b2o88b2o108b2o114b2o$

193bobo$194b2o3$595bo$595bobo$595b2o5$134b2o98b2o124b2o72b2o124b2o98b

2o$134b2o98b2o124b2o72b2o124b2o98b2o5$156bobo$156b2o$157bo2$412bo$410b

obo229bobo$411b2o230b2o$643bo2$378bo$378bobo$378b2o$126b2o114b2o108b2o

88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o12$134b2o98b2o

124b2o72b2o124b2o98b2o$134b2o98b2o124b2o72b2o124b2o98b2o17$126b2o114b

2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o67b2o$

736bobo$738bo3$62b2o$62bobo$62bo22$677b2o$126b2o114b2o108b2o88b2o224b

2o6bobo$126b2o114b2o108b2o88b2o109bobo112b2o8bo$550b2o2bo4bo$550bobo6b

2o$122b2o119b2o304b2obo2bo4b2o$122bobo117bo2bo2bo300b2o9b2o$122bo119bo

b4ob2o300b2obob5o$237b3o3bo2b2o2bo305bo2bo$236bo2bo9b2o305bo2bo$225bo

9b2obo329bo96bobo$225bo3b3obo18b2o289b2o22bo2bo94bob2o$225bo7bob4o13b

2o314b3o93b2o2b2o$234b2o3bo10bo2bo293bo20b3o88b3o7b2o$235bo2bo10bo2bo

285bo120bo8b2o$235bo2bo9bo4bo284bo4bo3b2o110bobo6bo$235b3o9b2o3bo286bo

bo5bobo110b2o$130bo117b2o291bobo4b2o$129b3o117bo11bo280b2o4b2o117bo$

128bo2b2o126bobo281bo2b3o119bo$127b4obo127b2o284b3o118bo$127bo4bo$128b

2o2bo$129b2o111b2o285bo22b2o114b2o$242b2o285bobo20b2o114b2o$134bo394b

2o$132bobo$133b2o2$617b2o$616bobo37bo$618bo37bobo$352b2o88b2o212b2o$

352b2o88b2o$182b2o$182bobo$134b2o46bo51b2o324b2o98b2o$134b2o98b2o324b

2o98b2o6$217bobo$217b2o$218bo3$581bobo$582b2o$582bo$435b2o$434b3o$434b

o2bo$126b2o114b2o190b2ob2o113b2o114b2o$126b2o114b2o190b2ob2o113b2o114b

2o$433b2ob2o$434bo$435b3o119b2o$359b3o74bo119bobo$359bo2bo195bo$358bo$

361b2o$242b2o113bo3b2o$242bobo112bo$242bo116bo$350b2o7b3o82b2o$134b2o

98b2o114b2o8b2o72b2o8b2o114b2o98b2o$134b2o98b2o125bo72b2o124b2o98b2o$

446bo$445bobo$444bo$445bo3bo$349bo95bo4bo$349bobo99bo$349b2o$349bo96bo

$348b2o99bo$348b2o7$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o

108b2o88b2o108b2o114b2o$497b2o$496bobo$498bo2$67bo$65b2o235b2o$66b2o

234bobo$302bo2$733bo$734b2o$134b2o98b2o124b2o72b2o124b2o98b2o71b2o$

134b2o98b2o124b2o72b2o124b2o98b2o17$126b2o66bo47b2o108b2o88b2o108b2o

114b2o$126b2o64bobo47b2o108b2o88b2o108b2o114b2o$193b2o3$596bo$596bobo$

596b2o6$134b2o98b2o124b2o72b2o124b2o98b2o$134b2o98b2o124b2o72b2o124b2o

98b2o4$157bobo$157b2o$158bo2$411bo$409bobo229bobo$410b2o230b2o$642bo2$

379bo$379bobo$379b2o2$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o

108b2o88b2o108b2o114b2o12$134b2o98b2o124b2o72b2o124b2o98b2o$134b2o98b

2o124b2o72b2o124b2o98b2o17$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o

114b2o108b2o88b2o108b2o114b2o$736b2o$735bobo$737bo3$63b2o$63bobo$63bo

22$126b2o114b2o108b2o88b2o109b3o112b2o6b2o$126b2o114b2o108b2o88b2o107b

5o112b2o5bobo$557b3o117bo$550bo7b2o$550bo3b2o3bo$123b2o118b3o305bo2b2o

bob2o$123bobo117b3o2bo303b6o$123bo119bob3obo303bo3bo2bo$236b3o8bobo

309bo10bo$231b2o5bo11bo312bo4bo2bo93bo$225b2o3b4obo14b2o310bo6bobo93b

2o$224b2o4bob2o4bo10bo2bo291b2o23b2o93b4o$224b2o12bo10bo2bo290bo2bo15b

3o96b3o3b2o$225b3o10bo10bo3bo284b3ob2ob3o113bo5bo$226b3o3bo2bo2bo10bo

2bo285b2o3bo2b3o112bo$230b2o4b2o10b2obo288b2obob2o2bo112bo4bo$248b2o

10bo281b12o110bo2b2o$258bobo285bo5bo112bob2o$130bo128b2o286b2o117b2o$

129b3o416bo2bo$128bo2b2o416bo$128bo401bo$129bo112b2o286bobo19b2o114b2o

$133bo108b2o286b2o20b2o114b2o$131bobo$132b2o3$657bo$616b2o39bobo$615bo

bo39b2o$352b2o88b2o173bo$352b2o88b2o2$183b2o$134b2o47bobo48b2o324b2o

98b2o$134b2o47bo50b2o324b2o98b2o5$218bobo$218b2o$219bo3$580bobo$581b2o

$581bo4$434b3o$126b2o114b2o189bo3bo114b2o114b2o$126b2o114b2o194bo113b

2o114b2o2$433b2o3bo$435b3o$556b2o$555bobo$359b3o195bo$359bo2bo$358bo3b

o$243b2o113bobob2o$243bobo113b2ob2o$243bo106b2o8b3o81b2o$134b2o98b2o

114b2o82b2o8b2o114b2o98b2o$134b2o98b2o198b2o124b2o98b2o6b3o$670bo$669b

o$446bo$350bo94b3o$130b3o217bobo91b2ob2o$130bo219b2o91bo$131bo310bo4bo

b2o$442bo4bobo$348b2o93bo4bo$348b2o7$126b2o114b2o108b2o88b2o108b2o114b

2o$126b2o114b2o108b2o88b2o108b2o114b2o2$496b2o$495bobo$497bo3$303b2o$

303bobo$303bo2$608b3o$134b2o98b2o124b2o72b2o124b2o48bo49b2o$134b2o98b

2o124b2o72b2o124b2o47bo50b2o3$190b3o$190bo$191bo11$193bo$126b2o63bobo

48b2o108b2o88b2o108b2o114b2o$126b2o64b2o48b2o108b2o88b2o108b2o114b2o3$

597bo$597bobo$597b2o4$548b3o$550bo$549bo$134b2o98b2o124b2o72b2o124b2o

98b2o$134b2o98b2o124b2o72b2o124b2o98b2o$250b3o$250bo$158bobo90bo$158b

2o$159bo2$410bo$408bobo229bobo$409b2o230b2o$641bo2$380bo$380bobo$380b

2o3$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o

114b2o7$488b3o$490bo$489bo3$134b2o98b2o74b3o47b2o72b2o124b2o98b2o$134b

2o98b2o74bo49b2o72b2o124b2o98b2o$311bo16$126b2o114b2o108b2o88b2o108b2o

114b2o$126b2o114b2o108b2o88b2o108b2o114b2o5$428b3o$430bo$429bo3$370b3o

$370bo$371bo18$126b2o114b2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o

88b2o108b2o114b2o3$368b3o$370bo$369bo3$430b3o$430bo$431bo20$126b2o114b

2o108b2o88b2o108b2o114b2o$126b2o114b2o108b2o88b2o108b2o114b2o$308b3o$

310bo$309bo3$490b3o$490bo$491bo22$126b2o114b2o4b3o101b2o88b2o108b2o

114b2o$126b2o114b2o6bo101b2o88b2o108b2o114b2o$249bo3$550b3o$550bo$551b

o22$188b3o$190bo$132b2o55bo52b2o108b2o88b2o108b2o$132bobo107b2o108b2o

88b2o108b2o$131bo2bo531bo$124b2o4b2o2b2o474b3o52b2o$124b2o4b2obo476bo

52b2obo$611bo58bo$135bo526bo2bo4b2o$135bo527b2obobo2b2o$662bobo2b2o$

131bo530bo2bo$662bo$133b2o528bobo$134bo529bo$133b3o$122b2o548b2o$122b

2o548b2o7$126b2o540b2o$126b2o540b2o4$128b3o$130bo$129bo2$242b2o108b2o

88b2o108b2o$242b2o108b2o88b2o108b2o116b3o$670bo$671bo$134b2o524b2o$

134b2o524b2o44bo$707bo$705b3o3$84bo$83bo$83b3o10$126b2o540b2o$80bo45b

2o540b2o$79b2o$79bobo3$710bo$710b2o$625bo83bobo$242b2o108b2o88b2o108b

2o69b2o$242b2o108b2o88b2o108b2o70b2o3$134b2o39bo484b2o$134b2o40b2o482b

2o$175b2o9$239bo$238b3o$237bo2b2o$237bob2o$239b2ob2o$236bo5bo316b3o$

140bo96bo4bo315bo$126b2o11b2o97bo2bo316bo2bo106b2o$126b2o11bobo98bo

318b2o107b2o$235bo323b2o$234bo323bo2bo$234b3o324bo88bo$558b2o90b2o$

649bobo3$352b2o88b2o$352b2o88b2o2$550b2o$134b2o98b2o314b2o8b2o98b2o$

134b2o98b2o324b2o98b2o2$549bo$548b3o$547bo3bo$546bo$545b2ob2o3bo$548b

2o$545bo6b2o$546b2o5$200bo$199b2o$199bobo$126b2o114b2o308b2o114b2o$

126b2o114b2o308b2o114b2o$590bo$590b2o$589bobo4$443bo$443b2o$442bobo$

442bobobo$442b2ob2obo$134b2o98b2o121b2o90bo110b2o98b2o$134b2o98b2o114b

o5bo2bo87b2o111b2o98b2o$357b3obo72bo$349bobo5bo3bo72bo$350bo10bo72bo6$

348b2o96b2o$348b2o96b2o2$260bo$259b2o$259bobo3$126b2o114b2o108b2o88b2o

86bo21b2o114b2o$126b2o114b2o108b2o88b2o86b2o20b2o114b2o$496bobo30bobo$

496b2o$497bo2$472bo92bo$302bobo165bobo90b2o$303b2o166b2o91b2o$232bo70b

o$231bo2bo$234b2o82bo$232bo3bo81bobo$134b2o96bo2bo82b2o40b2o72b2o124b

2o98b2o$134b2o97b2o125b2o72b2o124b2o98b2o12$615bo$616bo$614b3o3$126b2o

47bo66b2o108b2o52bobo33b2o108b2o114b2o$126b2o46bo67b2o108b2o52b2o34b2o

108b2o114b2o$174b3o230bo3$392bobo$393b2o$393bo6$134b2o224b2o72b2o224b

2o$134b2o224b2o72b2o224b2o17$126b2o114b2o108b2o88b2o108b2o114b2o$126b

2o114b2o108b2o88b2o108b2o114b2o12$134b2o224b2o72b2o224b2o$134b2o224b2o

72b2o224b2o!

It turned out that a 0B+21F collision can make interchanges at column 16 (mod 31), which means that only two rephasers need to be added between the rakes to get the required column 9 (mod 31) position. There may still be a better B+F rake pairing, but I wouldn't bet on it.

The really lucky thing was that the interchange showed up in exactly the right row -- at least I don't

think that the math made that inevitable... In general it can take up to 30 rephasers to align a slow-salvo rake with the leading side-puffer that makes the initial target, and there aren't really any shortcuts if you get an unlucky placement.

oblique wrote:Another problem with this notion is that I probably would have to make different adjustments for forward and backward rakes (an reaction that moves the construction site diagonally NE would not alter the state for the backrakes but it would alter the state fwd rakes).

My feeling is that slow salvos using both forward and backward rakes is too big a can of worms to open for the moment. All-forward and all-backward slow salvos are actually going to be significantly more efficient on average, because the rakes can be packed tighter together. When you have a backward glider stream, then a forward stream, then another backward stream, you have to build in a lot of vertical space to make sure the streams don't cross. Or if they do cross, that changes the collision order -- but whether they cross is dependent on how far away the target is. To me, at least, this all looks like a big unnecessary headache right now.

The really interesting generalization, if and when we ever get around to it, will be to hit targets with all possible simultaneous pairs and/or singletons of forward and backward gliders -- i.e., everything that can be made by appropriately spaced forerake-backrake pairs, at a reasonable distance from the block trails. The branching factor of this tree makes the current slow-salvo search tree look tame by comparison, but by the same token, it should be possible to construct seeds with a much lower total cost.

EDIT: Very likely a few four-rake combinations will happen to produce clean glider outputs on new lanes, which would count as fairly competitive new rakes. It will be tricky to find very many of these without some kind of search program, though...!