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:

Code: Select all

```
#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...!