ConwayLife.com • OWSS synthesis project

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OWSS synthesis project

Posted: July 14th, 2025, 7:57 pm

by Sokwe

This thread is for discussion of overweight spaceship syntheses. My hope is that this will lead to explicit constructions in Catagolue for all 780 "simple" flotillas, those consisting of a single OWSS supported by two standard spaceships. Other types of OWSS syntheses may also be discussed in this thread.

Below is a table containing what I believe to be all glide-symmetric OWSS flotillas supported by two standard spaceships:

Code: Select all

x = 569, y = 154, rule = B3/S23
130b3o9b3o9b3o9b3o167bo13bo$26bo11bo91bo2bo8bo2bo8bo2bo8bo2bo165b3o11b
3o$2bo11bo10b3o3b3o3b3o20b3o20b3o22b3o19bo5b3o3bo11bo5b3o3bo16b3o3b3o
3b3o9b3o3b3o3b3o9b3o3b3o3b3o20b3o19b3o20b3o20b2obo4b3o3b2obo15bo5b3o5b
o9bo5b3o5bo22b3o20b3o27b3o22b3o$b3o3b3o3b3o8b2obo2bo2bo2b2obo19bo2bo
19bo2bo21bo2bo19bo4bo2bo3bo3bo7bo4bo2bo3bo3bo12bo2bobo2bo3bo2bo8bo2bob
o2bo3bo2bo8bo2bobo2bo3bo2bo18bo2bo18bo2bo19bo2bo20b3o4bo2bo3b3o15b3o3b
o2bo4b3o7b3o3bo2bo4b3o15bo4bo2bo5bo8bo4bo2bo5bo20bo2bo21bo2bo$2obo2bo
2bo2b2obo8b3o6bo2b3o16bo6bo4bo10bo6bo4bo12bo6bo4bo14bo7bo3bo11bo7bo3bo
3bo12bo7bo3bo11bo7bo3bo11bo7bo3bo16b3o5bo3b3o7b3o5bo3b3o8b3o5bo3b3o14b
3o7bo3b3o14b2obo6bo3b2obo6b2obo6bo3b2obo14b3o6bo4b3o6b3o6bo4b3o14bo7bo
5bo10bo7bo5bo$3o6bo2b3o9b3o6bo2b3o15b3o5bo3b3o8b3o5bo3b3o10b3o5bo3b3o
14bobo4bo4bobo8bo7bo3bo16bo7bo3bo11bo7bo3bo3bo7bo7bo3bo3bo12bo2bo4bo3b
o2bo6bo2bo4bo3bo2bo7bo2bo4bo3bo2bo13b3o7bo3b3o14b3o7bo3b3o7b3o7bo3b3o
14b2obo2bo3bo3b2obo5b2obo2bo3bo3b2obo13b3o2bo3bo4b3o8b3o2bo3bo4b3o$3o
2bo3bo2b3o9b3o6bo2b3o14b2obo5bo2b2obo7b2obo5bo2b2obo9b2obo5bo2b2obo17b
o3bo16bobo4bo4bobo14bobo4bo4bobo8bo7bo3bo11bo7bo3bo3bo12bo7bo3bo9bo7bo
3bo10bo7bo3bo17b2o7bo4b2o14b3o7bo3b3o7b3o7bo3b3o14b3o7bo3b3o6b3o7bo3b
3o13b2obo2bo3bo3b2obo7b2obo2bo3bo3b2obo$b2o6bo3b2o10b2o6bo3b2o14b3o6bo
2b3o8b3o6bo2b3o10b3o6bo2b3o18bo3bo19bo3bo24bo3bo16bobo4bo4bobo8bo7bo3b
o16bo7bo3bo9bo7bo3bo3bo6bo7bo3bo3bo18bo3bo21b2o7bo4b2o7b3o7bo3b3o14b3o
7bo3b3o6b3o7bo3b3o13b3o7bo3b3o8b3o7bo3b3o$9bo19bo3bo20b2o2bo3bo3b2o8b
3o2bo3bo2b3o10b3o2bo3bo2b3o22bo23bo28bo23bo16bob2o3bo4bobo14bob2o3bo4b
obo6bo7bo3bo10bo7bo3bo3bo22bo30bo14b2o3bo3bo4b2o15b2o3bo3bo4b2o6b3o7bo
3b3o13b3o3bo3bo3b3o8b3o7bo3b3o$5bo3bo20bobo26bobo15b2o2bo2bo4b2o10b3o
2bo2bo3b3o19bobo21bobo26bobo21bobo21bobo26bobo15bobobobo5bobo7bo3b2obo
4bo23bobo28bobo21bobo28bobo14b2o4bobo5b2o14b2o4bobo5b2o8b3o3b2obo4b3o$
6bobo93b2o10b2o190bobo9bobo178b2o12b2o7$154b3o9b3o167bo13bo$2bo11bo11b
o11bo115bo2bo8bo2bo165b3o11b3o$b3o3b3o3b3o9b3o3b3o3b3o20b3o20b3o22b3o
43bo5b3o3bo17b3o3b3o3b3o8b3o3b3o3b3o9b3o3b3o3b3o20b3o19b3o20b3o20b2obo
4b3o3b2obo15bo5b3o5bo9bo5b3o5bo22b3o20b3o27b3o22b3o$2obo2bo2bo2b2obo8b
2obo2bo2bo2b2obo19bo2bo19bo2bo21bo2bo43bo4bo2bo3bo3bo13bo2bobo2bo3bo2b
o7bo2bobo2bo3bo2bo8bo2bobo2bo3bo2bo18bo2bo18bo2bo19bo2bo20b3o4bo2bo3b
3o15b3o3bo2bo4b3o7b3o3bo2bo4b3o15bo4bo2bo5bo8bo4bo2bo5bo20bo2bo21bo2bo
$3o6bo2b3o9b3o6bo2b3o16bo6bo4bo10bo6bo4bo12bo6bo4bo38bo7bo3bo3bo13bo7b
o3bo10bo7bo3bo11bo7bo3bo16b3o5bo3b3o7b3o5bo3b3o8b3o5bo3b3o14b3o7bo3b3o
14b2obo6bo3b2obo6b2obo6bo3b2obo14b3o6bo4b3o6b3o6bo4b3o14bo7bo5bo10bo7b
o5bo$3o2bo3bo2b3o9b3o6bo2b3o15b3o5bo3b3o8b3o5bo3b3o10b3o5bo3b3o37bo7bo
3bo17bo7bo3bo10bo7bo3bo3bo7bo7bo3bo3bo12bo2bo4bo3bo2bo6bo2bo4bo3bo2bo
7bo2bo4bo3bo2bo13b3o7bo3b3o14b3o7bo3b3o7b3o7bo3b3o14b2obo2bo3bo3b2obo
5b2obo2bo3bo3b2obo13b3o2bo3bo4b3o8b3o2bo3bo4b3o$b2o6bo3b2o9b3o6bo2b3o
14b2obo5bo2b2obo7b2obo5bo2b2obo9b2obo5bo2b2obo38bobo4bo4bobo15bobo4bo
4bobo7bo7bo3bo11bo7bo3bo3bo12bo7bo3bo9bo7bo3bo10bo7bo3bo17b2o7bo4b2o
14b3o7bo3b3o7b3o7bo3b3o14b3o7bo3b3o6b3o7bo3b3o13b2obo2bo3bo3b2obo7b2ob
o2bo3bo3b2obo$9bo15b2o6bo3b2o14b3o6bo2b3o8b3o6bo2b3o10b3o6bo2b3o42bo3b
o25bo3bo15bobo4bo4bobo8bo7bo3bo16bo7bo3bo9bo7bo3bo3bo6bo7bo3bo3bo18bo
3bo21b2o7bo4b2o7b3o7bo3b3o14b3o7bo3b3o6b3o7bo3b3o13b3o7bo3b3o8b3o7bo3b
3o$9bo23bo20b2o6bo3b2o8b3o2bo3bo2b3o10b3o6bo2b3o42bo3bo25bo3bo18bo3bo
16bobo4bo4bobo14bobo4bo4bobo6bo7bo3bo10bo7bo3bo3bo18bo3bo26bo3bo14b2o
7bo4b2o15b2o7bo4b2o6b3o7bo3b3o13b3o7bo3b3o8b3o7bo3b3o$9bo19bo3bo24bo3b
o14b2o6bo3b2o10b3o2bo3bo2b3o46bo29bo22bo23bo28bo14bob2o3bo4bobo7bo7bo
3bo26bo30bo23bo30bo13b2o3bo3bo4b2o14b2o3bo3bo4b2o8b3o7bo3b3o$6bobo21bo
bo26bobo20bobo17b2o2bo2bo4b2o43bobo27bobo20bobo21bobo26bobo19bobo16bob
obobo5bobo20bobo28bobo21bobo28bobo20bobo27bobo16b2o4bobo5b2o9$2bo11bo
11bo11bo$b3o3b3o3b3o9b3o3b3o3b3o20b3o20b3o22b3o96b3o3b3o3b3o9b3o3b3o3b
3o20b3o19b3o20b3o53bo5b3o5bo9bo5b3o5bo22b3o20b3o27b3o22b3o28b3o$2obo2b
o2bo2b2obo8b2obo2bo2bo2b2obo19bo2bo19bo2bo21bo2bo96bo2bobo2bo3bo2bo8bo
2bobo2bo3bo2bo18bo2bo18bo2bo19bo2bo52b3o3bo2bo4b3o7b3o3bo2bo4b3o15bo4b
o2bo5bo8bo4bo2bo5bo20bo2bo21bo2bo22b3o2bo2bo3b3o$3o6bo2b3o9b3o6bo2b3o
16bo6bo4bo10bo6bo4bo12bo6bo4bo91bo7bo3bo11bo7bo3bo16b3o5bo3b3o7b3o5bo
3b3o8b3o5bo3b3o45b2obo6bo3b2obo6b2obo6bo3b2obo14b3o6bo4b3o6b3o6bo4b3o
14bo7bo5bo10bo7bo5bo15bo2bo5bo2bo2bo$3o2bo3bo2b3o9b3o6bo2b3o15b3o5bo3b
3o8b3o5bo3b3o10b3o5bo3b3o90bo7bo3bo3bo7bo7bo3bo3bo12bo2bo4bo3bo2bo6bo
2bo4bo3bo2bo7bo2bo4bo3bo2bo44b3o7bo3b3o7b3o7bo3b3o14b2obo2bo3bo3b2obo
5b2obo2bo3bo3b2obo13b3o2bo3bo4b3o8b3o2bo3bo4b3o17bo5bo5bo$b2o6bo3b2o9b
3o6bo2b3o14b2obo5bo2b2obo7b2obo5bo2b2obo9b2obo5bo2b2obo90bo7bo3bo11bo
7bo3bo3bo12bo7bo3bo9bo7bo3bo10bo7bo3bo47b3o7bo3b3o7b3o7bo3b3o14b3o7bo
3b3o6b3o7bo3b3o13b2obo2bo3bo3b2obo7b2obo2bo3bo3b2obo13bo3bo5bobo3bo$9b
o15b2o6bo3b2o14b3o6bo2b3o8b3o6bo2b3o10b3o6bo2b3o92bobo4bo4bobo8bo7bo3b
o16bo7bo3bo9bo7bo3bo3bo6bo7bo3bo3bo44b2o7bo4b2o7b3o7bo3b3o14b3o7bo3b3o
6b3o7bo3b3o13b3o7bo3b3o8b3o7bo3b3o18bo2bo2bo5bo$9bo23bo20b2o6bo3b2o8b
3o2bo3bo2b3o10b3o6bo2b3o95bo3bo16bobo4bo4bobo14bobo4bo4bobo6bo7bo3bo
10bo7bo3bo3bo49bo3bo14b2o7bo4b2o15b2o7bo4b2o6b3o7bo3b3o13b3o7bo3b3o8b
3o7bo3b3o15bobo6bo2bobo$5bo3bo23bo28bo14b2o6bo3b2o10b3o6bo2b3o95bo3bo
19bo3bo24bo3bo14bobo4bo4bobo7bo7bo3bo53bo3bo19bo3bo26bo3bo13b2o7bo4b2o
14b2o7bo4b2o8b3o7bo3b3o24bo$9bo23bo24bo3bo18bo3bo16b2o6bo3b2o99bo23bo
28bo21bo15bob2o3bo4bobo54bo23bo30bo22bo29bo15b2o3bo3bo4b2o24bo$6bobo
21bobo26bobo20bobo22bobo102bobo21bobo26bobo19bobo20bobo59bobo21bobo28b
obo20bobo27bobo22bobo28bobo9$2bo11bo11bo11bo$b3o3b3o3b3o9b3o3b3o3b3o
20b3o20b3o22b3o120b3o3b3o3b3o20b3o19b3o20b3o77bo5b3o5bo22b3o20b3o27b3o
22b3o28b3o20b3o$2obo2bo2bo2b2obo8b2obo2bo2bo2b2obo19bo2bo19bo2bo21bo2b
o120bo2bobo2bo3bo2bo18bo2bo18bo2bo19bo2bo76b3o3bo2bo4b3o15bo4bo2bo5bo
8bo4bo2bo5bo20bo2bo21bo2bo22b3o2bo2bo3b3o8b3o2bo2bo3b3o$3o6bo2b3o9b3o
6bo2b3o16bo6bo4bo10bo6bo4bo12bo6bo4bo115bo7bo3bo16b3o5bo3b3o7b3o5bo3b
3o8b3o5bo3b3o69b2obo6bo3b2obo14b3o6bo4b3o6b3o6bo4b3o14bo7bo5bo10bo7bo
5bo15bo2bo5bo2bo2bo7bo2bo5bo2bo2bo$3o2bo3bo2b3o9b3o6bo2b3o15b3o5bo3b3o
8b3o5bo3b3o10b3o5bo3b3o114bo7bo3bo3bo12bo2bo4bo3bo2bo6bo2bo4bo3bo2bo7b
o2bo4bo3bo2bo68b3o7bo3b3o14b2obo2bo3bo3b2obo5b2obo2bo3bo3b2obo13b3o2bo
3bo4b3o8b3o2bo3bo4b3o17bo5bo5bo10bo5bo5bo$b2o6bo3b2o9b3o6bo2b3o14b2obo
5bo2b2obo7b2obo5bo2b2obo9b2obo5bo2b2obo114bo7bo3bo3bo12bo7bo3bo9bo7bo
3bo10bo7bo3bo71b3o7bo3b3o14b3o7bo3b3o6b3o7bo3b3o13b2obo2bo3bo3b2obo7b
2obo2bo3bo3b2obo13bo3bo5bobo3bo6bo3bo5bobo3bo$9bo15b2o6bo3b2o14b3o6bo
2b3o8b3o6bo2b3o10b3o6bo2b3o115bo7bo3bo16bo7bo3bo9bo7bo3bo3bo6bo7bo3bo
3bo67b3o7bo3b3o14b3o7bo3b3o6b3o7bo3b3o13b3o7bo3b3o8b3o7bo3b3o18bo2bo2b
o5bo6bo3bo2bo2bobo3bo$9bo23bo20b2o6bo3b2o8b3o2bo3bo2b3o10b3o6bo2b3o
116bobo4bo4bobo14bobo4bo4bobo6bo7bo3bo10bo7bo3bo3bo68b2o7bo4b2o15b2o7b
o4b2o6b3o7bo3b3o13b3o7bo3b3o8b3o7bo3b3o15bobo6bo2bobo11bo2bo2bo5bo$5bo
3bo23bo28bo14b2o6bo3b2o10b3o6bo2b3o119bo3bo24bo3bo14bobo4bo4bobo7bo7bo
3bo77bo3bo26bo3bo13b2o7bo4b2o14b2o7bo4b2o8b3o7bo3b3o24bo13bobo6bo2bobo
$5bo3bo19bo3bo28bo22bo16b2o6bo3b2o119bo3bo24bo3bo17bo3bo15bobo4bo4bobo
74bo3bo26bo3bo18bo3bo25bo3bo15b2o7bo4b2o20bo3bo22bo$9bo23bo28bo18bo3bo
20bo3bo128bo28bo21bo22bo85bo30bo22bo29bo24bo30bo22bo$6bobo21bobo26bobo
20bobo22bobo126bobo26bobo19bobo20bobo83bobo28bobo20bobo27bobo22bobo28b
obo20bobo9$26bo11bo$25b3o3b3o3b3o20b3o20b3o22b3o177b3o20b3o137b3o27b3o
22b3o28b3o20b3o$24b2obo2bo2bo2b2obo19bo2bo19bo2bo21bo2bo176bo2bo19bo2b
o131bo4bo2bo5bo20bo2bo21bo2bo22b3o2bo2bo3b3o8b3o2bo2bo3b3o$24b3o6bo2b
3o16bo6bo4bo10bo6bo4bo12bo6bo4bo166b3o5bo3b3o8b3o5bo3b3o124b3o6bo4b3o
14bo7bo5bo10bo7bo5bo15bo2bo5bo2bo2bo7bo2bo5bo2bo2bo$24b3o6bo2b3o15b3o
5bo3b3o8b3o5bo3b3o10b3o5bo3b3o165bo2bo4bo3bo2bo7bo2bo4bo3bo2bo122b2obo
2bo3bo3b2obo13b3o2bo3bo4b3o8b3o2bo3bo4b3o17bo5bo5bo10bo5bo5bo$24b3o6bo
2b3o14b2obo5bo2b2obo7b2obo5bo2b2obo9b2obo5bo2b2obo165bo7bo3bo10bo7bo3b
o125b3o7bo3b3o13b2obo2bo3bo3b2obo7b2obo2bo3bo3b2obo13bo3bo5bobo3bo6bo
3bo5bobo3bo$25b2o6bo3b2o14b3o6bo2b3o8b3o6bo2b3o10b3o6bo2b3o166bo7bo3bo
3bo6bo7bo3bo3bo121b3o7bo3b3o13b3o7bo3b3o8b3o7bo3b3o18bo2bo2bo5bo6bo3bo
2bo2bobo3bo$33bo20b2o6bo3b2o8b3o2bo3bo2b3o10b3o6bo2b3o166bo7bo3bo10bo
7bo3bo3bo121b3o7bo3b3o13b3o7bo3b3o8b3o7bo3b3o15bobo6bo2bobo11bo2bo2bo
5bo$33bo28bo14b2o6bo3b2o10b3o6bo2b3o167bobo4bo4bobo7bo7bo3bo126b2o7bo
4b2o14b2o7bo4b2o8b3o7bo3b3o24bo13bobo6bo2bobo$29bo3bo28bo22bo16b2o6bo
3b2o170bo3bo15bobo4bo4bobo128bo3bo25bo3bo15b2o7bo4b2o20bo3bo22bo$29bo
3bo24bo3bo22bo24bo175bo3bo18bo3bo135bo3bo25bo3bo20bo3bo26bo3bo18bo3bo$
33bo28bo22bo20bo3bo179bo22bo139bo29bo24bo30bo22bo$30bobo26bobo20bobo
22bobo177bobo20bobo137bobo27bobo22bobo28bobo20bobo10$60b3o20b3o22b3o
200b3o192b3o51b3o$59bo2bo19bo2bo21bo2bo199bo2bo191bo2bo45b3o2bo2bo3b3o
$55bo6bo4bo10bo6bo4bo12bo6bo4bo189b3o5bo3b3o180bo7bo5bo38bo2bo5bo2bo2b
o$54b3o5bo3b3o8b3o5bo3b3o10b3o5bo3b3o188bo2bo4bo3bo2bo178b3o2bo3bo4b3o
40bo5bo5bo$53b2obo5bo2b2obo7b2obo5bo2b2obo9b2obo5bo2b2obo188bo7bo3bo
180b2obo2bo3bo3b2obo36bo3bo5bobo3bo$53b3o6bo2b3o8b3o6bo2b3o10b3o6bo2b
3o189bo7bo3bo3bo176b3o7bo3b3o37bo3bo2bo2bobo3bo$54b2o6bo3b2o8b3o2bo3bo
2b3o10b3o6bo2b3o189bo7bo3bo3bo176b3o7bo3b3o41bo2bo2bo5bo$62bo14b2o6bo
3b2o10b3o6bo2b3o189bo7bo3bo180b3o7bo3b3o38bobo6bo2bobo$62bo22bo16b2o6b
o3b2o190bobo4bo4bobo178b2o7bo4b2o47bo$58bo3bo22bo24bo198bo3bo190bo3bo
49bo3bo$58bo3bo18bo3bo24bo198bo3bo190bo3bo49bo3bo$62bo22bo24bo202bo
194bo53bo$59bobo20bobo22bobo200bobo192bobo51bobo9$83b3o22b3o$82bo2bo
21bo2bo$78bo6bo4bo12bo6bo4bo$77b3o5bo3b3o10b3o5bo3b3o$76b2obo5bo2b2obo
9b2obo5bo2b2obo$76b3o6bo2b3o10b3o6bo2b3o$76b3o2bo3bo2b3o10b3o6bo2b3o$
77b2o6bo3b2o10b3o6bo2b3o$85bo16b2o6bo3b2o$85bo24bo$81bo3bo24bo$81bo3bo
20bo3bo$85bo24bo$82bobo22bobo8$108b3o$107bo2bo$103bo6bo4bo$102b3o5bo3b
3o$101b2obo5bo2b2obo$101b3o6bo2b3o$101b3o6bo2b3o$101b3o6bo2b3o$102b2o
6bo3b2o$110bo$110bo$106bo3bo$106bo3bo$110bo$107bobo!

Each row of the above table represents the "length" of the OWSS, with lengths ranging from 7 to 14. A length-n OWSS is typically referred to as an nWSS (7WSS, 8WSS, etc.). The columns of the table represent the placement of the supporting standard spaceship relative to the front of the OWSS.

Naturally, all simple OWSS flotillas can be constructed from the interactions in the above collection. Given a fixed-length OWSS with N different glide-symmetric supports, the total number of simple flotillas is Nth triangular number: N*(N+1)/2. This gives the following simple OWSS flotilla counts for different OWSS lengths:

Length 7: 20 * (20+1)/2 = 210
Length 8: 19 * (19+1)/2 = 190
Length 9: 17 * (17+1)/2 = 153
Length 10: 16 * (16+1)/2 = 136
Length 11: 11 * (11+1)/2 = 66
Length 12: 6 * (6+1)/2 = 21
Length 13: 2 * (2+1)/2 = 3
Length 14: 1 * (1+1)/2 = 1
All lengths: 780

Many of these have already been synthesized, primarily by Mark Niemiec, David Buckingham, Martin Grant, and Dieter Leithner. I'm not sure at the moment which OWSS syntheses remain unsolved. Hopefully subsequent posts in this thread will help elucidate the problem.

Edit: All OWSS flotillas consisting of a single OWSS supported on either side by a single standard spaceship can be synthesized. See the following several posts for details.

Re: OWSS synthesis project

Posted: July 15th, 2025, 4:39 am

by Sokwe

7WSS syntheses
All simple 7WSS flotillas can be synthesized. The following is based on the work of Mark Niemiec and David Buckingham, with additions and simplifications by myself.

There are 20 different standard spaceship escorts for a 7WSS, numbered by Niemiec as follows:

Code: Select all

#C 20 Possible escorts for 7WSS (LWSS1-3, MWSS1-8, HWSS1-9)
x = 131, y = 39
3o3b3o6b3o12b3o$o2bobo2bo6bo2bo11bo2bo$o7bo6bo5b3o6bo6bo$o7bo6bo4bo2bo
6bo5b3o$o4bobo7bo7bo6bo5bob2o$o3bo10bo7bo6bo6b3o$o14bo3b2obo7bo3bo2b2o
$bobo12bobo12bobo6$36b3o$35bo2bo28bo$3o3b3o6b3o12b3o5bo6b3o5bo6b3o3b3o
6b3o12b3o12b3o$o2bobo2bo6bo2bo11bo2bo4bo6bo2bo3b3o5bo2bo2bob2o5bo2bo
11bo2bo4bo6bo2bo$o7bo6bo5b3o6bo7bo6bo6bob2o4bo6b3o5bo6bo7bo6b3o5bo7bo$
o7bo6bo4bo2bo6bo4bobo7bo7b3o4bo3bo2b3o5bo5b3o6bo3bo2bob2o4bo3bo2b3o$o
7bo6bo7bo6bo3bo10bo7b3o4bo6b2o6bo5bob2o5bo7b3o4bo3bo2bob2o$o4bobo7bo7b
o6bo3bo10bo7b2o5bo14bo6b3o5bo7b3o4bo7b3o$o14bo7bo6bo14bo14bo3bo10bo3bo
2b3o5bo3bo3b2o5bo3bo3b3o$bobo12bobobobo8bobo12bobo12bobo12bo2bo2b2o7bo
bo12bobo4b2o6$36b3o89bo$35bo2bo28bo59b3o$3o3b3o6b3o12b3o5bo6b3o5bo6b3o
3b3o6b3o12b3o12b3o12b3o4bob2o$o2bobo2bo6bo2bo11bo2bo4bo6bo2bo3b3o5bo2b
o2bob2o5bo2bo11bo2bo4bo6bo2bo11bo2bo4b3o$o7bo6bo5b3o6bo7bo6bo6bob2o4bo
6b3o5bo6bo7bo6b3o5bo7bo6bo7b3o$o7bo6bo4bo2bo6bo7bo6bo7b3o4bo6b3o5bo5b
3o6bo3bo2bob2o4bo3bo2b3o5bo7b3o$o7bo6bo7bo6bo4bobo7bo7b3o4bo6b3o5bo5bo
b2o5bo7b3o4bo3bo2bob2o4bo7b2o$o7bo6bo7bo6bo3bo10bo7b3o4bo6b2o6bo6b3o5b
o7b3o4bo7b3o4bo3bo$o3b2obo7bo7bo6bo14bo3bo3b2o5bo3bo10bo3bo2b3o5bo7b3o
4bo7b3o4bo$bobo12bob2o3bo7bobo12bobo12bobo12bo2bo2b3o6bobo4b2o6bob2o3b
3o5bobo$20bobo59b2o29b2o!

The easiest way to see that every simple 7WSS flotilla is synthesizable is to use the shillelagh method:

Code: Select all

#C 7WSS synthesis from a shillelagh
x = 12, y = 23, rule = B3/S23
4$bobo$2b2o$2bo3$3b2o$4bo$3bo$3bobo$4b2o2$2o6b2o$b2o4b2o$o8bo!

Using the above synthesis, we can construct all 20 escorts on the right-hand side like so:

Code: Select all

x = 216, y = 304, rule = B3/S23
14bobo$14b2o$15bo38bobo$3bobo37bobo8b2o27bobo8bo$4b2o38b2o9bo28b2o8bob
o$4bo39bo39bo9b2o$12b2o$12b2o$5b2o18b3o3b3o11b2o5b2o11b3o17b2o18b3o$6b
o18bo2bobo2bo12bo5b2o11bo2bo17bo5b2o11bo2bo$5bo11b2o6bo7bo11bo19bo5b3o
11bo6b2o11bo6bo$5bobo9bobo5bo7bo11bobo17bo4bo2bo11bobo17bo5b3o$6b2o9bo
7bo4bobo13b2o9b2o6bo7bo12b2o17bo5bob2o$25bo3bo27bobo5bo7bo23b2o6bo6b3o
$2b2o6b2o13bo16b2o6b2o5bo7bo3b2obo9b2o6b2o4b2o7bo3bo2b2o$3b2o4b2o15bob
o14b2o4b2o15bobo14b2o4b2o7bo7bobo$2bo8bo30bo8bo30bo8bo24$94bobo$94b2o$
14bobo78bo$14b2o119bo$15bo38bobo78bobo$3bobo37bobo8b2o27bobo37bobo9b2o
$4b2o38b2o9bo28b2o6b2o30b2o$4bo39bo39bo6bobo30bo$12b2o78bo18b3o$11bobo
96bo2bo19b2o$5b2o5bo12b3o3b3o11b2o5b2o11b3o17b2o10b3o5b3o5bo11b2o5bobo
10b3o5bo$6bo18bo2bobo2bo12bo4bobo11bo2bo17bo10bo7bo2bo4bo12bo6bo11bo2b
o3b3o$5bo11b3o5bo7bo11bo6bo12bo5b3o11bo12bo6bo7bo11bo13bo5bo6bob2o$5bo
bo9bo7bo7bo11bobo17bo4bo2bo11bobo17bo4bobo12bobo10b2o5bo7b3o$6b2o10bo
6bo7bo12b2o9b3o5bo7bo12b2o17bo3bo16b2o10bobo4bo7b3o$25bo4bobo24bo7bo7b
o31bo3bo35bo7b2o$2b2o6b2o13bo16b2o6b2o6bo6bo7bo8b2o6b2o13bo16b2o6b2o
13bo$3b2o4b2o15bobo14b2o4b2o15bobobobo10b2o4b2o15bobo14b2o4b2o15bobo$
2bo8bo30bo8bo30bo8bo30bo8bo9$14bo$14bobo$14b2o79bo$3bobo37bobo8bo28bob
o9bobo25bobo9bo$4b2o38b2o8bobo27b2o9b2o27b2o9bobo$4bo39bo9b2o28bo39bo
10b2o$12b2o$11bobo18bo$5b2o5bo12b3o3b3o11b2o18b3o17b2o6b2o10b3o17b2o
18b3o$6bo11bo6bo2bo2bob2o11bo5b2o11bo2bo17bo5bobo10bo2bo4bo12bo6b2o10b
o2bo$5bo11b2o6bo6b3o10bo5bobo11bo6bo12bo7bo11bo6b3o10bo6bobo10bo7bo$5b
obo9bobo5bo3bo2b3o10bobo4bo12bo5b3o11bobo11bo5bo3bo2bob2o9bobo5bo11bo
3bo2b3o$6b2o17bo6b2o12b2o10bo6bo5bob2o11b2o10b2o5bo7b3o10b2o11bo5bo3bo
2bob2o$25bo31b2o6bo6b3o23bobo4bo7b3o22b2o5bo7b3o$2b2o6b2o13bo3bo12b2o
6b2o5bobo5bo3bo2b3o7b2o6b2o13bo3bo3b2o7b2o6b2o6bobo4bo3bo3b3o$3b2o4b2o
15bobo14b2o4b2o15bo2bo2b2o9b2o4b2o15bobo14b2o4b2o15bobo4b2o$2bo8bo30bo
8bo30bo8bo30bo8bo33$7bobo$8b2o$2bobo3bo$3b2o$3bo4$42bo141bobo$42bobo
139b2o$42b2o141bo3$173bobo14bo$29b2o2b2o69bobo67b2o6b2o4b2o$28bobob2o
59bobo8b2o68bo6bo2bo4b2o$30bo3bo59b2o9bo75bo2bo$94bo87b2o$15b2o158b2o
28b3o$16bo93bo65bo16b2o10bo2bo$15bo79b2o5b2o4b2o15b3o47bo11b2o3b2o11bo
5b3o$15bobo78bo4bo2bo4b2o14bo2bo46bobo9bobo4bo10bo4bo2bo$16b2o77bo5bo
2bo20bo5b3o42b2o9bo17bo7bo$95bobo4b2o21bo4bo2bo71bo7bo$96b2o27bo7bo38b
2o6b2o23bo7bo$113b2o10bo7bo39b2o4b2o25bob2o3bo$92b2o6b2o5b2o3b2o11bo7b
o38bo8bo28bobo$93b2o4b2o6bobo4bo11bob2o3bo$92bo8bo5bo22bobo7$b2o28b2o$
2b2o26b2o$bo30bo3$45b3o3b3o$45bo2bobo2bo$45bo7bo$45bo7bo$45bo7bo$45bo
7bo$45bo3b2obo$46bobo19$207bo$88bo117bo$9bo76bobo117b3o$bobo3bobo71bob
o3b2o72bobo$2b2o4b2o72b2o78b2o$2bo79bo79bo4$124bo$45bo76b2o$43b2o78b2o
$44b2o$195bobo$188bobo4b2o$189b2o5bo$189bo$108b2o3b3o$29b2o3b3o72b2o2b
o$30b2o2bo73bo5bo$15b2o12bo5bo59b2o78b2o$16bo79bo79bo$15bo79bo79bo$15b
obo77bobo77bobo$16b2o78b2o78b2o2$190b2o$190bobo$190bo10$2o30b2o46b2o
30b2o46b2o30b2o$b2o28b2o48b2o28b2o48b2o28b2o$o32bo46bo32bo46bo32bo3$
132bo$45b3o5bo71b3o3b3o71b3o$45bo2bo3b3o70bo2bo2bob2o70bo2bo$45bo6bob
2o69bo6b3o70bo6bo$45bo7b3o69bo6b3o70bo5b3o$45bo7b3o69bo6b3o70bo5bob2o$
45bo7b3o69bo6b2o71bo6b3o$45bo3bo3b2o70bo3bo75bo3bo2b3o$46bobo77bobo77b
o2bo2b3o$212b2o16$48bo$47bo121bo$47b3o117bobo$168b2o$bobo123bo33bobo$
2b2o122bo35b2o$2bo123b3o33bo$82bobo$83b2o$83bo121bo$203b2o$204b2o2$36b
obo$29bobo4b2o$30b2o5bo$30bo$115bobo71b2o3b3o$110bobo2b2o73b2o2bo$111b
2o3bo72bo5bo$111bo$15b2o158b2o$16bo159bo$15bo79b2o78bo$15bobo78bo78bob
o$16b2o77bo80b2o$31b2o62bobo$31bobo62b2o$31bo78b2o$110bobo$110bo9$2o
30b2o126b2o30b2o$b2o28b2o48b2o28b2o48b2o28b2o$o32bo48b2o26b2o48bo32bo$
81bo30bo$213bo$212b3o$45b3o77b3o77b3o4bob2o$45bo2bo4bo71bo2bo76bo2bo4b
3o$45bo6b3o70bo7bo71bo7b3o$45bo3bo2bob2o69bo3bo2b3o70bo7b3o$45bo7b3o
69bo3bo2bob2o69bo7b2o$45bo7b3o69bo7b3o69bo3bo$45bo7b3o69bo7b3o69bo$46b
obo4b2o71bob2o3b3o70bobo$133b2o!

On the left hand side we can construct all of the 20 escorts except HWSS6:

Code: Select all

x = 168, y = 231, rule = B3/S23
15bo$16b2o$15b2o38bo$56b2o38bo$55b2o40bo$22bobo37bobo30b3o4bobo$23b2o
38b2o38b2o$18b2o3bo39bo39bo$18b2o$58b2o$24b2o12b3o3b3o11b2o4b2o18b3o
11b2o4b2o18b3o$25bo11bo2bo3bo2bo17bo18bo2bo10b2o5bo18bo2bo$12b3o9bo15b
o3bo19bo13b3o3bo19bo14bo4bo$14bo9bobo13bo3bo19bobo10bo2bo3bo19bobo11b
3o3bo$13bo11b2o10bobo4bo7b3o10b2o13bo3bo8bo11b2o11bob2o2bo$44bo9bo25bo
3bo8b2o24b3o2bo$21b2o6b2o13bo8bo7b2o6b2o6bobo4bo7bobo6b2o6b2o8b2o3bo$
22b2o4b2o15bo16b2o4b2o15bo16b2o4b2o15bo$21bo8bo30bo8bo30bo8bo27$15bo$
16b2o78bo38bo$15b2o38bo41b2o37bo$56b2o38b2o36b3o$55b2o$22bobo37bobo37b
obo37bobo$23b2o38b2o38b2o38b2o$18b2o3bo39bo34b2o3bo39bo$17bobo78bobo
17b3o16b2o$17b2o39b2o39bo17bo2bo16bobo$24b2o12b3o3b3o10bobo4b2o18b3o6b
2o9b2o14bo3b3o11bo5b2o12bo5b3o$25bo11bo2bo3bo2bo9b2o6bo18bo2bo4bobo10b
o10bo3bo3bo2bo17bo11b3o4bo2bo$12b2o10bo15bo3bo19bo13b3o3bo9bo9bo15bo3b
o6b2o11bo12bob2o3bo$13b2o9bobo9bo3bo3bo19bobo10bo2bo3bo19bobo10bobo4bo
7b2o10bobo11b3o3bo$12bo12b2o13bo3bo7b2o11b2o13bo3bo20b2o17bo6bo13b2o
11b3o3bo$37bobo4bo8b2o21bo3bo3bo39bo33b2o4bo$21b2o6b2o13bo7bo8b2o6b2o
9bo3bo16b2o6b2o13bo16b2o6b2o13bo$22b2o4b2o15bo16b2o4b2o7bobo5bo16b2o4b
2o15bo16b2o4b2o15bo$21bo8bo30bo8bo30bo8bo30bo8bo14$95bo$17bo38bo39bo
38bo$18bo38bo36b3o39bo$16b3o3bobo30b3o4bobo37bobo29b3o5bobo$23b2o38b2o
38b2o38b2o$23bo39bo39bo39bo2$18b2o19bo57b2o$18bobo3b2o12b3o3b3o11b2o4b
2o18b3o10bobo4b2o18b3o10b2o5b2o18b3o$19bo5bo12bob2o2bo2bo10bobo4bo18bo
2bo10bo6bo12bo5bo2bo9bobo5bo18bo2bo$13b2o9bo14b3o2bo14bo4bo14bo4bo19bo
12b3o4bo13bo5bo13bo5bo$14b2o8bobo12b3o2bo19bobo11b3o3bo6b2o11bobo10bob
2o3bo19bobo10b3o4bo$13bo11b2o12b2o3bo7b2o11b2o11bob2o2bo7b2o11b2o11b3o
3bo6b2o12b2o10bob2o3bo$44bo8b2o24b3o2bo6bo26b3o3bo7b2o24b3o3bo$21b2o6b
2o13bo7bo8b2o6b2o8b3o2bo16b2o6b2o7b2o4bo6bo9b2o6b2o7b3o3bo$22b2o4b2o
15bo16b2o4b2o9b2o4bo16b2o4b2o15bo16b2o4b2o8b2o5bo$21bo8bo30bo8bo30bo8b
o30bo8bo31$115bobo$116b2o$17bobo35bo60bo$18b2o4bo28bobo18bo47bo$18bo6b
2o27b2o11bobo5b2o46b2o$24b2o42b2o4b2o35bo5b2o3b2o14b3o$68bo43b2o2bo2bo
17bo2bo$13bo5b2o17b3o3b3o47b3o14b2o3bo2bo20bo3b3o$14b2o2bo2bo3b2o10bo
2bo3bo2bo27b2o17bo2bo19b2o4b2o11bo3bo3bo2bo$13b2o3bo2bo4bo13bo3bo16bob
o5b2o5bo11b3o3bo12b2o15bo11bo3bo3bo$19b2o4bo10bo3bo3bo17b2o6bo4bo11bo
2bo3bo13b2o3b2o8bo16bo3bo$9b2o14bobo8bo3bo3bo17bo6bo5bobo12bo3bo12bo4b
obo8bobo11bobo4bo$10b2o3b2o9b2o12bo3bo21bobo7b2o8bo3bo3bo19bo9b2o18bo$
9bo4bobo6bo6bo6bobo4bo21b2o5bo6bo5bo3bo3bo26bo6bo15bo$16bo6b2o4b2o14bo
27b2o4b2o9bo4bo25b2o4b2o16bo$22bobo4bobo40bobo4bobo5bobo30bobo4bobo24$
9bobo$10b2o$4bo5bo$5bo63bo$3b3o61bobo4bo$68b2o5b2o$74b2o$2bo86bo$3bo
60bo4b2o17b3o3b3o$b3o11b2o48bo2bo2bo3b2o11bob2o2bo2bo$16bo46b3o2bo2bo
4bo12b3o2bo$15bo53b2o4bo13b3o2bo$15bobo41b3o13bobo11b3o2bo$16b2o43bo3b
2o9b2o11b2o3bo$60bo5b2o5bo6bo13bo$13bo51bo7b2o4b2o14bo$12b2o58bobo4bob
o$12bobo23bo5b3o$37b3o4bo2bo$24b2o11bob2o3bo$23b2o13b3o3bo$25bo12b3o3b
o$4b3o31b3o3bo$6bo6bo24b2o4bo$5bo6b3o30bo$12bob2o$bo11b3o$b2o10b2o$obo
12$8bobo101bobo$9b2o102b2o$9bo103bo$3bo104bo$4bo48bo20bo34bo$2b3o49b2o
19b2o30b3o$53b2o13bo5b2o$66bobo$bo65b2o25b3o9bo$2bo11b2o59b2o17bo2bo9b
o10b2o$3o12bo60bo11bo5bo10b3o11bo$14bo47bo5b2o5bo11b3o4bo23bo$14bobo
43bobo6bo5bobo9bob2o3bo23bobo$15b2o44b2o5bo7b2o10b3o3bo24b2o$65bobo5bo
6bo7b3o3bo20bo$65b2o6b2o4b2o7b3o4bo18b2o22bo$12bo59bobo4bobo6b2o24bobo
20b3o$11b2o31b3o90bob2o3b3o$11bobo24bo5bo2bo90b3o3bo2bo$23b2o12b3o4bo
82b2o9b3o3bo$22b2o13bob2o3bo81b2o10b3o3bo$24bo13b3o3bo83bo9b2o4bo$38b
3o3bo99bo$12bo7b2o16b3o3bo71bo27bo$11b3o6bobo4b2o9b2o5bo69b3o27bo$10b
2obo6bo6bobo84b2obo11b3o$10b3o14bo86b3o12bo$11b2o102b2o13bo!

By combining right-hand and left-hand escort syntheses, we can construct all simple 7WSS flotillas except the flotilla supported on both sides by HWSS6. In that case a special synthesis is needed. Since I couldn't find Mark's solution, I created my own:

Code: Select all

x = 143, y = 30, rule = B3/S23
111bo$112bo$110b3o4bobo12bo$118b2o12bobo$35bo82bo13b2o$11bo23bobo41bo$
9bobo23b2o40bobo27bo$10b2o7bobo56b2o25bobo29bo$19b2o85b2o28bo$20bo20b
2o22b2o4b2o42b2o4b2o13b3o$34bo7bo21bo2bo4bo41bo2bo4bo5b2o$34b2o5bo22bo
2bo3bo8bo33bo2bo3bo5bo2bo$33bobo4bo24b2o3bo8b2o34b2o3bo6bo2bo$17bo21bo
29bo9bobo37bo8b2o$16b2o20bo29bo49bo$16bobo18bo29bo49bo$7b2o27bo29bo35b
2o12bo$6bobo4bo21bo29bo35bobo4bo6bo24b3o$8bo3b2o21b2o28b2o36bo4b2o5b2o
8b2o8b2o3bo$12bobo92bobo15bobo6b2o5bo$125bo10bo$b2o$obo111b2o$2bo96bo
15b2o$99b2o13bo$98bobo21b3o$122bo2bo$122bo$122bo$123bobo!

I'm sure a much better synthesis exists for this ship.

While the shillelagh method is the most versatile for constructing 7WSS flotillas, it often results in syntheses that are more expensive than necessary. There are two other methods, based on the boat and the long ship, that can yield cheaper syntheses in many cases:

Code: Select all

x = 157, y = 65, rule = B3/S23
107bo$105bobo$106b2o11$112bo$113bo$111b3o4$130bo$131bo$129b3o4$130bo$
130b2o$3bobo27bobo93bobo$4b2o28b2o$4bo29bo3$5b2o28b2o97b2o$5bobo27bobo
95bobo$6bo29bo95bobo$3o28b2o99b2o$2bo27bobo$bo30bo$8b3o27b3o$8bo24bo4b
o$9bo22b2o5bo$32bobo$27b2o$26bobo$28bo14$114b2o$115b2o$114bo2$154b3o$
154bo$155bo!

All right-hand escorts can be constructed using the boat method:

Code: Select all

x = 178, y = 242, rule = B3/S23
24bobo$24b2o$25bo38bobo$15bobo37bobo6b2o29bobo6bo$16b2o38b2o7bo30b2o6b
obo$16bo6b2o11b3o3b3o11bo19b3o17bo7b2o10b3o$23b2o11bo2bobo2bo31bo2bo
36bo2bo$16b2o18bo7bo11b2o5b2o11bo5b3o11b2o18bo6bo$16bobo8b2o7bo7bo11bo
bo4b2o11bo4bo2bo11bobo4b2o11bo5b3o$12b3o2bo9bobo6bo4bobo8b3o2bo18bo7bo
7b3o2bo5b2o11bo5bob2o$14bo12bo8bo3bo13bo12b2o7bo7bo9bo21bo6b3o$13bo22b
o16bo13bobo6bo3b2obo9bo13b2o7bo3bo2b2o$18b3o16bobo18b3o6bo9bobo18b3o5b
2o9bobo$18bo39bo39bo9bo$19bo39bo39bo17$104bobo$104b2o$24bobo78bo$24b2o
119bo$25bo38bobo78bobo$15bobo37bobo6b2o29bobo5b2o17b3o10bobo7b2o$16b2o
38b2o7bo30b2o4bobo16bo2bo11b2o$16bo6b2o11b3o3b3o11bo19b3o17bo6bo12b3o
5bo11bo19b3o5bo$22bobo11bo2bobo2bo31bo2bo27b3o6bo2bo4bo19b2o10bo2bo3b
3o$16b2o5bo12bo7bo11b2o5b2o11bo5b3o11b2o9bo8bo7bo11b2o5bobo10bo6bob2o$
16bobo8b3o6bo7bo11bobo3bobo11bo4bo2bo11bobo9bo7bo4bobo12bobo5bo4bo6bo
7b3o$12b3o2bo9bo8bo7bo7b3o2bo5bo12bo7bo7b3o2bo18bo3bo11b3o2bo10b2o6bo
7b3o$14bo13bo7bo4bobo10bo12b3o6bo7bo9bo21bo3bo13bo13bobo5bo7b2o$13bo
22bo16bo13bo8bo7bo8bo22bo16bo22bo$18b3o16bobo18b3o7bo8bobobobo14b3o16b
obo18b3o16bobo$18bo39bo39bo39bo$19bo39bo39bo39bo8$24bo$24bobo$24b2o79b
o$15bobo37bobo6bo30bobo7bobo27bobo7bo$16b2o25bo12b2o6bobo29b2o7b2o29b
2o7bobo$16bo6b2o11b3o3b3o11bo7b2o10b3o17bo19b3o17bo8b2o9b3o$22bobo11bo
2bo2bob2o30bo2bo36bo2bo4bo31bo2bo$16b2o5bo4bo7bo6b3o10b2o18bo6bo12b2o
6b2o10bo6b3o10b2o18bo7bo$16bobo8b2o7bo3bo2b3o10bobo4b2o11bo5b3o11bobo
4bobo10bo3bo2bob2o9bobo5b2o10bo3bo2b3o$12b3o2bo9bobo6bo6b2o7b3o2bo4bob
o11bo5bob2o6b3o2bo6bo4bo6bo7b3o5b3o2bo5bobo10bo3bo2bob2o$14bo21bo17bo
8bo4bo7bo6b3o8bo13b2o6bo7b3o7bo9bo4bo6bo7b3o$13bo22bo3bo12bo13b2o7bo3b
o2b3o7bo14bobo5bo3bo3b2o7bo14b2o6bo3bo3b3o$18b3o16bobo18b3o6bobo7bo2bo
2b2o13b3o16bobo18b3o7bobo6bobo4b2o$18bo39bo39bo39bo$19bo39bo39bo39bo
23$129bobo$130b2o$9bobo118bo$10b2o$4bobo3bo113bobo$5b2o118b2o$5bo119bo
2$164bo$164bobo$44bo119b2o$44bobo$44b2o2$151b2o2b2o$150bobob2o$31b2o2b
2o49bobo63bo3bo$30bobob2o39bobo8b2o$32bo3bo39b2o9bo$76bo$17b2o118b2o$
17bobo117bobo$18bo58b2o5b2o4bobo14b3o28bo$77bobo3bo2bo3b2o15bo2bo$78bo
4bobo5bo15bo5b3o$72b3o9bo22bo4bo2bo$74bo32bo7bo$73bo33bo7bo$80b3o11b2o
11bo7bo$80bo8b2o2b2o13bob2o3bo$81bo6b2o5bo16bobo$90bo3$b3o117b3o$3bo
119bo$2bo119bo$31b3o117b3o$31bo119bo$32bo119bo$173b3o$172bo2bo$47b3o3b
3o111b3o5bo$47bo2bobo2bo111bo2bo4bo$47bo7bo111bo7bo$47bo7bo111bo7bo$
47bo7bo111bo4bobo$47bo7bo111bo3bo$47bo3b2obo112bo$48bobo19bo97bobo$11b
o56bobo$3bobo3bobo51bobo3b2o$4b2o4b2o52b2o$4bo59bo4$106bo$47bo56b2o$
45b2o58b2o$46b2o5$90b2o3b3o$31b2o3b3o52b2o2bo$32b2o2bo53bo5bo38bobo8bo
$17b2o12bo5bo39b2o57b2o8bobo$17bobo57bobo56bo9b2o$18bo59bo2$137b2o12bo
15b3o$137bobo4b2o4bo16bo2bo$138bo4bo2bo3b3o14bo6bo$132b3o8bo2bo20bo5b
3o$134bo9b2o21bo5bob2o$133bo33bo6b3o$140b3o11b3o10bo3bo2b3o$140bo8b2o
3bo13bo2bo2b3o$141bo6b2o5bo18b2o$150bo2$3o57b3o$2bo59bo$bo59bo$32b3o
57b3o$32bo59bo$33bo59bo3$114bo$47b3o5bo51b3o3b3o$47bo2bo3b3o50bo2bo2bo
b2o$47bo6bob2o49bo6b3o$47bo7b3o49bo6b3o$47bo7b3o49bo6b3o$47bo7b3o49bo
6b2o15bo$47bo3bo3b2o50bo3bo17bobo$48bobo57bobo19b2o$3bobo5bo111bobo$4b
2o3bobo112b2o$4bo5b2o112bo3$167bo$165b2o$166b2o$47bo$45b2o$46b2o61bo$
108bo$108b3o$64bobo84b2o3b3o$65b2o85b2o2bo$65bo85bo5bo$31b2o3b3o$17b2o
13b2o2bo100b2o$17bobo11bo5bo99bobo$18bo119bo4$97bobo$92bobo2b2o$93b2o
3bo$93bo3$77b2o$77bobo$78bo$3o117b3o$2bo119bo$bo90b2o27bo$32b3o57bobo
57b3o$32bo59bo59bo$33bo119bo2$175bo$174b3o$47b3o57b3o57b3o4bob2o$47bo
2bo4bo51bo2bo56bo2bo4b3o$47bo6b3o4b3o43bo7bo51bo7b3o$47bo3bo2bob2o5bo
43bo3bo2b3o50bo7b3o$47bo7b3o4bo44bo3bo2bob2o49bo7b2o$47bo7b3o33b3o13bo
7b3o49bo3bo$47bo7b3o33bo15bo7b3o49bo$48bobo4b2o35bo15bob2o3b3o50bobo$
115b2o!

However, on the left-hand side the boat method allows far fewer escorts. I only have examples for 2 out of 3 LWSS escorts, 4 out of 8 MWSS escorts, and 3 out of 9 HWSS escorts:

Code: Select all

x = 186, y = 155, rule = B3/S23
46bo$7bo39b2o$8b2o36b2o$7b2o44bobo$54b2o$54bo$14bobo$9b2o4b2o32b2o$9b
2o4bo13b3o3b3o11b2o4b2o18b3o$28bo2bo3bo2bo16bobo17bo2bo$15b2o14bo3bo
20bo12b3o3bo$4b3o8bobo13bo3bo15b2o15bo2bo3bo$6bo4b3o2bo11bobo4bo7b3o4b
obo18bo3bo$5bo7bo21bo9bo6bo18bo3bo$12bo22bo8bo13b3o7bobo4bo$17b3o16bo
16bo4bo17bo$17bo34b2o5bo$18bo27b2o4bobo$47b2o$46bo18$46bo$7bo39b2o$8b
2o36b2o79bo$7b2o34bo9bobo72bo$44bo9b2o70b3o$42b3o9bo$14bobo117bobo$9b
2o4b2o32b2o84b2o$9bobo3bo13b3o3b3o12bo4b2o18b3o50b2o5bo13bo5b3o$10bo
17bo2bo3bo2bo8b3o5bobo17bo2bo49bobo17b3o4bo2bo$4b2o9b2o14bo3bo11bo8bo
12b3o3bo53bo5b2o11bob2o3bo$3bobo9bobo9bo3bo3bo15b2o15bo2bo3bo47b2o10bo
bo11b3o3bo$5bo5b3o2bo14bo3bo14bobo18bo3bo48b2o5b3o2bo12b3o3bo$13bo14bo
bo4bo16bo14bo3bo3bo47bo9bo15b2o4bo$12bo22bo22b3o10bo3bo56bo22bo$17b3o
16bo16bo4bo9bobo5bo60b3o16bo$17bo34b2o5bo77bo$18bo27b2o4bobo83bo$47b2o
$46bo12$8bo$9bo$7b3o3$14bobo$9b2o4b2o13bo$9bobo3bo13b3o3b3o$10bo18bob
2o2bo2bo$4b2o9b2o13b3o2bo$5b2o8bobo12b3o2bo$4bo6b3o2bo13b2o3bo$13bo21b
o$12bo22bo$17b3o16bo$17bo$18bo17$122bo$120bobo$2bo118b2o$obo59bo$b2o
57bobo$61b2o3$19bobo57bobo57bobo$20b2o58b2o58b2o$20bo59bo59bo2$132bo$
133b2o4bo$12bo119b2o3b2o$13b2o4bo52bo65b2o$12b2o3b2o54b2o4bo$18b2o52b
2o3b2o$78b2o6$32b2o58b2o58b2o$32bobo57bobo42b3o12bobo$33bo59bo45bo13bo
$17b3o118bo$19bo57b3o$18bo60bo$78bo8$16b3o58b2o57b3o$18bo57bobo59bo$
17bo60bo58bo$46b3o57b3o57b3o$46bo54bo4bo59bo$47bo52b2o5bo59bo$72b2o26b
obo73bo$73b2o100b3o$56bo5b3o7bo49b3o50bob2o3b3o$55b3o4bo2bo50bo5bo2bo
50b3o3bo2bo$55bob2o3bo52b3o4bo53b3o3bo$56b3o3bo52bob2o3bo53b3o3bo$56b
3o3bo53b3o3bo53b2o4bo$56b3o3bo53b3o3bo59bo$56b2o4bo53b3o3bo59bo$63bo
52b2o5bo59bo!

The long ship method allows right-hand side constructions of all LWSS escorts, 5 out of 8 MWSS escorts, and 4 out of 9 HWSS escorts:

Code: Select all

x = 238, y = 494, rule = B3/S23
18bo59bo59bo$16bobo57bobo57bobo$17b2o58b2o58b2o9$127bobo$66bobo58b2o
58bo$23bo42b2o15bo44bo14bo43bobo$24bo42bo16bo59bo42b2o$22b3o57b3o57b3o
4$41bo59bo59bo$42bo59bo59bo$40b3o57b3o57b3o2$41bo59bo59bo$41b2o58b2o
58b2o$40bobo57bobo57bobo6$44b2o58b2o58b2o$43bobo57bobo57bobo$42bobo4bo
52bobo4bo52bobo$42b2o5bobo50b2o5bobo50b2o5bo$49b2o58b2o58bobo$52b2o58b
2o55b2o$52bobo57bobo57b2o$52bo59bo59bobo$172bo15$69b3o$69bo60b3o58bo$
25b2o43bo14b2o43bo14b2o43b2o$26b2o58b2o43bo14b2o42bobo$25bo59bo59bo2$
63b3o57b3o57b3o$63bo59bo59bo$64bo59bo59bo6$41b3o3b3o51b3o57b3o$41bo2bo
bo2bo51bo2bo56bo2bo$41bo7bo51bo5b3o51bo6bo$41bo7bo51bo4bo2bo51bo5b3o$
41bo4bobo52bo7bo51bo5bob2o$41bo3bo55bo7bo51bo6b3o$41bo59bo3b2obo52bo3b
o2b2o$42bobo57bobo57bobo44$2bo59bo119bo$obo57bobo117bobo$b2o58b2o118b
2o9$111bobo$50bobo58b2o$7bo42b2o15bo44bo74bo43bo$8bo42bo16bo119bo42bob
o$6b3o57b3o117b3o42b2o4$25bo59bo119bo$26bo59bo119bo$24b3o57b3o117b3o2$
25bo59bo119bo$25b2o58b2o118b2o$24bobo57bobo117bobo5$37bo59bo$28b2o5b2o
51b2o5b2o111b2o$27bobo6b2o49bobo6b2o109bobo$26bobo57bobo117bobo$26b2o
11bo46b2o11bo106b2o$38b2o58b2o115bo$38bobo57bobo110b2o2bobo$212b2ob2o$
211bo16$51bo183bo$50b2o60bo121b2o$9b2o39bobo16b2o40b2o76b2o43bobo$10b
2o58b2o39bobo76b2o$9bo59bo119bo2$47b3o57b3o117b3o$47bo59bo119bo$48bo
59bo119bo6$25b3o3b3o51b3o117b3o5bo$25bo2bobo2bo51bo2bo116bo2bo3b3o$25b
o7bo51bo5b3o111bo6bob2o$25bo7bo51bo4bo2bo111bo7b3o$25bo7bo51bo7bo111bo
7b3o$25bo4bobo52bo7bo111bo7b2o$25bo59bo7bo111bo$26bobo57bobobobo113bob
o5$62bo59bo59bo$60bobo57bobo57bobo$61b2o58b2o58b2o9$172bo$111bo60bobo
57bo$67bo43bobo13bo44b2o13bo44bobo$68bo42b2o15bo59bo43b2o$66b3o57b3o
57b3o4$85bo59bo59bo$86bo59bo59bo$84b3o57b3o57b3o2$85bo59bo59bo$85b2o
58b2o58b2o$84bobo57bobo57bobo6$88b2o6bo51b2o58b2o$87bobo5bo51bobo57bob
o$86bobo6b3o48bobo57bobo$86b2o58b2o7bo50b2o$98b2o51b2o2bobo57bo$98bobo
51b2ob2o54b2o2bobo$98bo52bo60b2ob2o$211bo16$176bo$175b2o59bo$69b2o40b
2o16b2o44bobo11b2o44b2o$70b2o39bobo16b2o58b2o43bobo$69bo41bo17bo59bo2$
107b3o57b3o57b3o$107bo59bo59bo$108bo59bo59bo6$85b3o57b3o57b3o$85bo2bo
56bo2bo4bo51bo2bo$85bo6bo52bo6b3o50bo7bo$85bo5b3o51bo3bo2bob2o49bo3bo
2b3o$85bo5bob2o50bo7b3o49bo3bo2bob2o$85bo6b3o50bo7b3o49bo7b3o$85bo3bo
2b3o50bo3bo3b2o50bo3bo3b3o$86bo2bo2b2o52bobo57bobo4b2o63$38bo69bo$36bo
bo67bobo$37b2o68b2o8$88bo$88bobo67bo$88b2o68bobo$43bo69bo44b2o$44bo69b
o$42b3o48bo18b3o$92bo70bo$92b3o67bo$162b3o$61bo69bo$62bo69bo$60b3o67b
3o2$61bo69bo$61b2o68b2o$60bobo67bobo6$64b2o68b2o$63bobo67bobo$62bobo
67bobo$62b2o5bobo60b2o$69b2o68bobo$70bo68b2o$140bo$70b2o$70bobo67b2o$
70bo69bobo$140bo14$96b3o$45b2o44b2o3bo18b2o49b3o$46b2o42b2o5bo18b2o43b
2o3bo$45bo46bo22bo44b2o5bo$162bo$83b3o67b3o$83bo69bo$84bo69bo6$61b3o5b
o61b3o$61bo2bo3b3o60bo2bo4bo$61bo6bob2o59bo6b3o$61bo7b3o59bo3bo2bob2o$
61bo7b3o59bo7b3o$61bo7b3o59bo7b3o$61bo3bo3b2o60bo7b3o$62bobo67bobo4b2o
5$38bo69bo$36bobo67bobo$37b2o68b2o6$158bo$158bobo$158b2o2$88bo$43bo44b
obo22bo49bo$44bo43b2o24bo47bo$42b3o67b3o47b3o2$93bo$92bo$61bo30b3o36bo
$62bo69bo$60b3o67b3o2$61bo69bo$61b2o68b2o$60bobo67bobo6$64b2o68b2o$63b
obo67bobo3bobo$62bobo67bobo4b2o$62b2o68b2o6bo2$69bobo68b2o$69b2o69bobo
$70bo69bo2$70b2o$70bobo$70bo11$166b3o$161b2o3bo$160b2o5bo$45b2o68b2o
45bo$46b2o48b3o17b2o$45bo45b2o3bo18bo$90b2o5bo$83b3o6bo60b3o$83bo69bo$
84bo69bo4$139bo$138b3o$61b3o67b3o4bob2o$61bo2bo66bo2bo4b3o$61bo7bo61bo
7b3o$61bo3bo2b3o60bo7b3o$61bo3bo2bob2o59bo7b2o$61bo7b3o59bo3bo$61bo7b
3o59bo$62bob2o3b3o60bobo$69b2o!

On the left-hand side, the long ship method allows the construction of all 20 escorts:

Code: Select all

x = 308, y = 486, rule = B3/S23
25bo69bo69bo$23bobo67bobo67bobo$24b2o68b2o68b2o8$23bo$24b2o$23b2o68bo$
30bo63b2o4bo63bo5bo$31bo61b2o6bo63bo5bo$29b3o67b3o61b3o3b3o4$48bo69bo
69bo$49bo69bo69bo$47b3o67b3o67b3o2$48bo69bo69bo$48b2o68b2o68b2o$47bobo
67bobo67bobo5$39bo$37bobo11b2o68b2o68b2o$38b2o10bobo56bo10bobo67bobo$
41b2o6bobo55bobo9bobo57bo9bobo$40bobo6b2o57b2o9b2o56bobo9b2o$42bo68b2o
65b2o$110bobo68b2o$112bo67bobo$182bo15$20b2o$19bobo$21bo68b2o$32b2o55b
obo10b2o56b2o10b2o$33b2o56bo11b2o56b2o10b2o$32bo69bo57bo11bo2$70b3o67b
3o67b3o$70bo69bo69bo$71bo69bo69bo6$42b3o3b3o67b3o67b3o$41bo2bo3bo2bo
66bo2bo66bo2bo$44bo3bo63b3o3bo64bo4bo$44bo3bo62bo2bo3bo63b3o3bo$41bobo
4bo65bo3bo63bob2o2bo$48bo65bo3bo64b3o2bo$48bo62bobo4bo64b2o3bo$49bo69b
o69bo35$174bo$13bo59bo99bo19bo$11bobo57bobo99b3o15bobo$12b2o58b2o118b
2o8$11bo$12b2o118bo58bo$11b2o58bo61b2o57bo$18bo53b2o4bo53b2o4bo51b3o5b
o$19bo51b2o6bo59bo59bo$17b3o57b3o47bobo7b3o57b3o$128b2o$128bo2$36bo59b
o59bo59bo$37bo59bo59bo59bo$35b3o57b3o57b3o57b3o2$36bo59bo59bo59bo$36b
2o58b2o58b2o58b2o$35bobo57bobo57bobo57bobo5$31bo$32bo6b2o58b2o58b2o49b
o8b2o$30b3o5bobo50bo6bobo57bobo50bo6bobo$37bobo52bo4bobo57bobo49b3o5bo
bo$32bo4b2o51b3o4b2o50bobo5b2o58b2o$31b2o117b2o59bo$31bobo58bo57bo59b
2o$91b2o117bobo$91bobo55b2o$148bobo$150bo13$8b2o$7bobo177b2o$9bo58b2o
56b2o60b2o$20b2o45bobo10b2o43bobo12b2o45bo12b2o$21b2o46bo11b2o44bo13b
2o58b2o$20bo59bo59bo59bo2$58b3o57b3o57b3o57b3o$58bo59bo59bo59bo$59bo
59bo59bo59bo4$150b3o$149bo2bo$30b3o3b3o57b3o53bo3b3o51bo5b3o$29bo2bo3b
o2bo56bo2bo48bo3bo3bo2bo49b3o4bo2bo$32bo3bo53b3o3bo55bo3bo52bob2o3bo$
28bo3bo3bo52bo2bo3bo52bobo4bo53b3o3bo$32bo3bo55bo3bo59bo53b3o3bo$29bob
o4bo51bo3bo3bo59bo53b2o4bo$36bo55bo3bo59bo59bo$37bo51bobo5bo59bo59bo
15$13bo59bo59bo59bo$11bobo57bobo57bobo57bobo$12b2o58b2o58b2o58b2o8$12b
o$13bo$11b3o$18bo53bo5bo59bo59bo$19bo53bo5bo59bo59bo$17b3o51b3o3b3o52b
o4b3o57b3o$133bo58bo$131b3o59bo$191b3o$36bo59bo59bo59bo$37bo59bo59bo
59bo$35b3o57b3o57b3o57b3o2$36bo59bo59bo59bo$36b2o58b2o58b2o58b2o$35bob
o57bobo57bobo57bobo5$31bo$32bo6b2o58b2o58b2o58b2o$30b3o5bobo57bobo57bo
bo57bobo$37bobo51bo5bobo57bobo57bobo$32bo4b2o53bo4b2o51bo6b2o58b2o$31b
2o57b3o58bo58bo$31bobo115b3o59bo$92bo116b3o$91b2o58bo$91bobo56b2o59bo$
150bobo57b2o$210bobo12$8b2o$9b2o$8bo$20b2o46b2o10b2o46b2o10b2o58b2o$
21b2o46b2o10b2o46b2o10b2o45b2o11b2o$20bo47bo11bo47bo11bo48b2o9bo$188bo
$58b3o57b3o57b3o57b3o$58bo59bo59bo59bo$59bo59bo59bo59bo5$31bo$30b3o3b
3o57b3o57b3o57b3o$30bob2o2bo2bo56bo2bo50bo5bo2bo56bo2bo$31b3o2bo54bo4b
o52b3o4bo53bo5bo$31b3o2bo53b3o3bo52bob2o3bo52b3o4bo$31b2o3bo53bob2o2bo
53b3o3bo52bob2o3bo$36bo54b3o2bo53b3o3bo53b3o3bo$36bo54b3o2bo53b2o4bo
53b3o3bo$37bo53b2o4bo59bo52b2o5bo42$191bo$10bo69bo109bo29bo$8bobo67bob
o109b3o25bobo$9b2o68b2o138b2o8$8bo$9b2o138bo68bo$8b2o68bo71b2o67bo$15b
o63b2o4bo63b2o4bo61b3o5bo$16bo61b2o6bo69bo69bo$14b3o67b3o67b3o67b3o$4b
o$5b2o138bo68bo$4b2o68bo71b2o67bo$33bo41b2o26bo41b2o26bo39b3o27bo$34bo
39b2o28bo69bo69bo$32b3o67b3o67b3o67b3o2$33bo69bo69bo69bo$33b2o68b2o68b
2o68b2o$32bobo67bobo67bobo67bobo5$28bo139bo$26bobo7b2o68b2o58bobo7b2o
59bo8b2o$27b2o6bobo60bo6bobo59b2o6bobo57bobo7bobo$34bobo59bobo5bobo67b
obo59b2o6bobo$28b3o3b2o61b2o5b2o62b3o3b2o68b2o$28bo139bo68b3o$29bo68b
3o68bo67bo$98bo139bo$99bo16$142bo$bo140b2o3bo$b2o3bo10b2o68b2o52bobo3b
2o8b2o51b2o15b2o$obo3b2o10b2o51bo16b2o56bobo9b2o49bobo3b2o11b2o$5bobo
9bo53b2o3bo10bo69bo53bo2bobo10bo$70bobo3b2o138bo$55b3o17bobo47b3o67b3o
67b3o$55bo69bo69bo69bo$56bo69bo69bo69bo4$167b3o$166bo2bo$27b3o3b3o67b
3o63bo3b3o61bo5b3o$26bo2bo3bo2bo66bo2bo58bo3bo3bo2bo59b3o4bo2bo$29bo3b
o63b3o3bo61bo3bo3bo62bob2o3bo$25bo3bo3bo62bo2bo3bo65bo3bo63b3o3bo$25bo
3bo3bo65bo3bo62bobo4bo63b3o3bo$29bo3bo61bo3bo3bo69bo63b3o3bo$26bobo4bo
61bo3bo3bo69bo63b2o4bo$34bo64bo4bo69bo69bo$96bobo13$301bo$10bo69bo59bo
59bo99bo$8bobo67bobo57bobo57bobo99b3o$9b2o68b2o58b2o58b2o8$9bo$10bo
177bo$8b3o175bobo70bo$15bo63bo5bo43bo15bo41b2o16bo54bo4bo$16bo63bo5bo
40bobo16bo59bo51b3o5bo$14b3o61b3o3b3o41b2o14b3o57b3o57b3o$5bo$6bo$4b3o
248bo$33bo41bo27bo59bo59bo32bo26bo$34bo41bo27bo59bo59bo29b3o27bo$32b3o
39b3o25b3o57b3o57b3o57b3o2$33bo69bo59bo34bo24bo59bo$33b2o68b2o58b2o34b
2o14bo7b2o58b2o$32bobo67bobo34bo22bobo33b2o13b2o7bobo57bobo$140b2o12bo
59b2o$139b2o11b2o$153b2o2$28bo$26bobo7b2o68b2o58b2o58b2o49bo8b2o$27b2o
6bobo67bobo57bobo57bobo47bobo7bobo$34bobo61bo5bobo57bobo57bobo49b2o6bo
bo$28b3o3b2o60bobo5b2o58b2o58b2o58b2o$28bo68b2o178b3o$29bo247bo$98b3o
177bo$98bo$99bo7$144b3o56b3o$146bo58bo$145bo58bo7$b2o248b2o$obo3b2o9b
2o68b2o58b2o58b2o41bobo3b2o9b2o$2bo2bobo10b2o68b2o58b2o58b2o42bo2bobo
10b2o$7bo9bo53b2o14bo59bo59bo49bo9bo$70bobo3b2o$55b3o14bo2bobo47b3o57b
3o57b3o57b3o$55bo21bo47bo59bo59bo59bo$56bo69bo59bo59bo59bo4$277bo$28bo
247b3o$27b3o3b3o67b3o57b3o57b3o50bob2o3b3o$27bob2o2bo2bo66bo2bo50bo5bo
2bo56bo2bo50b3o3bo2bo$28b3o2bo64bo4bo52b3o4bo53bo5bo53b3o3bo$28b3o2bo
63b3o3bo52bob2o3bo52b3o4bo53b3o3bo$28b3o2bo63bob2o2bo53b3o3bo52bob2o3b
o53b2o4bo$28b2o3bo64b3o2bo53b3o3bo53b3o3bo59bo$33bo64b3o2bo53b3o3bo53b
3o3bo59bo$34bo63b3o3bo52b2o5bo52b3o4bo59bo$98b2o117b2o!

Constructing all 210 simple 7WSS flotillas would be a tedious task. Can it be automated using the above one-sided escort syntheses?

Re: OWSS synthesis project

Posted: July 15th, 2025, 9:48 pm

by Sokwe

8WSS syntheses
All simple 8WSS flotillas can be synthesized. In this case there are 19 escorts:

Code: Select all

#C 19 Possible escorts for 8WSS (LWSS1-3, MWSS1-7, HWSS1-9)
x = 170, y = 49, rule = B3/S23
7b3o11b3o3b3o17b3o$6bo2bo11bo2bobo2bo16bo2bo$2bo6bo11bo7bo11b3o5bo$b3o
5bo11bo7bo11bo2bo4bo$2obo5bo12bobo4bo11bo7bo$3o6bo15bo3bo11bo7bo$b2o6b
o15bo3bo12bobo4bo$5bo3bo19bo19bo$6bobo17bobo17bobo11$2bo$b3o3b3o17b3o
11b3o3b3o17b3o11bo5b3o17b3o17b3o$2obo2bo2bo16bo2bo11bo2bobo2bo16bo2bo
10b3o3bo2bo11bo4bo2bo16bo2bo$3o6bo12bo6bo11bo7bo11b3o5bo9b2obo6bo10b3o
6bo11bo7bo$3o2bo3bo11b3o5bo11bo7bo11bo2bo4bo9b3o7bo9b2obo2bo3bo10b3o2b
o3bo$b2o6bo10b2obo5bo11bo7bo11bo7bo9b3o7bo9b3o7bo9b2obo2bo3bo$9bo10b3o
6bo12bobo4bo11bo7bo10b2o7bo9b3o7bo9b3o7bo$9bo10b3o2bo3bo15bo3bo11bo7bo
15bo3bo10b2o7bo9b3o7bo$9bo11b2o6bo19bo12bob2o3bo19bo19bo10b2o3bo3bo$6b
obo17bobo17bobo17bobo17bobo17bobo17bobo10$41b3o57bo$2bo38bo2bo55b3o$b
3o3b3o17b3o11bo5b3o11b3o3b3o17b3o9b2obo4b3o11bo5b3o17b3o17b3o$2obo2bo
2bo16bo2bo11bo4bo2bo11bo2bobo2bo16bo2bo9b3o4bo2bo10b3o3bo2bo11bo4bo2bo
16bo2bo$3o6bo12bo6bo11bo7bo11bo7bo11b3o5bo9b3o7bo9b2obo6bo10b3o6bo11bo
7bo$3o6bo11b3o5bo11bo7bo11bo7bo11bo2bo4bo9b3o7bo9b3o7bo9b2obo2bo3bo10b
3o2bo3bo$3o6bo10b2obo5bo12bobo4bo11bo7bo11bo7bo10b2o7bo9b3o7bo9b3o7bo
9b2obo2bo3bo$b2o6bo10b3o6bo15bo3bo11bo7bo11bo7bo15bo3bo9b3o7bo9b3o7bo
9b3o7bo$9bo10b3o6bo15bo3bo12bobo4bo11bo7bo15bo3bo10b2o7bo9b3o7bo9b3o7b
o$5bo3bo10b3o2bo3bo19bo19bo11bo7bo19bo19bo10b2o3bo3bo9b3o7bo$6bobo12b
2o2bo2bo17bobo17bobo13bobobobo17bobo17bobo17bobo11b2o4bobo!

As with the 7WSS, we can use a shillelagh to synthesize the 8WSS:

Code: Select all

x = 63, y = 22, rule = B3/S23
bobo33bobo$2b2o34b2o$2bo35bo3$3b2o13b3o18b2o18b3o$4bo13bo2bo18bo18bo2b
o$3bo14bo20bo19bo$3bobo12bo20bobo17bo$4b2o12bo21b2o3b2o12bo$18bo25b2o
13bo$10bo7bo27bo12bo$b2o6b2o7bo30b2o8bo$obo6bobo7bo16b2o4b2o5bobo8bo$
2bo34b2o3bobo4bo$36bo5bo4$37b2o$36bobo$38bo!

Almost all of the simple 8WSS flotillas can be constructed using one of the two syntheses above. Note that these syntheses work slightly differently, so we need to be careful about compatibility of left-hand and right-hand escort syntheses.

All but two (HWSS2 and HWSS9) of the escorts can be synthesized on the right-hand side using one of the two shillelagh-based 8WSS syntheses:

Code: Select all

x = 226, y = 267, rule = B3/S23
74bobo$74b2o$75bo38bobo$23bobo8bo28bobo37bobo8b2o$24b2o8bobo27b2o38b2o
9bo$24bo9b2o28bo39bo$72b2o$72b2o$25b2o18b3o17b2o18b3o3b3o11b2o5b2o11b
3o$26bo5b2o11bo2bo17bo18bo2bobo2bo12bo5b2o11bo2bo$25bo6b2o11bo6bo12bo
11b2o6bo7bo11bo19bo5b3o$25bobo17bo5b3o11bobo9bobo5bo7bo11bobo17bo4bo2b
o$26b2o17bo5bob2o11b2o3b2o4bo7bo4bobo13b2o9b2o6bo7bo$37b2o6bo6b3o15b2o
13bo3bo27bobo5bo7bo$32bo3b2o7bo6b2o18bo12bo3bo22bo4bo7bo4bobo$23b2o6b
2o5bo6bo3bo25b2o8bo17b2o6b2o12bo$22bobo6bobo12bobo13b2o4b2o5bobo8bobo
13bobo6bobo12bobo$24bo38b2o3bobo4bo28bo$62bo5bo4$63b2o$62bobo$64bo26$
34bo79bobo$34bobo77b2o$34b2o79bo38bobo$23bobo37bobo8bo28bobo37bobo8b2o
$24b2o38b2o8bobo27b2o38b2o9bo$24bo39bo9b2o28bo39bo$32b2o78b2o$31bobo
18bo58bobo$25b2o5bo12b3o3b3o11b2o18b3o17b2o5bo12b3o3b3o11b2o5b2o11b3o$
26bo11bo6bo2bo2bob2o11bo5b2o11bo2bo17bo18bo2bobo2bo12bo5bobo10bo2bo$
25bo11b2o6bo6b3o10bo6bobo10bo6bo12bo11b3o5bo7bo11bo7b2o10bo5b3o$25bobo
9bobo5bo3bo2b3o10bobo5b2o10bo5b3o11bobo9bo7bo7bo11bobo17bo4bo2bo$26b2o
17bo6b2o12b2o17bo5bob2o11b2o10bo6bo7bo12b2o10b2o5bo7bo$45bo31b3o5bo6b
3o30bo4bobo24b2o6bo7bo$32bo12bo26bo4bo7bo3bo2b3o17bo12bo3bo22bo6bo5bo
7bo$23b2o6b2o12bo17b2o6b2o5bo6bo6b2o9b2o6b2o12bo17b2o6b2o12bo3b2obo$
22bobo6bobo12bobo13bobo6bobo12bobo13bobo6bobo12bobo13bobo6bobo12bobo$
24bo39bo39bo39bo14$35bo$35bobo37bo$23bobo9b2o26bobo9bobo25bobo9bo$24b
2o38b2o9b2o27b2o9bobo$24bo39bo39bo10b2o2$33b2o$25b2o5bobo10b3o5bo11b2o
6b2o10b3o17b2o18b3o$26bo6bo11bo2bo3b3o11bo5bobo10bo2bo4bo12bo6b2o10bo
2bo$25bo13bo5bo6bob2o9bo7bo11bo6b3o10bo6bobo10bo7bo$25bobo10b2o5bo7b3o
9bobo11bo5bo3bo2bob2o9bobo5bo11bo3bo2b3o$26b2o10bobo4bo7b3o10b2o10b2o
5bo7b3o10b2o11bo5bo3bo2bob2o$45bo7b2o23bobo4bo7b3o22b2o5bo7b3o$32bo12b
o3bo22bo12bo7b2o17bo5bobo4bo7b3o$23b2o6b2o12bo17b2o6b2o12bo17b2o6b2o
12bo3bo3b2o$22bobo6bobo12bobo13bobo6bobo12bobo13bobo6bobo12bobo$24bo
39bo39bo42$8bo$6bobo$bobo3b2o$2b2o$2bo4$44bo$42b2o40bobo$43b2o39b2o$
85bo48bobo61bo$134b2o62bobo$135bo48bobo11b2o$73bobo14bo32bobo47bobo8b
2o$74b2o6b2o4b2o34b2o48b2o9bo$28b2o3b3o38bo6bo2bo4b2o33bo15bo33bo$29b
2o2bo47bo2bo26b3o18b2o4b2o$28bo5bo47b2o26bo2bo17bo2bo4b2o49bobo$15b2o
58b2o28b3o5bo11b2o4bo2bo20b3o3b3o11b2o5b2o6b2o13b3o$16bo59bo28bo2bo4bo
12bo5b2o21bo2bobo2bo12bo5bo8bo13bo2bo$15bo59bo11b2o16bo7bo11bo29bo7bo
11bo7bo21bo5b3o$15bobo57bobo9bobo15bo7bo11bobo15b2o10bo7bo11bobo6bobo
18bo4bo2bo$16b2o58b2o3b2o4bo17bo4bobo13b2o9b2o3b2o11bo7bo12b2o7b2o18bo
7bo$80b2o23bo3bo27bobo4bo10bo7bo41bo7bo$82bo22bo3bo22bo4bo17bo4bobo19b
o22bo7bo$85b2o18bo17b2o6b2o22bo17b2o6b2o22bo7bo$72b2o4b2o5bobo18bobo
13bobo6bobo22bobo13bobo6bobo22bobobobo$73b2o3bobo4bo4b2o32bo49bo$72bo
5bo11bobo$90bo7$34bo$b2o30b2o$obo30bobo$2bo2$52bo$45b3o3b3o$45bo2bo2bo
b2o$45bo6b3o$45bo6b3o$45bo6b3o$45bo6b2o$45bo$45bo3bo$46bobo17$218bo$9b
o207bo$7bobo207b3o$8b2o89bo$bobo87bobo3bobo71bobo$2b2o88b2o4b2o72b2o$
2bo89bo79bo3$45bo$43b2o$44b2o89bo$133b2o$134b2o70bobo$199bobo4b2o$200b
2o5bo$200bo$29b2o3b3o$30b2o2bo$29bo5bo83b2o3b3o$120b2o2bo$15b2o88b2o
12bo5bo59b2o$16bo89bo79bo$15bo89bo79bo$15bobo87bobo77bobo$16b2o88b2o
78b2o$201b2o$201bobo$201bo9$33b2o$32b2o$34bo2b3o84bo79bo$37bo53b2o30b
2o46b2o30b2o$2o28b2o6bo51bobo30bobo44bobo30bobo$b2o27bobo59bo79bo$o29b
o22bo$52b3o$45b3o4bob2o79b3o5bo71b3o$45bo2bo4b3o79bo2bo3b3o70bo2bo4bo$
45bo7b3o79bo6bob2o69bo6b3o$45bo7b3o79bo7b3o69bo3bo2bob2o$45bo7b2o80bo
7b3o69bo7b3o$45bo3bo85bo7b3o69bo7b3o$45bo3bo85bo7b2o70bo7b3o$45bo89bo
79bo3bo3b2o$46bobo87bobo77bobo2$24bo$23b3o$23bob2o$24b3o$24b2o!

Notice that those using the second 8WSS syntheses each have slightly different glider arrangements, but this only affects debris cleanup and not left-hand compatibility.

On the left-hand side all escorts can be synthesized, regardless of which 8WSS synthesis is used:

Code: Select all

x = 428, y = 234, rule = B3/S23
20bo39bo229bo$21bo39b2o228b2o$19b3o4bobo31b2o4bobo31bo5bobo137bobo41b
2o4bobo41bo5bobo$27b2o38b2o32b2o4b2o132bo5b2o48b2o42b2o4b2o$27bo39bo
32b2o5bo134bo4bo49bo42b2o5bo$240b3o$62b2o228b2o$22b2o4b2o18b3o11b2o4b
2o12b3o3b3o17b2o18b3o117b2o28b3o11b2o4b2o22b3o3b3o17b2o28b3o$22b2o5bo
18bo2bo17bo11bo2bo3bo2bo10b2o5bo18bo2bo117bo28bo2bo17bo21bo2bo3bo2bo
10b2o5bo28bo2bo$28bo14bo4bo19bo15bo3bo13b2o4bo13b3o3bo113b2o4bo24bo4bo
19bo25bo3bo13b2o4bo23b3o3bo$28bobo11b3o3bo8b3o8bobo13bo3bo19bobo10bo2b
o3bo113b2o4bobo21b3o3bo8b3o8bobo23bo3bo19bobo20bo2bo3bo$17bo11b2o11bob
2o2bo10bo9b2o10bobo4bo20b2o13bo3bo120b2o3b2o16bob2o2bo10bo9b2o3b2o15bo
bo4bo20b2o3b2o18bo3bo$17b2o24b3o2bo9bo29bo8b3o24bo3bo109bo14b2o18b3o2b
o9bo14b2o23bo8b3o13b2o19bo3bo$16bobo16bo7b2o3bo26bo12bo10bo15bo5bobo4b
o109b2o15bo17b2o3bo26bo22bo10bo15bo15bobo4bo$26b2o6b2o12bo17b2o6b2o12b
o9bo7b2o6b2o12bo108bobo18b2o18bo29b2o18bo9bo19b2o18bo$25bobo6bobo12bo
15bobo6bobo12bo15bobo6bobo12bo115b2o4b2o5bobo18bo15b2o4b2o5bobo18bo15b
2o4b2o5bobo18bo$27bo39bo39bo138b2o3bobo4bo37b2o3bobo4bo37b2o3bobo4bo$
245bo5bo43bo5bo43bo5bo4$246b2o48b2o48b2o$245bobo47bobo47bobo$247bo49bo
49bo8$5bo$6bo$4b3o3$5bo$6b2o$5b2o19$20bo$21bo$19b3o$60bo39bo140bo98bo$
61bo39b2o139bo98b2o$26bobo30b3o4bobo31b2o4bobo31bo5bobo91b3o3bobo47bob
o41b2o4bobo41bo5bobo$16bo10b2o38b2o38b2o32b2o4b2o98b2o42bo5b2o48b2o42b
2o4b2o$8bo5bobo5b2o3bo39bo39bo32b2o5bo99bo44bo4bo49bo42b2o5bo$8b2o5b2o
4bo2bo265b3o$7bobo11bo2bo18bo58b2o138b2o25bo72b2o$22b2o4b2o12b3o3b3o
11b2o4b2o18b3o10bobo4b2o12b3o3b3o17b2o12b3o3b3o71bobo3b2o18b3o3b3o21b
2o24b3o15bobo3b2o18b3o3b3o21b2o18b3o3b3o$29bo12bob2o2bo2bo10bobo4bo18b
o2bo9b2o6bo11bo2bo3bo2bo10b2o5bo11bo2bo3bo2bo71bo5bo18bob2o2bo2bo21bo
24bo2bo15bo5bo17bo2bo3bo2bo14b2o5bo17bo2bo3bo2bo$11b2o15bo14b3o2bo14bo
4bo14bo4bo8bo10bo15bo3bo12bobo4bo15bo3bo68b2o9bo20b3o2bo17b2o4bo20bo4b
o12b2o9bo21bo3bo16bobo4bo21bo3bo$10bobo4bo10bobo12b3o2bo19bobo11b3o3bo
8b2o9bobo9bo3bo3bo12b2o5bobo9bo3bo3bo69b2o8bobo18b3o2bo17bobo3bobo17b
3o3bo11bobo9bobo15bo3bo3bo16b2o5bobo15bo3bo3bo$12bo4b2o10b2o12b2o3bo7b
2o11b2o11bob2o2bo7bobo10b2o13bo3bo8bo11b2o13bo3bo68bo11b2o3b2o13b2o3bo
18bo5b2o3b2o12bob2o2bo13bo10b2o3b2o14bo3bo12bo11b2o3b2o14bo3bo$16bobo
29bo8b2o24b3o2bo32bobo4bo8b2o22bobo4bo84b2o19bo12b2o14b2o14b3o2bo28b2o
12bobo4bo12b2o14b2o12bobo4bo$35bo12bo7bo18bo7b3o2bo26bo12bo7bobo16bo
12bo86bo18bo13b2o15bo13b3o2bo30bo18bo11bobo16bo18bo$26b2o6b2o12bo17b2o
6b2o7b2o3bo17b2o6b2o12bo17b2o6b2o12bo89b2o14bo12bo20b2o9b2o3bo33b2o14b
o33b2o14bo$25bobo6bobo12bo15bobo6bobo12bo15bobo6bobo12bo15bobo6bobo12b
o75b2o4b2o5bobo14bo19b2o4b2o5bobo14bo19b2o4b2o5bobo14bo19b2o4b2o5bobo
14bo$27bo39bo39bo39bo98b2o3bobo4bo37b2o3bobo4bo37b2o3bobo4bo37b2o3bobo
4bo$245bo5bo43bo5bo43bo5bo43bo5bo4$246b2o48b2o48b2o48b2o$245bobo47bobo
47bobo47bobo$247bo49bo49bo49bo5$9bo$10bo38bo$8b3o39bo38bo$48b3o39bo
149bo$16bobo37bobo29b3o5bobo142bo4bobo41bo5bobo47bobo$17b2o38b2o38b2o
140b3o5b2o42bo5b2o41bo6b2o$17bo39bo39bo149bo41b3o5bo43bo5bo$11b2o326b
3o$11bobo37b2o$12bo5b2o12bo5b3o10bobo4b2o18b3o10b2o5b2o18b3o120b2o5b2o
18bo5b3o21b2o24b3o21b2o24b3o$19bo11b3o4bo2bo10bo6bo12bo5bo2bo9bobo5bo
18bo2bo119bobo5bo17b3o4bo2bo13b2o6bo18bo5bo2bo21bo24bo2bo$5b2o11bo12bo
b2o3bo19bo12b3o4bo13bo5bo13bo5bo123bo5bo18bob2o3bo16bobo4bo18b3o4bo16b
2o5bo19bo5bo$6b2o10bobo11b3o3bo6b2o11bobo10bob2o3bo19bobo10b3o4bo117b
2o10bobo17b3o3bo17bo5bobo16bob2o3bo16bobo4bobo16b3o4bo$5bo13b2o11b3o3b
o7b2o11b2o11b3o3bo6b2o12b2o10bob2o3bo118b2o10b2o3b2o12b3o3bo11b2o11b2o
3b2o12b3o3bo17bo6b2o3b2o11bob2o3bo$32b2o4bo6bo26b3o3bo7b2o24b3o3bo117b
o16b2o13b2o4bo12b2o14b2o13b3o3bo11b2o15b2o13b3o3bo$25bo12bo26bo6b2o4bo
6bo19bo6b3o3bo136bo18bo11bo18bo12b2o4bo12b2o16bo12b3o3bo$16b2o6b2o12bo
17b2o6b2o12bo17b2o6b2o6b2o4bo139b2o14bo33b2o14bo11bo21b2o8b2o4bo$15bob
o6bobo12bo15bobo6bobo12bo15bobo6bobo12bo125b2o4b2o5bobo14bo19b2o4b2o5b
obo14bo19b2o4b2o5bobo14bo$17bo39bo39bo148b2o3bobo4bo37b2o3bobo4bo37b2o
3bobo4bo$245bo5bo43bo5bo43bo5bo4$246b2o48b2o48b2o$245bobo47bobo47bobo$
247bo49bo49bo24$10bo$11bo98bo$9b3o99b2o$60bo49b2o$61bo$16bobo40b3o4bob
o47bobo$6bo10b2o48b2o48b2o$4bobo5b2o3bo49bo37bobo4b2o3bo$5b2o4bo2bo91b
2o3bo2bo17b3o$11bo2bo18bo22bo49bo4bo2bo16bo2bo$12b2o4b2o12b3o3b3o13bob
o5b2o4b2o18b3o21b2o4b2o14bo3b3o$19bo12bob2o2bo2bo13b2o4bo2bo4bo18bo2bo
10bo16bo10bo3bo3bo2bo210bo$b2o15bo14b3o2bo22bo2bo3bo14bo4bo13b2o14bo
11bo3bo3bo214b2o$obo4bo10bobo12b3o2bo23b2o4bobo11b3o3bo12bobo3b3o8bobo
13bo3bo102bo110b2o$2bo4b2o10b2o12b3o2bo30b2o11bob2o2bo20bo9b2o10bobo4b
o103bo$6bobo24b2o3bo12b2o30b3o2bo19bo29bo101b3o3bobo53bobo53bobo$25bo
12bo11bobo4bo17bo7b3o2bo36bo12bo108b2o48bo5b2o54b2o$16b2o6b2o12bo13bo
4b2o7b2o6b2o7b3o2bo27b2o6b2o12bo108bo50bo4bo43bobo4b2o3bo$15bobo6bobo
12bo16bobo6bobo6bobo6b2o4bo25bobo6bobo12bo156b3o49b2o3bo2bo23b3o$17bo
49bo49bo119bo4b2o25bo78bo4bo2bo22bo2bo$235bobo3bo2bo3b2o18b3o3b3o27b2o
24b3o21b2o4b2o20bo3b3o$236b2o3bo2bo4bo18bob2o2bo2bo27bo24bo2bo10bo16bo
16bo3bo3bo2bo$242b2o4bo20b3o2bo18bo4b2o4bo20bo4bo13b2o14bo17bo3bo3bo$
232b2o14bobo18b3o2bo16bobo3bo2bo3bobo17b3o3bo12bobo3b3o8bobo19bo3bo$
231bobo4bo10b2o3b2o13b3o2bo17b2o3bo2bo4b2o3b2o12bob2o2bo20bo9b2o3b2o
11bobo4bo$233bo4b2o13b2o14b2o3bo23b2o9b2o14b3o2bo19bo14b2o19bo$237bobo
15bo18bo13b2o21bo13b3o2bo36bo18bo$258b2o14bo12bobo4bo19b2o9b3o2bo39b2o
14bo$245b2o4b2o5bobo14bo13bo4b2o5b2o4b2o5bobo8b2o4bo25b2o4b2o5bobo14bo
$246b2o3bobo4bo34bobo6b2o3bobo4bo43b2o3bobo4bo$245bo5bo49bo5bo49bo5bo
2$110bo$10bo100bo$11b2o96b3o134b2o54b2o54b2o$10b2o4bobo41bo5bobo47bobo
126bobo53bobo53bobo$17b2o42b2o4b2o48b2o128bo55bo55bo$17bo42b2o5bo49bo$
106bo4b2o19bo$5bobo4b2o90bobo3bo2bo17b3o$6b2o3bo2bo3b2o12b3o3b3o27b2o
18b3o14b2o3bo2bo4b2o11bob2o3b3o$6bo4bo2bo4bo11bo2bo3bo2bo13bobo4b2o5bo
18bo2bo19b2o6bo12b3o3bo2bo$12b2o4bo15bo3bo17b2o3bo2bo3bo13b3o3bo12b2o
15bo13b3o3bo213bo$2bo15bobo9bo3bo3bo17bo4bo2bo3bobo10bo2bo3bo11bobo4bo
10bobo11b3o3bo101bo112bo$2b2o15b2o9bo3bo3bo23b2o5b2o13bo3bo13bo4b2o10b
2o11b2o4bo102b2o108b3o$bobo3b3o24bo3bo13bo27bo3bo3bo17bobo29bo101b2o4b
obo47bo5bobo53bobo$9bo15bo5bobo4bo13b2o21bo4bo3bo3bo36bo12bo108b2o48b
2o4b2o54b2o$8bo7b2o6b2o12bo12bobo3b3o6b2o6b2o8bo3bo27b2o6b2o12bo108bo
48b2o5bo55bo$15bobo6bobo12bo19bo5bobo6bobo4bobo5bo25bobo6bobo12bo208bo
4b2o25bo$17bo40bo8bo49bo117bobo4b2o102bobo3bo2bo23b3o$236b2o3bo2bo3b2o
18b3o3b3o27b2o24b3o14b2o3bo2bo4b2o17bob2o3b3o$236bo4bo2bo4bo17bo2bo3bo
2bo13bobo4b2o5bo24bo2bo19b2o6bo18b3o3bo2bo$242b2o4bo21bo3bo17b2o3bo2bo
3bo19b3o3bo12b2o15bo19b3o3bo$232bo15bobo15bo3bo3bo17bo4bo2bo3bobo16bo
2bo3bo11bobo4bo10bobo17b3o3bo$232b2o15b2o3b2o10bo3bo3bo23b2o5b2o3b2o
14bo3bo13bo4b2o10b2o3b2o12b2o4bo$231bobo3b3o13b2o15bo3bo13bo20b2o11bo
3bo3bo17bobo14b2o19bo$239bo15bo11bobo4bo13b2o21bo10bo3bo3bo36bo18bo$
238bo19b2o14bo12bobo3b3o18b2o10bo3bo39b2o14bo$245b2o4b2o5bobo14bo19bo
5b2o4b2o5bobo6bobo5bo25b2o4b2o5bobo14bo$246b2o3bobo4bo35bo7b2o3bobo4bo
43b2o3bobo4bo$245bo5bo49bo5bo49bo5bo2$59bo$60bo48bo$10bo47b3o49bo135b
2o54b2o54b2o$11bo4bobo47bobo39b3o5bobo126bobo53bobo53bobo$9b3o5b2o48b
2o48b2o128bo55bo55bo$17bo49bo49bo$55bo$53bobo5b2o42bo$6bo4b2o5b2o12bo
5b3o13b2o4bo2bo4b2o18b3o12bobo5b2o5b2o18b3o$4bobo3bo2bo5bo11b3o4bo2bo
18bo2bo5bo12bo5bo2bo12b2o4bo2bo5bo18bo2bo$5b2o3bo2bo4bo12bob2o3bo22b2o
5bo12b3o4bo21bo2bo4bo13bo5bo$11b2o5bobo11b3o3bo29bobo10bob2o3bo22b2o5b
obo10b3o4bo$b2o16b2o11b3o3bo11b2o17b2o11b3o3bo30b2o10bob2o3bo101bo$obo
4bo24b3o3bo10bobo4bo25b3o3bo11b2o30b3o3bo102bo4bobo47bo5bobo53bobo$2bo
4b2o16bo6b2o4bo12bo4b2o17bo6b3o3bo10bobo4bo18bo6b3o3bo100b3o5b2o48bo5b
2o47bo6b2o$6bobo7b2o6b2o12bo16bobo8b2o6b2o6b2o4bo12bo4b2o8b2o6b2o6b3o
3bo108bo47b3o5bo49bo5bo$15bobo6bobo12bo25bobo6bobo12bobo13bobo7bobo6bo
bo5b2o5bobo209b3o$17bo49bo49bo$236bo4b2o5b2o18bo5b3o27b2o24b3o27b2o24b
3o$234bobo3bo2bo5bo17b3o4bo2bo14bo4b2o6bo18bo5bo2bo27bo24bo2bo$235b2o
3bo2bo4bo18bob2o3bo15bobo3bo2bo4bo18b3o4bo17bo4b2o5bo19bo5bo$241b2o5bo
bo17b3o3bo16b2o3bo2bo4bobo16bob2o3bo15bobo3bo2bo4bobo16b3o4bo$231b2o
16b2o3b2o12b3o3bo22b2o6b2o3b2o12b3o3bo16b2o3bo2bo5b2o3b2o11bob2o3bo$
230bobo4bo15b2o13b3o3bo12b2o20b2o13b3o3bo22b2o10b2o13b3o3bo$232bo4b2o
16bo12b2o4bo11bobo4bo17bo12b3o3bo12b2o22bo12b3o3bo$236bobo19b2o14bo13b
o4b2o19b2o8b2o4bo11bobo4bo20b2o8b3o3bo$245b2o4b2o5bobo14bo16bobo6b2o4b
2o5bobo14bobo10bo4b2o6b2o4b2o5bobo7b2o5bobo$246b2o3bobo4bo43b2o3bobo4b
o33bobo7b2o3bobo4bo$245bo5bo49bo5bo49bo5bo4$246b2o54b2o54b2o$245bobo
53bobo53bobo$247bo55bo55bo!

By combining the left-hand and right-hand escort syntheses, all 8WSS flotillas can be constructed, except those that use only HWSS2 and/or HWSS9. Fortunately, those can be constructed using the table method:

Code: Select all

x = 191, y = 30, rule = B3/S23
25bo69bo69bo$26b2o68b2o68b2o$17bo7b2o60bo7b2o60bo7b2o$18b2o10b2o56b2o
10b2o56b2o10b2o$17b2o11b2o55b2o11b2o55b2o11b2o$2bo37bo30bo38bo30bo39bo
$obo35b2o29bobo36b2o29bobo37b2o$b2o11bobo22b2o29b2o11bobo23b2o29b2o11b
obo24b2o$15b2o67b2o68b2o$15bo68bo69bo$25b2ob2o65b2ob2o65b2ob2o$25b2obo
14bobo49b2obo14bobo49b2obo15bobo$8bobo17bo14b2o32bobo18bo14b2o32bobo
18bo15b2o$9b2o17b2o14bo33b2o18b2o14bo33b2o18b2o15bo$9bo68bo69bo$33b2o
68b2o69b2o$20b2o10bo2bo53b2o11bo2bo53b2o12bo2bo$21bo10bo2bo54bo11bo2bo
54bo12bo2bo$20bo12b2o54bo13b2o54bo14b2o$17bobo66bobo67bobo$17b2o67b2o
68b2o2$21b3o67b3o67b3o$23bo24bo44bo24bo44bo25bo$22bo24b2o43bo24b2o43bo
25b2o$35bo5b3o3bobo55bo5b3o3bobo55bo6b3o3bobo$34b2o5bo62b2o5bo62b2o6bo
$21b2o11bobo5bo48b2o11bobo5bo48b2o11bobo6bo$20bobo67bobo67bobo$22bo69b
o69bo!

As with the 7WSS flotillas, the shillelagh method does not always yield the cheapest synthesis. Here are some alternate 8WSS syntheses that may give smaller syntheses for some of the 8WSS flotillas:

Code: Select all

x = 255, y = 94, rule = B3/S23
225bobo$226b2o$226bo5$157bobo$158b2o$158bo4$231bo$232b2o$231b2o4$249bo
$163bo86b2o$164b2o83b2o$163b2o2$249b3o$251bo$42bo29bo108bo68bo$43b2o
28b2o107b2o$42b2o28b2o107b2o$47b2o28b2o$47b2o28b2o$126bobo52b3o69b2o$
3b3o121b2o54bo68bobo$5bo3bo117bo54bo68bobo$4bo3b2o241b2o$8bobo$15b2o
28b2o27b2o52b2o$15bobo27bo29bo52bobo$bo13bo26b2obo29bob2o50bo55b2o$b2o
39b2ob2o27b2ob2o44b3o58bobo$obo122bo57bobo$13b2o109bo58b2o$12b2o116b3o
$14bo115bo$131bo$34b2o49b2o37b3o$35b2o47b2o40bo$34bo51bo38bo$38b3o27b
3o$40bo29bo$39bo29bo$53b3o27b3o$53bo29bo$54bo29bo12$164b3o$42bo29bo93b
o$43b2o28b2o90bo$34bo7b2o28b2o12bo$35b2o10b2o28b2o5b2o115b3o$34b2o11b
2o28b2o6b2o114bo$202bo5$42b2ob2o27b2ob2o$42b2obo29bob2o173bo$45bo29bo
175b3o$45b2o27b2o174b2obo$250b3o$251b2o7$38b3o27b3o$40bo29bo$39bo29bo$
53b3o27b3o$53bo29bo$54bo29bo!

Re: OWSS synthesis project

Posted: July 20th, 2025, 4:00 am

by Sokwe

9WSS syntheses
All simple 9WSS flotillas can be synthesized. In this case there are 17 escorts:

Code: Select all

#C 17 Possible escorts for 9WSS (LWSS1-2, MWSS1-8, HWSS1-7)
x = 187, y = 102, rule = B3/S23
10$10b3o17b3o$10bo2bo16bo2bo$10bo6bo12bo5b3o$10bo5b3o11bo4bo2bo$10bo5b
ob2o10bo7bo$10bo6b3o10bo7bo$10bo6b2o11bo4bobo$10bo19bo3bo$10bo3bo15bo$
11bobo17bobo20$17bo$10b3o3b3o11b3o17b3o3b3o11b3o17b3o5bo11b3o17b3o17b
3o$10bo2bo2bob2o10bo2bo16bo2bobo2bo11bo2bo16bo2bo3b3o10bo2bo4bo11bo2bo
16bo2bo2b3o$10bo6b3o10bo6bo12bo7bo11bo5b3o11bo6bob2o9bo6b3o10bo7bo11bo
5bo2bo$10bo3bo2b3o10bo5b3o11bo7bo11bo4bo2bo11bo7b3o9bo3bo2bob2o9bo3bo
2b3o10bo5bo$10bo6b2o11bo5bob2o10bo7bo11bo7bo11bo7b3o9bo7b3o9bo3bo2bob
2o9bo5bo3bo$10bo19bo6b3o10bo4bobo12bo7bo11bo7b2o10bo7b3o9bo7b3o9bo2bo
2bo$10bo19bo3bo2b3o10bo3bo15bo7bo11bo3bo15bo7b2o10bo7b3o9bo6bobo$10bo
3bo15bo6b2o11bo3bo15bo4bobo12bo3bo15bo3bo15bo7b2o10bo$10bo19bo3bo15bo
19bo19bo19bo19bo19bo$11bobo17bobo17bobo17bobo17bobo17bobo17bobo17bobo
20$17bo$10b3o3b3o11b3o17b3o3b3o11b3o17b3o5bo11b3o17b3o$10bo2bo2bob2o
10bo2bo16bo2bobo2bo11bo2bo16bo2bo3b3o10bo2bo4bo11bo2bo$10bo6b3o10bo6bo
12bo7bo11bo5b3o11bo6bob2o9bo6b3o10bo7bo$10bo6b3o10bo5b3o11bo7bo11bo4bo
2bo11bo7b3o9bo3bo2bob2o9bo3bo2b3o$10bo6b3o10bo5bob2o10bo7bo11bo7bo11bo
7b3o9bo7b3o9bo3bo2bob2o$10bo6b2o11bo6b3o10bo7bo11bo7bo11bo7b3o9bo7b3o
9bo7b3o$10bo19bo6b3o10bo4bobo12bo7bo11bo7b2o10bo7b3o9bo7b3o$10bo19bo6b
3o10bo3bo15bo7bo11bo3bo15bo7b2o10bo7b3o$10bo19bo6b2o11bo19bo3b2obo12bo
19bo19bo3bo3b2o$11bobo17bobo17bobo17bobo17bobo17bobo17bobo!

Most simple 9WSS flotillas can be constructed using the long ship method:

Code: Select all

x = 126, y = 66, rule = B3/S23
2bo79bo$obo77bobo$b2o78b2o11$7bo79bo$8bo79bo$6b3o77b3o4$25bo79bo$26bo
79bo$24b3o77b3o2$25bo79bo$25b2o78b2o$24bobo77bobo6$28b2o78b2o$27bobo
77bobo$26bobo77bobo$26b2o78b2o23$43bo40b2o$42b2o39bobo$42bobo40bo2$3b
2o119b2o$2bobo118b2o$4bo78b3o39bo$85bo$84bo!

All left-hand escorts can be synthesized using the long ship method:

Code: Select all

x = 615, y = 401, rule = B3/S23
11bo79bo$9bobo77bobo$10b2o78b2o10$89bo$10bo5bo73b2o4bo$11bo5bo71b2o6bo
$9b3o3b3o77b3o4$34bo79bo$35bo79bo$33b3o77b3o2$34bo79bo$34b2o78b2o$33bo
bo77bobo6$37b2o66bo11b2o$36bobo67bo9bobo$35bobo66b3o8bobo$35b2o78b2o$
107b2o$28b2o76bobo$28b2o78bo19$7bo78b3o$7b2o43bo35bo43bo$6bobo42b2o34b
o43b2o$51bobo77bobo2$12b2o78b2o$11bobo77bobo$13bo79bo38$34b3o77b3o$34b
o2bo76bo2bo$29bo4bo73b3o3bo$28b3o3bo72bo2bo3bo$28bob2o2bo75bo3bo$29b3o
2bo75bo3bo$29b2o3bo72bobo4bo$34bo79bo$34bo79bo$35bo79bo30$11bo79bo79bo
79bo79bo79bo79bo79bo$9bobo77bobo77bobo77bobo77bobo77bobo77bobo77bobo$
10b2o78b2o78b2o78b2o78b2o78b2o78b2o78b2o8$10bo158bo$11bo158b2o157bo$9b
3o157b2o78bo80bo78bo$16bo73bo5bo79bo73b2o4bo71b3o5bo73bo5bo72bo6bo72bo
bo4bo$17bo73bo5bo79bo71b2o6bo79bo70b3o6bo72bo6bo72b2o5bo$15b3o71b3o3b
3o77b3o77b3o77b3o77b3o70b3o4b3o72bo4b3o4$34bo79bo79bo79bo79bo79bo79bo
79bo$35bo79bo79bo79bo79bo79bo79bo79bo$33b3o77b3o77b3o77b3o77b3o77b3o
77b3o77b3o2$34bo79bo79bo79bo79bo79bo79bo79bo$34b2o78b2o78b2o78b2o78b2o
78b2o78b2o78b2o$33bobo77bobo77bobo77bobo77bobo77bobo77bobo77bobo5$29bo
159bo$30bo6b2o78b2o71bo6b2o78b2o69bo8b2o78b2o78b2o78b2o$28b3o5bobo77bo
bo69b3o5bobo70bo6bobo70bo6bobo69bo7bobo77bobo70bo6bobo$35bobo77bobo77b
obo72bo4bobo69b3o5bobo71bo5bobo70bo6bobo72bo4bobo$30bo4b2o78b2o73bo4b
2o71b3o4b2o78b2o70b3o5b2o72bo5b2o71b3o4b2o$29b2o158b2o158bo157b3o$29bo
bo76b2o79bobo78bo77b2o79bo160bo$107bobo159b2o77bobo77b2o79bo79b2o$107b
2o160bobo156bobo77b2o79bobo$508bobo14$6b2o158b2o$7b2o156bobo157b2o$6bo
160bo78b2o78b2o77b2o159b3o$245bobo77bo80b2o77b2o81bo$52bo34b2o43bo79bo
34bo44bo79bo32bo46bo33b2o44bo34bo5b2o$51b2o33bobo42b2o78b2o78b2o78b2o
78b2o32bo45b2o39bobo$51bobo34bo42bobo77bobo77bobo77bobo77bobo77bobo40b
o2$12b2o78b2o78b2o78b2o78b2o78b2o78b2o119b2o$11bobo77bobo77bobo77bobo
77bobo77bobo77bobo118b2o$13bo79bo79bo79bo79bo79bo79bo78b3o39bo$574bo$
573bo35$29bo$28b3o3b3o77b3o71b3o3b3o77b3o71bo5b3o77b3o77b3o77b3o$28bob
2o2bo2bo76bo2bo69bo2bo3bo2bo76bo2bo69b3o4bo2bo70bo5bo2bo76bo2bo70b3o3b
o2bo$29b3o2bo74bo4bo75bo3bo73b3o3bo72bob2o3bo72b3o4bo73bo5bo73bo2bo2bo
$29b3o2bo73b3o3bo71bo3bo3bo72bo2bo3bo73b3o3bo72bob2o3bo72b3o4bo73bo5bo
$29b2o3bo73bob2o2bo75bo3bo75bo3bo73b3o3bo73b3o3bo72bob2o3bo73bo3bobo$
34bo74b3o2bo72bobo4bo71bo3bo3bo73b2o4bo73b3o3bo73b3o3bo73bo5bo$34bo74b
3o2bo79bo75bo3bo79bo73b2o4bo73b3o3bo74bobo2bo$34bo74b2o3bo79bo72bobo4b
o79bo79bo73b2o4bo79bo$34bo79bo79bo79bo79bo79bo79bo79bo$35bo79bo79bo79b
o79bo79bo79bo79bo40$11bo79bo79bo79bo79bo79bo79bo$9bobo77bobo77bobo77bo
bo77bobo77bobo77bobo$10b2o78b2o78b2o78b2o78b2o78b2o78b2o8$10bo158bo$
11bo158b2o157bo$9b3o157b2o78bo80bo78bo$16bo73bo5bo79bo73b2o4bo71b3o5bo
73bo5bo72bo6bo$17bo73bo5bo79bo71b2o6bo79bo70b3o6bo72bo6bo$15b3o71b3o3b
3o77b3o77b3o77b3o77b3o70b3o4b3o$6bo157bobo$4bobo158b2o80bo77bo$5b2o
158bo82b2o73bobo79bo81bo$34bo51bo27bo79bo52b2o25bo49b2o28bo48bobo28bo
53bo25bo$35bo48bobo28bo79bo79bo79bo48b2o29bo50b3o26bo$33b3o49b2o26b3o
77b3o77b3o77b3o77b3o77b3o2$34bo79bo79bo79bo79bo79bo79bo$34b2o78b2o78b
2o78b2o78b2o78b2o78b2o$33bobo77bobo77bobo77bobo77bobo77bobo77bobo6$37b
2o78b2o78b2o78b2o78b2o78b2o78b2o$36bobo77bobo77bobo77bobo77bobo77bobo
77bobo$35bobo77bobo77bobo77bobo77bobo77bobo77bobo$27bobo5b2o78b2o70bob
o5b2o78b2o78b2o78b2o78b2o$28b2o158b2o156bobo$28bo159bo81b2o75b2o77bobo
$107bobo160bo76bo79b2o80b2o$27b2o79b2o77b2o82b3o153bo81bo$26bobo79bo
77bobo84bo72b2o162b3o$28bo159bo156bobo78b2o84bo$107b2o238bo77bobo$106b
obo318bo$108bo5$252b2o$251bobo237b2o$253bo238b2o$491bo3$b2o158bo$obo4b
o153b2o157b2o$2bo4b2o151bobo3b3o150bobo4bo73b2o$6bobo43bo28b2o49bo35bo
43bo79bo28bo4b2o44bo26bobo4bo45bo79bo$51b2o27bobo4bo43b2o34bo43b2o78b
2o32bobo43b2o28bo4b2o43b2o78b2o$51bobo28bo4b2o42bobo77bobo77bobo77bobo
31bobo43bobo77bobo$86bobo$12b2o78b2o78b2o78b2o78b2o78b2o78b2o$11bobo
77bobo39bo37bobo77bobo77bobo77bobo77bobo$13bo79bo38b2o39bo79bo79bo79bo
79bo$132bobo36$29bo$28b3o3b3o77b3o71b3o3b3o77b3o71bo5b3o77b3o77b3o$28b
ob2o2bo2bo76bo2bo69bo2bo3bo2bo76bo2bo69b3o4bo2bo70bo5bo2bo76bo2bo$29b
3o2bo74bo4bo75bo3bo73b3o3bo72bob2o3bo72b3o4bo73bo5bo$29b3o2bo73b3o3bo
71bo3bo3bo72bo2bo3bo73b3o3bo72bob2o3bo72b3o4bo$29b3o2bo73bob2o2bo71bo
3bo3bo75bo3bo73b3o3bo73b3o3bo72bob2o3bo$29b2o3bo74b3o2bo75bo3bo71bo3bo
3bo73b3o3bo73b3o3bo73b3o3bo$34bo74b3o2bo72bobo4bo71bo3bo3bo73b2o4bo73b
3o3bo73b3o3bo$34bo74b3o2bo79bo75bo3bo79bo73b2o4bo73b3o3bo$34bo74b2o3bo
79bo72bobo4bo79bo79bo73b2o4bo$35bo79bo79bo79bo79bo79bo79bo!

All but three (MWSS1, MWSS 8, and HWSS1) right-hand escorts can be synthesized using the long ship method:

Code: Select all

x = 596, y = 401, rule = B3/S23
2bo79bo$obo77bobo$b2o78b2o9$131bobo$51bo79b2o$7bo43bobo33bo44bo$8bo42b
2o35bo$6b3o77b3o4$25bo79bo$26bo79bo$24b3o77b3o2$25bo79bo$25b2o78b2o$
24bobo77bobo6$28b2o78b2o$27bobo77bobo$26bobo77bobo$26b2o78b2o4b2o$32b
2o78b2o$32b2o19$134b2o$54b2o78bobo$43bo9b2o68bo10bo$42b2o11bo66b2o$42b
obo77bobo2$3b2o78b2o$2bobo77bobo$4bo79bo38$25b3o77b3o$25bo2bo76bo2bo$
25bo6bo72bo5b3o$25bo5b3o71bo4bo2bo$25bo5bob2o70bo7bo$25bo6b3o70bo7bo$
25bo6b2o71bo4bobo$25bo79bo3bo$25bo3bo75bo$26bobo77bobo30$82bo79bo79bo
79bo79bo79bo$80bobo77bobo77bobo77bobo77bobo77bobo$81b2o78b2o78b2o78b2o
78b2o78b2o8$372bo$372bobo77bo$131bo78bobo159b2o78bobo77bo$87bo43bobo
33bo42b2o35bo79bo79bo44b2o33bo44bobo$88bo42b2o35bo42bo36bo41bobo35bo
79bo79bo43b2o$86b3o77b3o77b3o41b2o34b3o77b3o77b3o$291bo3$105bo79bo79bo
79bo79bo79bo$106bo79bo79bo79bo79bo79bo$104b3o77b3o77b3o77b3o77b3o77b3o
2$105bo79bo79bo79bo79bo79bo$105b2o78b2o78b2o78b2o78b2o78b2o$104bobo77b
obo77bobo77bobo77bobo77bobo6$108b2o78b2o78b2o78b2o78b2o78b2o$107bobo
77bobo77bobo77bobo77bobo77bobo$106bobo77bobo77bobo77bobo4b2o71bobo77bo
bo$106b2o78b2o4b2o72b2o78b2o4bobo71b2o5b2o71b2o$112b2o77bobo159bo78bob
o78b2o$111bobo78bo79b2o159bo78bobo$112bo158bobo239bo$272bo15$376bo$
213b3o159b2o79bo$135bo77bo161bobo77b2o79bo$134b2o78bo78b3o159bobo77b2o
$123bo10bobo66bo79bo9bo69bo79bo79bo11bobo$122b2o78b2o78b2o10bo67b2o78b
2o78b2o$122bobo77bobo77bobo77bobo77bobo77bobo2$83b2o78b2o78b2o78b2o78b
2o78b2o$82bobo77bobo77bobo77bobo77bobo77bobo$84bo79bo79bo79bo79bo79bo
37$32bo$25b3o3b3o71b3o77b3o3b3o71b3o77b3o5bo71b3o77b3o77b3o$25bo2bo2bo
b2o70bo2bo76bo2bobo2bo71bo2bo76bo2bo3b3o70bo2bo4bo71bo2bo76bo2bo2b3o$
25bo6b3o70bo6bo72bo7bo71bo5b3o71bo6bob2o69bo6b3o70bo7bo71bo5bo2bo$25bo
3bo2b3o70bo5b3o71bo7bo71bo4bo2bo71bo7b3o69bo3bo2bob2o69bo3bo2b3o70bo5b
o$25bo6b2o71bo5bob2o70bo7bo71bo7bo71bo7b3o69bo7b3o69bo3bo2bob2o69bo5bo
3bo$25bo79bo6b3o70bo4bobo72bo7bo71bo7b2o70bo7b3o69bo7b3o69bo2bo2bo$25b
o79bo3bo2b3o70bo3bo75bo7bo71bo3bo75bo7b2o70bo7b3o69bo6bobo$25bo3bo75bo
6b2o71bo3bo75bo4bobo72bo3bo75bo3bo75bo7b2o70bo$25bo79bo3bo75bo79bo79bo
79bo79bo79bo$26bobo77bobo77bobo77bobo77bobo77bobo77bobo77bobo40$82bo
79bo79bo79bo79bo79bo$80bobo77bobo77bobo77bobo77bobo77bobo$81b2o78b2o
78b2o78b2o78b2o78b2o8$372bo$291bobo78bobo77bo$131bo78bobo78b2o79b2o78b
obo77bo$87bo43bobo33bo42b2o35bo44bo34bo79bo44b2o33bo44bobo$88bo42b2o
35bo42bo36bo79bo79bo79bo43b2o$86b3o77b3o77b3o77b3o48bo28b3o77b3o$297bo
78bo80bo$136bo75bobo80b2o79b3o77bo80bo$135bo76b2o82b2o158b3o77bo$105bo
29b3o47bo27bo51bo79bo79bo79bo30b3o$106bo79bo79bo79bo79bo79bo$104b3o77b
3o77b3o77b3o77b3o77b3o2$105bo79bo79bo79bo79bo79bo$105b2o78b2o78b2o78b
2o78b2o78b2o$104bobo77bobo77bobo77bobo77bobo77bobo6$108b2o78b2o78b2o
78b2o78b2o78b2o$107bobo77bobo77bobo77bobo77bobo77bobo$106bobo77bobo77b
obo77bobo4b2o71bobo77bobo$106b2o78b2o78b2o4b2o72b2o4bo2bo70b2o5b2o71b
2o$112b2o157bo2bo77bo2bo76bo2bo77b2o$111bo2bo156bo2bo78b2o77bo2bo76bo
2bo$111bo2bo73bo83b2o159b2o77bo2bo$112b2o73bo325b2o$187b3o2$186bo$185b
2o$185bobo4$197b3o$197bo$198bo6$380b3o$300b2o73b2o3bo79b3o$123bo15b3o
61bo79bo10b2o3b2o62bo10b2o5bo61bo11b2o3bo62bo16b3o$122b2o10b2o3bo62b2o
78b2o10bobo4bo60b2o12bo65b2o10b2o5bo60b2o11b2o3bo$122bobo8b2o5bo61bobo
77bobo9bo67bobo77bobo11bo65bobo9b2o5bo$135bo400bo$83b2o78b2o78b2o78b2o
78b2o78b2o$82bobo77bobo77bobo77bobo77bobo77bobo$84bo79bo79bo79bo79bo
79bo37$32bo$25b3o3b3o71b3o77b3o3b3o71b3o77b3o5bo71b3o77b3o$25bo2bo2bob
2o70bo2bo76bo2bobo2bo71bo2bo76bo2bo3b3o70bo2bo4bo71bo2bo$25bo6b3o70bo
6bo72bo7bo71bo5b3o71bo6bob2o69bo6b3o70bo7bo$25bo6b3o70bo5b3o71bo7bo71b
o4bo2bo71bo7b3o69bo3bo2bob2o69bo3bo2b3o$25bo6b3o70bo5bob2o70bo7bo71bo
7bo71bo7b3o69bo7b3o69bo3bo2bob2o$25bo6b2o71bo6b3o70bo7bo71bo7bo71bo7b
3o69bo7b3o69bo7b3o$25bo79bo6b3o70bo4bobo72bo7bo71bo7b2o70bo7b3o69bo7b
3o$25bo79bo6b3o70bo3bo75bo7bo71bo3bo75bo7b2o70bo7b3o$25bo79bo6b2o71bo
79bo3b2obo72bo79bo79bo3bo3b2o$26bobo77bobo77bobo77bobo77bobo77bobo77bo
bo!

Notice that the left-hand HWSS3 synthesis is incompatible with the right-hand syntheses for both HWSS4 and HWSS7, but the ships that use these escorts can by constructed by synthesizing HWSS3 on the right-hand side and HWSS4 or HWSS7 on the left-hand side. This means that we can use the long ship method to synthesize all 9WSS flotillas where the escorts are not both in the set {MWSS1, MWSS8, HWSS1}.

For 9WSS flotillas where the escorts are both in the set {MWSS1, MWSS8, HWSS1}, we can use a new snake-activated method discovered by myself:

Code: Select all

x = 51, y = 63, rule = B3/S23
6bo$7bo$5b3o23$26b2o$27bo$26bo$26b2o18bobo$46b2o$47bo2$30bo$29bobo$29b
obo$30bo15$4b2o$5b2o$4bo$48b3o$48bo$5b2o42bo$4bobo$6bo2$20b2o$b2o18b2o
$obo17bo$2bo!

This method allows each of these escorts to be synthesized on both the left-hand and right-hand sides:

Code: Select all

x = 292, y = 304, rule = B3/S23
9bobo45bo61bobo107bobo$10b2o45bobo60b2o108b2o59bo$10bo46b2o61bo47bo61b
o58b2o$166b2o108bo13b2o$167b2o107bobo$276b2o3$282bo$282bobo$282b2o10$
153bo$154bo21bobo$152b3o21b2o$177bo$30b2o5b2o101b2o108b2o$31bo4bobo
102bo109bo$30bo6bo102bo6b2o101bo6b2o$30b2o18bo89b2o4bobo11bo89b2o5bo
12bo$50bobo94bo12bobo95bo11bobo$50b2o108b2o97bobo8b2o$260b2o$34bo109bo
109bo$33bobo107bobo107bobo$33bobo107bobo107bobo$34bo109bo109bo11$61bo$
60b2o$60bobo2$8b3o107b3o107b3o$10bo109bo109bo$9bo43bo65bo43bo65bo43bo$
52b2o108b2o108b2o$52bobo107bobo107bobo$9b2o108b2o108b2o$10b2o108b2o
108b2o$9bo109bo109bo2$24b3o107b3o107b3o$5b2o19bo109bo88b2o19bo$6b2o17b
o109bo90b2o17bo$5bo219bo17$195b2o$195bobo$195bo23$37bo219bo$30b3o3b3o
101b3o107b3o3b3o$30bo2bo2bob2o100bo2bo2b3o101bo2bo2bob2o$30bo6b3o100bo
5bo2bo100bo6b3o$30bo3bo2b3o100bo5bo103bo6b3o$30bo6b2o101bo5bo3bo99bo6b
3o$30bo109bo2bo2bo103bo6b2o$30bo109bo6bobo100bo$30bo3bo105bo109bo$30bo
109bo109bo$31bobo107bobo107bobo75$4bo219bo$5bo219bo$3b3o3bobo107bobo
101b3o3bobo$10b2o101bobo4b2o108b2o$10bo103b2o4bo109bo$114bo$220bo$218b
obo$219b2o17$24b2o218b2o$24bobo3b2o108b2o101bo2bo3b2o$25bo5bo102b2o5bo
101bo2bo4bo$30bo103bobo3bo103b2o4bo$30b2o18bo84bo4b2o18bo89b2o18bo$50b
obo107bobo107bobo$50b2o108b2o108b2o2$34bo109bo109bo$33bobo107bobo107bo
bo$33bobo107bobo107bobo$34bo109bo109bo11$2o$b2o212b2o$o109b3o101bobo4b
o$112bo103bo4b2o$8b3o100bo6b3o99bobo5b3o$10bo109bo109bo$9bo43bo65bo43b
o65bo43bo$52b2o108b2o108b2o$52bobo107bobo107bobo$9b2o108b2o108b2o$10b
2o108b2o108b2o$9bo109bo109bo2$24b3o107b3o107b3o$5b2o19bo88b2o19bo88b2o
19bo$6b2o17bo90b2o17bo90b2o17bo$5bo109bo109bo42$25bo219bo$24b3o3b3o
107b3o101b3o3b3o$24bob2o2bo2bo100b3o3bo2bo100bob2o2bo2bo$25b3o2bo103bo
2bo2bo104b3o2bo$25b3o2bo103bo5bo104b3o2bo$25b2o3bo103bo3bobo104b3o2bo$
30bo103bo5bo104b2o3bo$30bo104bobo2bo109bo$30bo109bo109bo$30bo109bo109b
o$31bo109bo109bo!

Notice that the right-hand MWSS8 synthesis has slightly different cleanup than the other escort syntheses. This cleanup can be substituted into the cleanup left-hand syntheses when necessary without any compatibility problems.

As with the 7WSS and 8WSS flotillas, smaller syntheses may be possible with alternate methods. I only know of one other 9WSS synthesis which is cheaper overall, but allows far fewer escorts to be synthesized on the left-hand side:

Code: Select all

x = 11, y = 16, rule = B3/S23
4bobo$5b2o$5bo3$6b2o$6bobo$7bo$b3o$3bo$2bo$8b3o$8bo$b2o6bo$obo$2bo!

Re: OWSS synthesis project

Posted: July 21st, 2025, 7:36 pm

by Sokwe

10WSS syntheses
All simple 10WSS flotillas can be synthesized. In this case there are 16 escorts:

Code: Select all

#C 16 Possible escorts for 10WSS (LWSS1-2, MWSS1-6, HWSS1-8)
x = 221, y = 51, rule = B3/S23
3o27b3o$o2bo26bo2bo$o6bo22bo5b3o$o5b3o21bo4bo2bo$o5bob2o20bo7bo$o6b3o
20bo7bo$o6b2o21bo4bobo$o29bo3bo$o29bo3bo$o29bo$bobo27bobo9$7bo$3o3b3o
21b3o27b3o27b3o27b3o27b3o$o2bo2bob2o20bo2bo26bo2bo26bo2bo4bo21bo2bo26b
o2bo2b3o$o6b3o20bo6bo22bo5b3o21bo6b3o20bo7bo21bo5bo2bo$o3bo2b3o20bo5b
3o21bo4bo2bo21bo3bo2bob2o19bo3bo2b3o20bo5bo$o6b2o21bo5bob2o20bo7bo21bo
7b3o19bo3bo2bob2o19bo5bo3bo$o29bo6b3o20bo7bo21bo7b3o19bo7b3o19bo2bo2bo
$o29bo3bo2b3o20bo7bo21bo7b2o20bo7b3o19bo6bobo$o3bo25bo6b2o21bo4bobo22b
o3bo25bo7b2o20bo$o3bo25bo29bo3bo25bo3bo25bo3bo25bo3bo$o29bo3bo25bo29bo
29bo29bo$bobo27bobo27bobo27bobo27bobo27bobo9$7bo$3o3b3o21b3o27b3o3b3o
21b3o27b3o5bo21b3o27b3o27b3o$o2bo2bob2o20bo2bo26bo2bobo2bo21bo2bo26bo
2bo3b3o20bo2bo4bo21bo2bo26bo2bo2b3o$o6b3o20bo6bo22bo7bo21bo5b3o21bo6bo
b2o19bo6b3o20bo7bo21bo5bo2bo$o6b3o20bo5b3o21bo7bo21bo4bo2bo21bo7b3o19b
o3bo2bob2o19bo3bo2b3o20bo5bo$o6b3o20bo5bob2o20bo7bo21bo7bo21bo7b3o19bo
7b3o19bo3bo2bob2o19bo5bo3bo$o6b2o21bo6b3o20bo7bo21bo7bo21bo7b3o19bo7b
3o19bo7b3o19bo2bo2bo3bo$o29bo6b3o20bo4bobo22bo7bo21bo7b2o20bo7b3o19bo
7b3o19bo2bo2bo$o29bo6b3o20bo3bo25bo7bo21bo3bo25bo7b2o20bo7b3o19bo6bobo
$o3bo25bo6b2o21bo3bo25bo4bobo22bo3bo25bo3bo25bo7b2o20bo$o29bo3bo25bo
29bo29bo29bo29bo29bo$bobo27bobo27bobo27bobo27bobo27bobo27bobo27bobo!

We again primarily use the long ship method:

Code: Select all

x = 108, y = 84, rule = B3/S23
2bo59bo$obo57bobo$b2o58b2o11$7bo59bo$8bo59bo$6b3o57b3o4$25bo59bo$26bo
59bo$24b3o57b3o2$25bo59bo$25b2o58b2o$24bobo57bobo6$28b2o58b2o$27bobo
57bobo$26bobo57bobo$26b2o58b2o4$29b2o58b2o$29b2o58b2o18$64b2o$63bobo$
40b3o22bo$40bo64b2o$41bo63bobo$6bo98bo$6b2o$5bobo2$38bo$37b2o66b2o$37b
obo64b2o$106bo10$81b3o$81bo2bo$81bo$81bo$82bobo!

All left-hand escorts for the 10WSS can be synthesized using the long ship method:

Code: Select all

x = 678, y = 402, rule = B3/S23
5bo79bo$3bobo77bobo$4b2o78b2o10$83bo$4bo5bo73b2o4bo$5bo5bo71b2o6bo$3b
3o3b3o77b3o4$28bo79bo$29bo79bo$27b3o77b3o2$28bo79bo$28b2o78b2o$27bobo
77bobo6$31b2o66bo11b2o$30bobo67bo9bobo$29bobo66b3o8bobo$29b2o78b2o$
101b2o$22b2o76bobo$22b2o78bo$32b2o78b2o$32b2o78b2o17$bo78b3o$b2o4b2o
73bo4b2o$obo3bobo72bo4bobo$8bo79bo$128b2o$46bo81bobo$4b3o38b2o81bo$6bo
38bobo$5bo3$128b2o$46b2o79b2o$45b2o82bo$47bo9$104b3o$104bo2bo$104bo$
104bo$105bobo18$28b3o77b3o$28bo2bo76bo2bo$23bo4bo73b3o3bo$22b3o3bo72bo
2bo3bo$22bob2o2bo75bo3bo$23b3o2bo75bo3bo$23b2o3bo72bobo4bo$28bo79bo$
28bo79bo$28bo79bo$29bo79bo14$314bo$315b2o$314b2o13$5bo79bo79bo79bo79bo
79bo$3bobo77bobo77bobo77bobo77bobo77bobo$4b2o78b2o78b2o78b2o78b2o78b2o
8$4bo$5bo$3b3o157bo79bo79bo$10bo73bo5bo73b2o4bo73bo5bo73bo5bo72bobo4bo
$11bo73bo5bo71b2o6bo70b3o6bo70b3o6bo72b2o5bo$9b3o71b3o3b3o77b3o77b3o
77b3o72bo4b3o3$319bo$28bo79bo79bo79bo48bobo28bo79bo$29bo79bo79bo79bo
48b2o29bo79bo$27b3o77b3o77b3o77b3o77b3o77b3o$302b3o8b2o$28bo79bo79bo
79bo35bo9b2o32bo79bo$28b2o78b2o78b2o78b2o33bo9bo34b2o78b2o$27bobo77bob
o77bobo77bobo77bobo77bobo5$23bo$24bo6b2o78b2o78b2o78b2o78b2o78b2o$22b
3o5bobo77bobo70bo6bobo69bo7bobo77bobo70bo6bobo$29bobo77bobo72bo4bobo
71bo5bobo77bobo72bo4bobo$24bo4b2o78b2o71b3o4b2o70b3o5b2o78b2o71b3o4b2o
$23b2o$23bobo76b2o80bo78bo76bobo81bo$101bobo79b2o77b2o77b2o80b2o$32b2o
67b2o9b2o69bobo6b2o68bobo7b2o67bo10b2o69bobo6b2o$32b2o78b2o78b2o78b2o
78b2o78b2o$340b2o$339bobo$341bo11$2o$b2o$o159b2o77b2o159b3o$159bobo78b
2o72b2o86bo$7b2o72b2o4b2o72bo77bo7b2o64bobo4bo80bo5b2o$6bobo71bobo3bob
o157bobo66bo4b2o84bobo$8bo73bo5bo114b3o42bo70bobo41b3o42bo$48b2o78b2o
73bo84b2o73bo$48bobo77bobo73bo83bobo73bo81bo$48bo79bo40bo118bo40bo115b
2o$169b2o158b2o114bobo$168bobo157bobo2$201bo159bo$48b2o78b2o70b2o86b2o
70b2o$47b2o78b2o71bobo84b2o71bobo$49bo79bo159bo10$24b3o77b3o157b3o$24b
o2bo76bo2bo156bo2bo$24bo79bo159bo$24bo79bo159bo$25bobo77bobo157bobo17$
23bo$22b3o3b3o77b3o77b3o77b3o77b3o77b3o$22bob2o2bo2bo76bo2bo76bo2bo70b
o5bo2bo76bo2bo70b3o3bo2bo75bo$23b3o2bo74bo4bo73b3o3bo72b3o4bo73bo5bo
73bo2bo2bo79b2o5bo$23b3o2bo73b3o3bo72bo2bo3bo72bob2o3bo72b3o4bo73bo5bo
78b2o7bo$23b2o3bo73bob2o2bo75bo3bo73b3o3bo72bob2o3bo73bo3bobo85b3o$28b
o74b3o2bo71bo3bo3bo73b3o3bo73b3o3bo73bo5bo$28bo74b3o2bo75bo3bo73b2o4bo
73b3o3bo74bobo2bo$28bo74b2o3bo72bobo4bo79bo73b2o4bo79bo$28bo79bo79bo
79bo79bo79bo$28bo79bo79bo79bo79bo79bo$29bo79bo79bo79bo79bo79bo2$520bo$
521bo$519b3o20$534bo$535b2o$534b2o9$476bo2bo$480bo$476bo3bo$477b4o134b
o$5bo78bo20bo79bo79bo79bo79bo119bo70bo18bo$3bobo79b2o5bo10bobo77bobo
77bobo77bobo77bobo117bobo68b3o4bobo9bobo$4b2o78b2o7bo10b2o78b2o78b2o
78b2o78b2o118b2o76b2o10b2o$91b3o528bo7$4bo178bo$5bo91bo86b2o157bo282bo
bo$3b3o92bo84b2o78bo80bo78bo119bo83b2o$10bo85b3o5bo5bo79bo73b2o4bo71b
3o5bo73bo5bo113bo5bo76bo5bobo4bo$11bo93bo5bo79bo71b2o6bo79bo70b3o6bo
110b3o6bo82b2o5bo$2bo6b3o91b3o3b3o69bo7b3o77b3o77b3o77b3o117b3o82bo4b
3o$3bo178b2o157bo$b3o177b2o78bo80bo$262b2o76b3o76bo119bo$28bo99bo79bo
52b2o25bo79bo48bobo28bo88bobo28bo89bo$29bo99bo79bo79bo79bo48b2o29bo88b
2o29bo89bo$27b3o97b3o77b3o77b3o77b3o77b3o117b3o87b3o$522b3o8b2o$28bo
99bo79bo79bo79bo79bo75bo9b2o32bo89bo$28b2o98b2o78b2o78b2o78b2o78b2o73b
o9bo34b2o88b2o$27bobo97bobo77bobo77bobo77bobo77bobo117bobo87bobo2$16bo
177bobo$14bobo52bo2bo122b2o405b2o$15b2o56bo121bo404b2ob2o$69bo3bo526b
4o$31b2o37b4o57b2o78b2o78b2o78b2o78b2o118b2o28b2o58b2o$30bobo97bobo77b
obo77bobo77bobo77bobo117bobo80bo6bobo$29bobo97bobo77bobo77bobo77bobo
77bobo117bobo82bo4bobo$29b2o98b2o78b2o78b2o78b2o78b2o118b2o81b3o4b2o2$
122b2o316bobo117bobo91bo$121bobo317b2o118b2o90b2o$32b2o87b2o9b2o78b2o
78b2o78b2o67bo10b2o107bo10b2o79bobo6b2o$32b2o98b2o78b2o78b2o78b2o78b2o
118b2o88b2o$440b2o76b2o40b2o$439bobo77b2o38bobo$441bo76bo42bo10$380bo$
379b2o$300b3o76bobo$37b3o178b2o80bo324b3o2b3o$37bo57b2o120b2o82bo112b
2o118b2o91bo4bo$7b2o29bo57b2o3b2o4b2o110bo193bobo4bo112bobo4bo85bo4bo
5b2o$6bobo86bo4bobo3bobo306bo4b2o113bo4b2o94bobo$8bo93bo5bo114b3o77b3o
77b3o33bobo41b3o73bobo41b3o52bo$48b2o98b2o73bo79bo79bo79bo119bo$48bobo
97bobo73bo79bo79bo79bo119bo91bo$48bo99bo40bo79bo79bo79bo119bo125b2o$
189b2o78b2o78b2o78b2o118b2o124bobo$188bobo77bobo77bobo77bobo117bobo2$
221bo79bo79bo79bo119bo$48b2o98b2o70b2o78b2o78b2o78b2o118b2o$47b2o98b2o
71bobo77bobo77bobo77bobo117bobo$49bo99bo10$24b3o97b3o$24bo2bo96bo2bo$
24bo99bo$24bo99bo$25bobo97bobo17$23bo$22b3o3b3o97b3o71b3o3b3o77b3o71bo
5b3o77b3o117b3o87b3o$22bob2o2bo2bo96bo2bo69bo2bo3bo2bo76bo2bo69b3o4bo
2bo70bo5bo2bo116bo2bo80b3o3bo2bo$23b3o2bo94bo4bo75bo3bo73b3o3bo72bob2o
3bo72b3o4bo113bo5bo83bo2bo2bo$23b3o2bo93b3o3bo71bo3bo3bo72bo2bo3bo73b
3o3bo72bob2o3bo112b3o4bo83bo5bo$23b3o2bo93bob2o2bo71bo3bo3bo75bo3bo73b
3o3bo73b3o3bo112bob2o3bo83bo3bobo$23b2o3bo94b3o2bo75bo3bo71bo3bo3bo73b
3o3bo73b3o3bo113b3o3bo83bo3bobo$28bo94b3o2bo72bobo4bo71bo3bo3bo73b2o4b
o73b3o3bo113b3o3bo83bo5bo$28bo94b3o2bo79bo75bo3bo79bo73b2o4bo113b3o3bo
84bobo2bo$28bo94b2o3bo79bo72bobo4bo79bo79bo113b2o4bo89bo$28bo99bo79bo
79bo79bo79bo119bo89bo$29bo99bo79bo79bo79bo79bo119bo89bo!

Notice that LWSS1 uses a slightly different arrangement of gliders at the back than the other two arrangements presented above. Fortunately, this does not affect compatibility with right-hand escort syntheses.

All but five (MWSS1, MWSS6, HWSS1, HWSS3, and HWSS8) right-hand escorts for the 10WSS can be synthesized using the long ship method:

Code: Select all

x = 666, y = 402, rule = B3/S23
2bo79bo$obo77bobo$b2o78b2o9$131bobo$51bo79b2o$7bo43bobo33bo44bo$8bo42b
2o35bo$6b3o77b3o4$25bo79bo$26bo79bo$24b3o77b3o2$25bo79bo$25b2o78b2o$
24bobo77bobo6$28b2o78b2o$27bobo77bobo$26bobo77bobo$26b2o78b2o4b2o$32b
2o78b2o$32b2o2$29b2o78b2o$29b2o78b2o16$134b2o$54b2o78bobo$53b2o79bo$
55bo$40b3o77b3o$40bo79bo$41bo79bo$6bo79bo$6b2o78b2o$5bobo77bobo2$38bo
79bo$37b2o78b2o$37bobo77bobo33$25b3o77b3o$25bo2bo76bo2bo$25bo6bo72bo5b
3o$25bo5b3o71bo4bo2bo$25bo5bob2o70bo7bo$25bo6b3o70bo7bo$25bo6b2o71bo4b
obo$25bo79bo3bo$25bo79bo3bo$25bo79bo$26bobo77bobo29$82bo79bo79bo79bo$
80bobo77bobo77bobo77bobo$81b2o78b2o78b2o78b2o9$211bobo78bo$131bo79b2o
79bobo77bo$87bo43bobo33bo44bo34bo44b2o33bo44bobo$88bo42b2o35bo79bo79bo
43b2o$86b3o77b3o77b3o77b3o4$105bo79bo79bo79bo$106bo79bo79bo79bo$104b3o
77b3o77b3o77b3o2$105bo79bo79bo79bo$105b2o78b2o78b2o78b2o$104bobo77bobo
77bobo77bobo6$108b2o78b2o78b2o78b2o$107bobo77bobo77bobo77bobo$106bobo
77bobo77bobo77bobo$106b2o78b2o4b2o72b2o5b2o71b2o$112b2o77bobo78bobo78b
2o$112bobo77bo80bo78bobo$113b2o238bo$109b2o78b2o78b2o78b2o$109b2o78b2o
78b2o78b2o15$296bo$214b3o78b2o79bo$134b3o77bo80bobo77b2o$134bo80bo159b
obo$135bo$120b3o77b3o77b3o77b3o$120bo79bo79bo79bo$121bo79bo79bo79bo6b
2o$86bo79bo79bo79bo40b2o$86b2o78b2o78b2o78b2o41bo$85bobo77bobo77bobo
77bobo2$118bo79bo79bo79bo$117b2o78b2o78b2o78b2o$117bobo77bobo77bobo77b
obo32$32bo$25b3o3b3o71b3o77b3o77b3o77b3o77b3o$25bo2bo2bob2o70bo2bo76bo
2bo76bo2bo4bo71bo2bo76bo2bo2b3o$25bo6b3o70bo6bo72bo5b3o71bo6b3o70bo7bo
71bo5bo2bo$25bo3bo2b3o70bo5b3o71bo4bo2bo71bo3bo2bob2o69bo3bo2b3o70bo5b
o$25bo6b2o71bo5bob2o70bo7bo71bo7b3o69bo3bo2bob2o69bo5bo3bo$25bo79bo6b
3o70bo7bo71bo7b3o69bo7b3o69bo2bo2bo$25bo79bo3bo2b3o70bo7bo71bo7b2o70bo
7b3o69bo6bobo$25bo3bo75bo6b2o71bo4bobo72bo3bo75bo7b2o70bo$25bo3bo75bo
79bo3bo75bo79bo3bo75bo3bo$25bo79bo3bo75bo79bo2bo76bo79bo$26bobo77bobo
77bobo77bo79bobo77bobo36$331bo$330bo$150bobo170bobo4b3o268bobo$82bo60b
o6b2o110bo60b2o47bo79bo79bo61bo6b2o$80bobo60bobo5bo108bobo61bo45bobo
77bobo77bobo61bobo5bo$81b2o60b2o116b2o108b2o78b2o78b2o61b2o7$318bobo$
138bo179b2o102bo166bo$138bobo170bobo5bo102bobo77bo86bobo$80bo50bo6b2o
120bo50b2o109b2o78bobo25bo51bo6b2o$81b2o4bo43bobo127b2o4bo44bo64bo79bo
44b2o27b2o4bo44bobo$80b2o6bo42b2o127b2o6bo109bo79bo71b2o6bo43b2o$86b3o
177b3o107b3o48bo28b3o77b3o$426bo80bo$426b3o77bo$506b3o$105bo179bo109bo
79bo79bo$106bo179bo109bo79bo79bo$104b3o177b3o107b3o77b3o77b3o2$105bo
179bo109bo79bo79bo$105b2o178b2o108b2o78b2o78b2o$104bobo177bobo107bobo
77bobo77bobo2$344b2o$163b4o176b2ob2o266b4o$163bo3bo176b4o266bo3bo$163b
o181b2o267bo$108b2o54bo2bo120b2o108b2o78b2o78b2o55bo2bo$100bo6bobo170b
o6bobo107bobo77bobo70bo6bobo$101bo4bobo172bo4bobo107bobo4b2o71bobo72bo
4bobo$99b3o4b2o171b3o4b2o4b2o102b2o4bo2bo70b2o5b2o64b3o4b2o$112b2o177b
obo108bo2bo76bo2bo77b2o$101bo10bobo166bo10bo110b2o77bo2bo65bo10bobo$
100b2o11b2o165b2o201b2o65b2o11bo$100bobo6b2o169bobo6b2o108b2o78b2o69bo
bo6b2o$109b2o178b2o108b2o78bobo77b2o$480bo15$77b2o61bo116b2o55b3o2b3o
108b3o94b2o57bo4bo$76bobo55b3o2b2o115bobo55bo4bo105b2o3bo79b3o13bobo
56b2o3b2o$78bo55bo4bobo116bo56bo4bo103b2o5bo73b2o3bo17bo56bobo2bobo$
135bo290bo77b2o5bo$120b3o177b3o107b3o77b3o13bo63b3o$120bo179bo109bo79b
o79bo$121bo179bo109bo79bo9b3o67bo6b2o$86bo179bo109bo79bo44bo34bo40b2o$
86b2o178b2o108b2o78b2o44bo33b2o41bo$85bobo177bobo107bobo77bobo77bobo2$
118bo179bo109bo79bo79bo$117b2o178b2o108b2o78b2o78b2o$117bobo177bobo
107bobo77bobo77bobo32$32bo$25b3o3b3o71b3o97b3o3b3o71b3o107b3o5bo71b3o
77b3o97b3o$25bo2bo2bob2o70bo2bo96bo2bobo2bo71bo2bo106bo2bo3b3o70bo2bo
4bo71bo2bo96bo2bo2b3o$25bo6b3o70bo6bo92bo7bo71bo5b3o101bo6bob2o69bo6b
3o70bo7bo91bo5bo2bo$25bo6b3o70bo5b3o91bo7bo71bo4bo2bo101bo7b3o69bo3bo
2bob2o69bo3bo2b3o90bo5bo$25bo6b3o70bo5bob2o90bo7bo71bo7bo101bo7b3o69bo
7b3o69bo3bo2bob2o89bo5bo3bo$25bo6b2o71bo6b3o90bo7bo71bo7bo101bo7b3o69b
o7b3o69bo7b3o89bo2bo2bo3bo$25bo79bo6b3o90bo4bobo72bo7bo101bo7b2o70bo7b
3o69bo7b3o89bo2bo2bo$25bo79bo6b3o90bo3bo75bo7bo101bo3bo75bo7b2o70bo7b
3o89bo6bobo$25bo3bo75bo6b2o91bo3bo75bo4bobo102bo3bo75bo3bo75bo7b2o90bo
$25bo79bo3bo95bo79bo109bo79bo79bo99bo$26bobo77bobo97bobo77bobo107bobo
77bobo77bobo97bobo!

Notice that HWSS6 uses a boat near the back in a place where all other escort syntheses use a block. Fortunately, this works with the two 10WSS syntheses given above, as well as the alternate arrangement used in the left-hand synthesis of LWSS1:

Code: Select all

x = 267, y = 84, rule = B3/S23
6bo99bo99bo$4bobo97bobo97bobo$5b2o98b2o98b2o9$56bo99bo99bo$4bo51bobo
45bo51bobo97bobo$5b2o4bo44b2o47b2o4bo44b2o47bo5bo44b2o$4b2o6bo91b2o6bo
93bo5bo$10b3o97b3o91b3o3b3o$61bo99bo99bo$60bo99bo99bo$60b3o97b3o97b3o$
29bo99bo99bo$30bo99bo99bo$28b3o97b3o97b3o2$29bo99bo99bo$29b2o98b2o98b
2o$28bobo97bobo97bobo6$32b2o86bo11b2o98b2o$24bo6bobo87bo9bobo97bobo$
25bo4bobo86b3o8bobo97bobo$23b3o4b2o5b2o91b2o5b2o91b2o5b2o$36bo2bo82b2o
12bo2bo96bo2bo$25bo10bo2bo81bobo12bo2bo83b2o11bo2bo$24b2o11b2o84bo13b
2o84b2o12b2o$24bobo6b2o98b2o98b2o$33bobo97bobo97bobo$34bo99bo99bo15$b
2o$obo61b3o34b3o60b3o35bo61b3o$2bo56b2o3bo38bo4b2o49b2o3bo37b2o4b2o49b
2o3bo$58b2o5bo36bo4bobo48b2o5bo35bobo3bobo48b2o5bo$44b3o13bo48bo50bo
48bo50bo$44bo104b2o$45bo9b3o91bobo3b3o89bo7b3o$10bo44bo93bo5bo49b3o38b
2o7bo$10b2o44bo99bo50bo38bobo7bo$9bobo194bo2$42bo$41b2o106b2o$41bobo
104b2o97b2o$150bo95b2o$248bo9$125b3o$125bo2bo$125bo$125bo$126bobo!

Therefore we can synthesize all simple 10WSS flotillas with the long ship method, except those in which the left-hand and right-hand escorts are both in the set {MWSS1, MWSS6, HWSS1, HWSS3, HWSS8}.

For 10WSS flotillas in which the left-hand and right-hand escorts are both in the set {MWSS1, MWSS6, HWSS1, HWSS3, HWSS8}, we can use a modification of the snake-activated 9WSS synthesis:

Code: Select all

x = 31, y = 34, rule = B3/S23
3bobo$4b2o$4bo9$11b2o$12bo$11bo$11b2o4$17bo$17bo$17bo3$2b3o$4bo$3bo3b
3o$9bo$8bo$3o8b2o$2bo7bobo$bo10bo8b3o$21bo6b2o$22bo5bobo$28bo!

Using the snake method, the escorts MWSS1, MWSS6, HWSS1, HWSS3, and HWSS8 can each be synthesized on both the left-hand and right-hand sides:

Code: Select all

x = 295, y = 207, rule = B3/S23
235bo$236bo$234b3o4bobo$242b2o$242bo7$4bo118bo60bo$5bo118b2o59bo60bobo
$3b3o3bobo57bobo51b2o4bobo51b3o3bobo55b2o10bobo$10b2o51bobo4b2o58b2o
58b2o55bo5bobo4b2o$10bo53b2o4bo59bo59bo63b2o4bo$64bo189bo$118bobo59bo$
119b2o57bobo52b2o$119bo59b2o50b2ob2o$231b4o$232b2o2$11b2o118b2o58b2o$
11bobo3b2o58b2o51bo2bo3b2o51bo2bo3b2o68b2o$12bo5bo52b2o5bo51bo2bo4bo
51bo2bo4bo62b2o5bo$17bo53bobo3bo53b2o4bo53b2o4bo63bobo3bo$17b2o53bo4b
2o58b2o58b2o63bo4b2o4$23bo59bo59bo59bo69bo$2o21bo59bo59bo59bo69bo$b2o
20bo59bo31bo27bo31b2o26bo69bo$o59b3o52b2o57bobo4bo63b3o2b3o$62bo51bobo
3b3o53bo4b2o64bo4bo$8b3o50bo6b3o51bo5b3o49bobo5b3o55bo4bo6b3o$10bo59bo
50bo8bo59bo69bo$9bo3b3o53bo3b3o53bo3b3o53bo3b3o63bo3b3o$15bo59bo59bo
59bo69bo$14bo59bo59bo59bo69bo$6b3o8b2o47b3o8b2o47b3o8b2o47b3o8b2o57b3o
8b2o$8bo7bobo49bo7bobo49bo7bobo49bo7bobo59bo7bobo$7bo10bo8b3o37bo10bo
8b3o37bo10bo8b3o37bo10bo8b3o47bo10bo8b3o$27bo6b2o51bo6b2o51bo6b2o51bo
6b2o61bo6b2o$28bo5bobo51bo5bobo51bo5bobo51bo5bobo61bo5bobo$34bo59bo59b
o59bo69bo29$12bo179bo$11b3o3b3o57b3o51b3o3b3o51b3o3b3o67b3o$11bob2o2bo
2bo50b3o3bo2bo49bo2bo3bo2bo50bob2o2bo2bo60b3o3bo2bo$12b3o2bo53bo2bo2bo
55bo3bo54b3o2bo63bo2bo2bo$12b3o2bo53bo5bo51bo3bo3bo54b3o2bo63bo5bo$12b
2o3bo53bo3bobo51bo3bo3bo54b3o2bo63bo3bobo$17bo53bo5bo55bo3bo54b2o3bo
63bo3bobo$17bo54bobo2bo52bobo4bo59bo63bo5bo$17bo59bo59bo59bo64bobo2bo$
17bo59bo59bo59bo69bo$17bo59bo59bo59bo69bo$18bo59bo59bo59bo69bo36$290bo
$284bo5bobo$282b2o6b2o$283b2o8$9bobo57bobo57bobo19bobo35bobo19bo37bobo
27bo$10b2o58b2o58b2o19b2o37b2o19bobo36b2o25b2o$10bo59bo21bo37bo21bo37b
o20b2o37bo21bo5b2o$30bo59b2o178b2o$30bobo58b2o178b2o$30b2o125bo58bo75b
2o$155b2o58bo75b4o$156b2o57b3o72b2ob2o$291b2o3$17b2o58b2o58b2o5b2o51b
2o5b2o51b2o$18bo59bo59bo4bo2bo51bo4bo2bo51bo$17bo6b2o51bo6b2o51bo5bo2b
o50bo5bo2bo50bo6b2o$17b2o4bobo51b2o4bobo51b2o5b2o51b2o5b2o51b2o4bobo$
24bo59bo179bo3$23bo59bo59bo59bo59bo$23bo59bo59bo59bo59bo$23bo10bo48bo
59bo59bo59bo$33b2o59b2o64b2o57b3o52b2o3b2o$33bobo58bobo57b2o3b2o53b2o
3bo54bobo2bobo$8b3o57b3o23bo33b3o23bobo4bo26b3o22b2o5bo27b3o23bo4bo$
10bo59bo59bo23bo35bo24bo34bo$9bo3b3o53bo3b3o53bo3b3o53bo3b3o53bo3b3o$
15bo59bo59bo59bo59bo$14bo59bo59bo59bo59bo$6b3o8b2o47b3o8b2o47b3o8b2o
47b3o8b2o47b3o8b2o$8bo7bobo49bo7bobo49bo7bobo49bo7bobo49bo7bobo$7bo10b
o8b3o37bo10bo8b3o37bo10bo8b3o37bo10bo8b3o37bo10bo8b3o$27bo6b2o51bo6b2o
51bo6b2o51bo6b2o51bo6b2o$28bo5bobo51bo5bobo51bo5bobo51bo5bobo51bo5bobo
$34bo59bo59bo59bo59bo29$24bo179bo$17b3o3b3o51b3o57b3o3b3o51b3o3b3o51b
3o$17bo2bo2bob2o50bo2bo2b3o51bo2bobo2bo51bo2bo2bob2o50bo2bo2b3o$17bo6b
3o50bo5bo2bo50bo7bo51bo6b3o50bo5bo2bo$17bo3bo2b3o50bo5bo53bo7bo51bo6b
3o50bo5bo$17bo6b2o51bo5bo3bo49bo7bo51bo6b3o50bo5bo3bo$17bo59bo2bo2bo
53bo7bo51bo6b2o51bo2bo2bo3bo$17bo59bo6bobo50bo4bobo52bo59bo2bo2bo$17bo
3bo55bo59bo3bo55bo59bo6bobo$17bo3bo55bo3bo55bo3bo55bo3bo55bo$17bo59bo
59bo59bo59bo$18bobo57bobo57bobo57bobo57bobo!

Re: OWSS synthesis project

Posted: July 21st, 2025, 9:40 pm

by Sokwe

May13 wrote: July 21st, 2025, 8:46 am Synthesised 4 2c/4 spaceships with "sidecar v2" on 7WSS, all in 23G:

Code: Select all

x = 185, y = 256, rule = B3/S23
169bo$168bo$168b3o$140bo$141bo$139b3o2$159bobo$143bo15b2o$136bo4bobo
16bo$137b2o3b2o19bo$136b2o25bobo13bobo$163b2o14b2o$173bo6bo$55bo115b2o
$56bo115b2o$54b3o75bo$130bobo$131b2o4$142bo$140bobo$10bo130b2o$9bo145b
2o$9b3o143b2o$77b2o88b2o$b2o68b2o4b2o76b2o4b2o4b2o$bo69bo83b2o4bo$2bo
69bo89bo$obo9b3o55bobo87bobo$2o10bo57b2o88b2o$13bo127b2o$142b2o$141bo
3$54b3o$56bo$55bo$182b2o$140b3o39bobo$142bo4bo26bo7bo$141bo5b2o24b2o$
146bobo24bobo25$169bo$168bo$168b3o$140bo$141bo$139b3o2$159bobo$143bo
15b2o$136bo4bobo16bo18bobo$137b2o3b2o19bo15b2o$136b2o25bobo14bo$163b2o
$173bo$55bo115b2o$56bo115b2o$54b3o75bo$130bobo$131b2o4$10bo131bo$9bo
130bobo$9b3o129b2o$77b2o76b2o10b2o$77b2o76b2o10b2o2$b2o68b2o82b2o4b2o$
bo10b3o56bo83b2o4bo$2bo9bo59bo89bo$obo10bo56bobo87bobo$2o68b2o88b2o$
141b2o$142b2o$141bo3$54b3o$56bo125b2o$55bo126bobo$182bo$140b3o$142bo4b
o26bo$141bo5b2o24b2o$146bobo24bobo25$169bo$168bo$168b3o$140bo$141bo$
139b3o2$159bobo$143bo15b2o$136bo4bobo16bo$137b2o3b2o19bo$136b2o25bobo
13bobo$163b2o14b2o$173bo6bo$55bo115b2o$56bo115b2o$54b3o75bo$130bobo$
131b2o$10bo$9bo$9b3o$142bo$140bobo$141b2o$155b2o$155b2o$77bo89bo$b2o
68b2o4bo77b2o4b2o4bo$bo8b2o59bo5bo77b2o4bo5bo$2bo7bobo59bo89bo$obo7bo
59bobo87bobo$2o68b2o88b2o$141b2o$142b2o$141bo3$54b3o$56bo$55bo$180bo$
140b3o36b2o$142bo4bo26bo4bobo$141bo5b2o24b2o$146bobo24bobo25$169bo$
168bo$168b3o$140bo$141bo$139b3o2$159bobo$143bo15b2o$136bo4bobo16bo18bo
bo$137b2o3b2o19bo15b2o$136b2o25bobo14bo$163b2o$173bo$55bo115b2o$56bo
115b2o$54b3o75bo$10bo119bobo$9bo121b2o$9b3o3$142bo$140bobo$141b2o$77bo
77b2o10bo$77bo77b2o10bo$10b2o65bo89bo$b2o7bobo58b2o82b2o4b2o$bo8bo60bo
83b2o4bo$2bo69bo89bo$obo67bobo87bobo$2o68b2o88b2o$141b2o$142b2o$141bo
3$54b3o$56bo123bo$55bo123b2o$179bobo$140b3o$142bo4bo26bo$141bo5b2o24b
2o$146bobo24bobo!

Excellent! This can be synthesized opposite to every single standard spaceship escort, as per the 7WSS analysis.

Here is a collection of "sidecars" that are unstable on their own but can mutually support an OWSS (Edit: added some additional supports):

Code: Select all

x = 688, y = 471, rule = B3/S23
314bo39bo$307b3o3b3o31b3o3b3o61b3o4b3o5bo$307bo2bo2bob2o30bo2bo2bob2o
60bo2bo2bo2bo4b3o$307bo6b2o31bo6b3o60bo5b2o2bo3bob2o$307bo3bob3o31bo3b
o2b3o60bo3bob4obo3b3o$308bo3bo5b3o27bo2bo2b3o61bobo8bo2b3o$312bo2bo2bo
2bo31bobo76b2o$314b2o2bo34b3o68bo$313bo4bo3bo31bo69bob2o$312bobo3bo34b
2o$319bobo$312bobo15$283bo$282b3o3b3o$281bo2b2o2bo2bo$284b2o2bo94b3o6b
o152bo6b3o$283bobo2bo93bo2bo5b3o150b3o5bo2bo$277b3o3b2o4bobo85b3o7bo2b
2obo143b3o3b2o2bo2bo4bo$277bo2bobo3bo90bo2bo4bobo2b3o144bo2bo4bo2bobob
o$277bo99bo4b3o5b3o144bo5bo3bobo4b2o$277bo7bo91bo8b2o2b3o144bo5b2o5bo$
277bo4bob2o91bo3bo4b2o3b2o144bo3bo3bo6bo$278bobo2bo94bobo157bobo2bo7bo
25$457b3o12bo$457bo2bo4b3o3b3o$457bo7bo2bo2bob2o$457bo3bo2bo7b3o$457bo
5b4o2bo2b3o$457bo5bo2bo5b2o$458bobob2o$463bo18$283bo$229b3o50b3o3b3o$
229bo2bo48bo2b2o2bo2bo$46bo118bo63bo54b2o2bo$13b3o29b3o116b3o57b3o2bo
53bobo2bo$7b3o3bo2bo20b3o4b2obo79b3o27b3o3b2obo50b3o4bo2bo2bobo14b3o
27b3o3b2o4bobo15b3o37b3o27b3o3b3o6bo$7bo2bo2bob2o20bo2bo3b3o80bo2bo26b
o2bo2bo53bo2bo3bo2bo19bo2bo26bo2bobo3bo20bo2bo36bo2bo26bo2bobo2bo5b3o$
b3o3bo5bo2bo14b3o3bo7b2o74b3o3bo6bo16b3o3bo7b3o43b3o3bo7bo15b3o3bo6bo
16b3o3bo23b3o3bo6bo26b3o3bo6bo16b3o3bo9bo2b2obo$o2bo3bo3bob3o14bo2bo3b
o3bo78bo2bo3bo5b3o14bo2bo3bo4b6o42bo2bo3bo5b2o15bo2bo3bo5b3o14bo2bo3bo
7bo14bo2bo3bo5b3o24bo2bo3bo5b3o14bo2bo3bo7bobo2b3o$3bo3bo4bob2o17bo3bo
5bo79bo3bo4bo2b2o16bo3bo5b2obo46bo3bo4bo4bo15bo3bo4bo2b2o3b3o10bo3bo4b
ob2o17bo3bo5bob2o26bo3bo5bob2o16bo3bo4b3o5b3o$3bo3bo6bo18bo3bo4bobo78b
o3bo4bo2bo17bo3bo4b2o49bo3bo4bo20bo3bo4bobo2bo2bo2bo9bo3bo5bo19bo3bo6b
2o27bo3bo6b3o16bo3bo8b2o2b3o$obo4bo3bobo16bobo4bo7bo74bobo4bo7bo14bobo
4bo52bobo4bo6b2o14bobo4bo5b2o2bo2bo9bobo4bo22bobo4bo3bob3o24bobo4bo3bo
2b3o13bobo4bo3bo4b2o3b2o$8bobo27bobobobo83bobo3b2o22bobo57bobo27bobo3b
o2bo2bo17bobo27bo3bo5b3o27bo2bo2b3o21bobo$43b2o87bobo120bo5bobo48bo2bo
2bo2bo31bobo$42b2o270b2o2bo34b3o$44bo87bobo178bo4bo3bo31bo$42b2o89bo
178bobo3bo34b2o$319bobo$312bobo13$229b3o$229bo2bo$229bo$224b3o2bo282bo
$217b3o4bo2bo2bobo184b3o37b3o12bo24b3o11b3o23b3o$217bo2bo3bo2bo189bo2b
o36bo2bo4b3o3b3o23bo2bo10bob2o22bo2bo4bo6b3o$211b3o3bo7bo185b3o3bo6b3o
5bo18b3o3bo7bo2bo2bob2o16b3o3bo14b3o16b3o3bo6b3o5bo2bo$210bo2bo3bo5b2o
185bo2bo3bo3bobo2bo4b3o16bo2bo3bo3bo2bo7b3o15bo2bo3bo3bo4bo5b2o16bo2bo
3bo5b2o2bo2bo4bo$213bo3bo4bo4bo185bo3bo3bob2o2bo3bob2o18bo3bo5b4o2bo2b
3o18bo3bo3bo3b3o25bo3bo7bo2bobobo$213bo3bo4bo190bo3bo5b4obo3b3o18bo3bo
5bo2bo5b2o19bo3bo5b2obob2o23bo3bo5bo3bobo4b2o$210bobo4bo6b2o184bobo4bo
11bo2b3o15bobo4bo4b2o26bobo4bo5b2obob2o20bobo4bo5b2o5bo$217bo199bo3bo
10b2o23bo5bo33bo6b3ob2o27bo3bo3bo6bo$218bobo197bobo3bo33bobo37bo2b2o2b
o2bo29bobo2bo7bo$424bob2o79bo17$229b3o$72b3o154bo2bo$72bo2bo89bo63bo$
72bo91b3o57b3o2bo$67b3o2bo84b3o3b2obo50b3o4bo2bo2bobo14b3o127b3o37b3o
117b3o37b3o5b3o29b3o$67bo2bo2bobo81bo2bo2bo53bo2bo3bo2bo19bo2bo126bo2b
o36bo2bo116bo2bo36bo2bo4bo2bo28bo2bo$61b3o3bo4b3o76b3o3bo7b3o43b3o3bo
7bo15b3o3bo6bo116b3o3bo5b3o6bo18b3o3bo6b3o5bo98b3o3bo7bo6b3o16b3o3bo7b
o5b3o17b3o3bo10b3o$60bo2bo3bo4bo77bo2bo3bo4b6o42bo2bo3bo5b2o15bo2bo3bo
5b3o114bo2bo3bo4bo2bo5b3o16bo2bo3bo3bobo2bo4b3o96bo2bo3bo3bo2b3o5bo2bo
14bo2bo3bo4bo2bo4bo2bo16bo2bo3bo5bo3bo2bo$63bo3bo5b2o78bo3bo5b2obo46bo
3bo4bo4bo15bo3bo4bo2b2o3b3o110bo3bo9bo2b2obo19bo3bo3bob2o2bo3bob2o98bo
3bo5b2o2bo2bo4bo17bo3bo3b3obo7bo19bo3bo4b3o5bo$63bo3bo2bo82bo3bo4b2o
49bo3bo4bo20bo3bo4bobo2bo2bo2bo109bo3bo7bobo2b3o20bo3bo5b4obo3b3o98bo
3bo7bo2bobobo20bo3bo5b3o7bo19bo3bo3bo2b2o4bo$60bobo4bo82bobo4bo52bobo
4bo6b2o14bobo4bo5b2o2bo2bo109bobo4bo4b3o5b3o17bobo4bo11bo2b3o95bobo4bo
5bo3bobo4b2o14bobo4bo4bo2bo4bobo17bobo4bo3bob2o5bo$67bo89bo59bo29bo6bo
2bo2bo116bo8b2o2b3o24bo14b2o103bo5b2o5bo26bo7bo3bo27bo5bo2bo3bo$67bo
89bo3bo55bo29bo7bo5bobo113bo3bo4b2o3b2o24bo6bo112bo3bo3bo6bo24bo7bo31b
o4b2o3bobo$68bobo87bobo57bobo27bobo127bobo37bobo3bob2o110bobo2bo7bo26b
obo5bobo29bobo17$229b3o$72b3o154bo2bo$72bo2bo89bo63bo$72bo91b3o57b3o2b
o$67b3o2bo84b3o3b2obo20b3o27b3o4bo2bo2bobo14b3o167b3o37b3o12bo104b3o5b
3o59b3o4b3o$67bo2bo2bobo81bo2bo2bo23bo2bo4bo21bo2bo3bo2bo19bo2bo166bo
2bo36bo2bo4b3o3b3o103bo2bo4bo2bo58bo2bo2bo2bo$61b3o3bo4b3o76b3o3bo7b3o
13b3o3bo6b3o14b3o3bo7bo15b3o3bo6bo156b3o3bo6b3o5bo18b3o3bo7bo2bo2bob2o
96b3o3bo7bo5b3o47b3o3bo9bo$60bo2bo3bo4bo77bo2bo3bo4b6o12bo2bo3bo5b2obo
13bo2bo3bo5b2o15bo2bo3bo5b3o154bo2bo3bo3bobo2bo4b3o16bo2bo3bo3bo2bo7b
3o95bo2bo3bo4bo2bo4bo2bo46bo2bo3bo4bo2bobo$63bo3bo5b2o78bo3bo5b2obo16b
o3bo5bo19bo3bo4bo4bo15bo3bo4bo2b2o3b3o150bo3bo3bob2o2bo3bob2o18bo3bo5b
4o2bo2b3o98bo3bo3b3obo7bo49bo3bo3bobobob2o$63bo3bo2bo82bo3bo4b2o19bo3b
o7b3o15bo3bo4bo20bo3bo4bobo2bo2bo2bo149bo3bo5b4obo3b3o18bo3bo5bo2bo5b
2o99bo3bo5b3o7bo49bo3bo3bo2bo2bo$60bobo4bo82bobo4bo22bobo4bo4b6o12bobo
4bo6b2o14bobo4bo5b2o2bo2bo149bobo4bo11bo2b3o15bobo4bo4b2o106bobo4bo4bo
2bo4bobo47bobo4bo4b6o$67bo89bo29bo5b2obo20bo29bo6bo2bo2bo156bo14b2o23b
o5bo113bo7bo3bo57bo3b4ob2o$67bo3bo85bo29bo4b2o23bo3bo25bo3bo3bo5bobo
153bo3bo2bo32bo119bo3bo3bo3bo57bo3bo$67bo89bo29bo29bo29bo169bo6bob2o
29bo119bo7bo61bo$68bobo87bobo27bobo27bobo27bobo167bobo37bobo117bobo5bo
bo59bobo16$229b3o$72b3o154bo2bo$72bo2bo89bo63bo$72bo91b3o57b3o2bo$67b
3o2bo54b3o27b3o3b2obo50b3o4bo2bo2bobo14b3o167b3o37b3o12bo104b3o5b3o$
67bo2bo2bobo51bo2bo26bo2bo2bo53bo2bo3bo2bo19bo2bo166bo2bo36bo2bo4b3o3b
3o103bo2bo4bo2bo$61b3o3bo4b3o46b3o3bo6bo16b3o3bo7b3o43b3o3bo7bo15b3o3b
o6bo156b3o3bo6b3o5bo18b3o3bo7bo2bo2bob2o96b3o3bo7bo5b3o$60bo2bo3bo4bo
47bo2bo3bo5b3o14bo2bo3bo4b6o42bo2bo3bo5b2o15bo2bo3bo5b3o154bo2bo3bo3bo
bo2bo4b3o16bo2bo3bo3bo2bo7b3o95bo2bo3bo4bo2bo4bo2bo$63bo3bo5b2o48bo3bo
4bo2b2o16bo3bo5b2obo46bo3bo4bo4bo15bo3bo4bo2b2o3b3o150bo3bo3bob2o2bo3b
ob2o18bo3bo5b4o2bo2b3o98bo3bo3b3obo7bo$59bo3bo3bo2bo48bo3bo3bo4bo2bo
13bo3bo3bo4b2o45bo3bo3bo4bo16bo3bo3bo4bobo2bo2bo2bo145bo3bo3bo5b4obo3b
3o14bo3bo3bo5bo2bo5b2o95bo3bo3bo5b3o7bo$63bo3bo55bo3bo7bo17bo3bo55bo3b
o6b2o17bo3bo5b2o2bo2bo152bo3bo11bo2b3o18bo3bo4b2o109bo3bo4bo2bo7bo$60b
obo4bo52bobo4bo6b2o14bobo4bo52bobo4bo22bobo4bo6bo2bo2bo149bobo4bo14b2o
16bobo4bo5bo106bobo4bo7bo4bobo$67bo3bo55bo4bobo22bo59bo3bo25bo3bo3bo5b
obo153bo3bo2bo32bo119bo3bo3bo3bo$67bo3bo55bo29bo3bo55bo3bo25bo3bo165bo
3bo2bob2o29bo3bo115bo3bo3bo3bo$67bo59bo4bobo22bo59bo29bo169bo39bo119bo
7bo$68bobo57bobo2bo24bobo57bobo27bobo167bobo37bobo117bobo5bobo16$102b
3o$102bo2bo59bo$102bo61b3o$97b3o2bo54b3o3b2obo20b3o267b3o12bo$97bo2bo
2bobo51bo2bo2bo23bo2bo4bo261bo2bo4b3o3b3o$91b3o3bo4b3o46b3o3bo7b3o13b
3o3bo6b3o254b3o3bo7bo2bo2bob2o$90bo2bo3bo4bo47bo2bo3bo4b6o12bo2bo3bo5b
2obo253bo2bo3bo3bo2bo7b3o$93bo3bo5b2o48bo3bo5b2obo16bo3bo5bo259bo3bo5b
4o2bo2b3o$89bo3bo3bo2bo48bo3bo3bo4b2o15bo3bo3bo7b3o251bo3bo3bo5bo2bo5b
2o$89bo3bo3bo51bo3bo3bo21bo3bo3bo4b6o251bo3bo3bo4b2o$93bo3bo5b3o47bo3b
o25bo3bo5b2obo256bo3bo5bo$90bobo4bo4bo2bo44bobo4bo22bobo4bo4b2o256bobo
4bo$97bo7bo51bo3bo25bo269bo3bo$97bo7bo51bo3bo25bo269bo3bo$97bo3b2obo
52bo29bo3bo265bo$98bobo57bobo27bobo267bobo15$102b3o$102bo2bo$102bo$97b
3o2bo24b3o57b3o$97bo2bo2bobo21bo2bo56bo2bo4bo$92bo4bo4b3o17bo4bo6bo47b
o4bo6b3o$91b3o3bo4bo18b3o3bo5b3o45b3o3bo5b2obo$91bob2o2bo5b2o16bob2o2b
o4bo2b2o44bob2o2bo5bo$92b3o2bo2bo21b3o2bo4bo2bo46b3o2bo7b3o$92b3o2bo
24b3o2bo7bo46b3o2bo4b6o$92b2o3bo5b3o16b2o3bo6b2o46b2o3bo5b2obo$97bo4bo
2bo21bo4bobo52bo4b2o$97bo7bo21bo59bo$97bo7bo21bo4bobo52bo$97bo4bobo22b
o5bo53bo$97bo29bo59bo$98bobo27bobo57bobo14$102b3o$102bo2bo$102bo$97b3o
2bo84b3o$97bo2bo2bobo81bo2bo4bo$92bo4bo4b3o77bo4bo6b3o$91b3o3bo4bo78b
3o3bo5b2obo$91bob2o2bo5b2o76bob2o2bo5bo$92b3o2bo2bo81b3o2bo7b3o$92b3o
2bo84b3o2bo4b6o$92b3o2bo5b3o76b3o2bo5b2obo$92b2o3bo4bo2bo76b2o3bo4b2o$
97bo7bo81bo$97bo7bo81bo$97bo4bobo82bo$97bo3bo85bo3bo$97bo89bo$98bobo
87bobo13$92b3o7b3o$92bo2bo6bo2bo$92bo9bo$92bo4b3o2bo84b3o$93bo3bo2bo2b
obo75bo5bo2bo4bo$97bo4b3o75b3o4bo6b3o$93b5o4bo76b2o2bo3bo5b2obo$94b2ob
o5b2o74b2ob3o2bo5bo$97bo2bo78b2o2b2o2bo7b3o$97bo85b2o2bo4b6o$91b3o3bo
5b3o73b2o6bo5b2obo$90bo2bo3bo4bo2bo78bo2bo4b2o$93bo3bo7bo77bo3bo$93bo
3bo7bo77bo3bo$90bobo4bo4bobo82bo$97bo3bo85bo3bo$97bo3bo85bo3bo$97bo89b
o$98bobo87bobo12$92b3o7b3o$92bo2bo6bo2bo$92bo9bo$92bo4b3o2bo$93bo3bo2b
o2bobo$97bo4b3o$93b5o4bo$94b2obo5b2o$97bo2bo$97bo$91b3o3bo5b3o$90bo2bo
3bo4bo2bo$93bo3bo7bo$89bo3bo3bo7bo$93bo3bo7bo$90bobo4bo4bobo$97bo3bo$
97bo3bo$97bo$98bobo11$92b3o7b3o$92bo2bo6bo2bo$92bo9bo$92bo4b3o2bo574b
3o$93bo3bo2bo2bobo571bo2bo$97bo4b3o567bo4bo6bo$93b5o4bo568b3o3bo5b3o$
94b2obo5b2o565bo2b2o2bo4bo2b2o$97bo2bo569bobo2bobo4b2o2bo$97bo571b2obo
2bobo3bo2bobo$91b3o3bo5b3o564bobo2bobo3bo2bo$90bo2bo3bo4bo2bo568b2obo
9bo$93bo3bo7bo564bo6bo3b2o3bo$89bo3bo3bo7bo568b2obo8bo$89bo3bo3bo7bo
563b2o6bo2bo$93bo3bo7bo571bo7bobo$90bobo4bo4bobo566b2o4bo7b2o$97bo3bo
570b2o3bo3bobo2bo$97bo3bo568bo3bo2bo4bo2bo$97bo576bo2bo6bo$98bobo570bo
2bo3bo4bo$673b2o5b2o$674b2o6bo$674b2o6bo7$92b3o7b3o$92bo2bo6bo2bo$92bo
9bo$92bo4b3o2bo$93bo3bo2bo2bobo$97bo4b3o$93b5o4bo$94b2obo5b2o$97bo2bo$
97bo$92bo4bo6bo$91b3o3bo5b3o$91bob2o2bo5bob2o$92b3o2bo6b3o$92b3o2bo3bo
2b3o$92b2o3bo6b2o$97bo$97bo$97bo3bo$97bo3bo$97bo$98bobo9$92b3o7b3o$92b
o2bo6bo2bo$92bo9bo$92bo4b3o2bo$93bo3bo2bo2bobo$97bo4b3o$93b5o4bo$94b2o
bo5b2o$97bo2bo$97bo$92bo4bo6bo$91b3o3bo5b3o$91bob2o2bo5bob2o$92b3o2bo
6b3o$92b3o2bo6b3o$92b3o2bo6b3o$92b2o3bo6b2o$97bo$97bo$97bo3bo$97bo3bo$
97bo$98bobo!

This includes a 15WSS supported on either side by pushalong 1. On Discord, Mark Niemiec noted that five OWSS escorts can interact with a trailing MWSS like so:

Code: Select all

x = 16, y = 106, rule = B3/S23
bo11bo$3o3b3o3b3o$ob2o2bo2bo2bob2o$b3o2bo6b3o$b3o2bo3bo2b3o$b2o3bo6b2o
$6bo$6bo$6bo5bo$6bo4b3o$7bo3bob2o$12b3o$12b3o$12b2o9$bo11bo$3o3b3o3b3o
$ob2o2bo2bo2bob2o$b3o2bo6b3o$b3o2bo6b3o$b3o2bo6b3o$b2o3bo6b2o$6bo$6bo$
6bo5bo$6bo4b3o$7bo3bob2o$12b3o$12b3o$12b2o9$6b3o$6bo2bo$bo4bo6bo$3o3bo
5b3o$ob2o2bo5bob2o$b3o2bo6b3o$b2o3bo6b2o$6bo$6bo$6bo5bo$6bo4b3o$7bo3bo
b2o$12b3o$12b3o$12b2o8$6b3o$6bo2bo$bo4bo6bo$3o3bo5b3o$ob2o2bo5bob2o$b
3o2bo6b3o$b3o2bo3bo2b3o$b2o3bo6b2o$6bo$6bo$6bo5bo$6bo4b3o$7bo3bob2o$
12b3o$12b3o$12b2o7$6b3o$6bo2bo$bo4bo6bo$3o3bo5b3o$ob2o2bo5bob2o$b3o2bo
6b3o$b3o2bo6b3o$b3o2bo6b3o$b2o3bo6b2o$6bo$6bo$6bo5bo$6bo4b3o$7bo3bob2o
$12b3o$12b3o$12b2o!

I do not know how to synthesize any of these, except the case in the quoted post by May13.

Re: OWSS synthesis project

Posted: July 23rd, 2025, 2:36 am

by Sokwe

11WSS syntheses
All simple 11WSS flotillas can be synthesized. In this case there are 11 escorts:

Code: Select all

#C 11 Possible escorts for 11WSS (LWSS1, MWSS1-4, HWSS1-6)
x = 161, y = 52, rule = B3/S23
3o$o2bo$o6bo$o5b3o$o5bob2o$o6b3o$o6b2o$o$o$o3bo$o$bobo9$3o27b3o27b3o
27b3o$o2bo26bo2bo26bo2bo26bo2bo2b3o$o6bo22bo5b3o21bo7bo21bo5bo2bo$o5b
3o21bo4bo2bo21bo3bo2b3o20bo5bo$o5bob2o20bo7bo21bo3bo2bob2o19bo5bo3bo$o
6b3o20bo7bo21bo7b3o19bo2bo2bo$o3bo2b3o20bo7bo21bo7b3o19bo6bobo$o6b2o
21bo4bobo22bo7b2o20bo$o29bo3bo25bo3bo25bo3bo$o29bo3bo25bo3bo25bo3bo$o
29bo29bo29bo$bobo27bobo27bobo27bobo8$7bo$3o3b3o21b3o27b3o27b3o27b3o27b
3o$o2bo2bob2o20bo2bo26bo2bo26bo2bo4bo21bo2bo26bo2bo2b3o$o6b3o20bo6bo
22bo5b3o21bo6b3o20bo7bo21bo5bo2bo$o6b3o20bo5b3o21bo4bo2bo21bo3bo2bob2o
19bo3bo2b3o20bo5bo$o6b3o20bo5bob2o20bo7bo21bo7b3o19bo3bo2bob2o19bo5bo
3bo$o6b2o21bo6b3o20bo7bo21bo7b3o19bo7b3o19bo2bo2bo3bo$o29bo6b3o20bo7bo
21bo7b3o19bo7b3o19bo2bo2bo$o29bo6b3o20bo7bo21bo7b2o20bo7b3o19bo6bobo$o
3bo25bo6b2o21bo4bobo22bo3bo25bo7b2o20bo$o3bo25bo29bo3bo25bo3bo25bo3bo
25bo3bo$o29bo3bo25bo29bo29bo29bo$bobo27bobo27bobo27bobo27bobo27bobo!

In this case, all 11WSS flotillas can be constructed with a modification of the snake method used for the 9WSS and 10WSS syntheses:

Code: Select all

x = 29, y = 44, rule = B3/S23
3bobo$4b2o$4bo11$13b2o$14bo$13bo$13b2o11$2b3o$4bo3bo$3bo4b2o$7bobo16b
3o$26bo$22bo4bo$b2o18b2o$obo18bobo$2bo13b3o$16bo$17bo4$21b2o$20b2o$22b
o!

Here are the left-hand escort syntheses:

Code: Select all

x = 401, y = 285, rule = B3/S23
15bobo$10bo5b2o$11bo4bo$9b3o10$25b2o$26bo$19b2o4bo$19b2o4b2o10$7bo$7b
2o5b3o$6bobo7bo3bo$15bo4b2o$19bobo16b3o$38bo$34bo4bo$13b2o18b2o$12bobo
18bobo$14bo13b3o$28bo$29bo4$33b2o$32b2o$34bo20$25b3o$25bo2bo$20bo4bo$
19b3o3bo$19bob2o2bo$20b3o2bo$20b2o3bo$25bo$25bo$25bo$25bo$26bo26$15bob
o61bo5bobo67bobo67bobo$10bo5b2o62b2o4b2o61bo6b2o61bobo4b2o$11bo4bo25bo
36b2o5bo63bo5bo63b2o4bo$9b3o28b2o106b3o69bo$41b2o9$25b2o68b2o68b2o68b
2o$26bo62b2o5bo69bo62b2o5bo$19b2o4bo6b2o55bobo3bo62b2o5bo63bobo3bo$18b
obo4b2o4bobo56bo4b2o61bobo4b2o63bo4b2o$18b2o12bo126bo8$44b2o30b2o138b
3o$44bobo28bobo67b2o71bo$6b3o5b3o27bo32bo6b3o59b2o6b3o60bo6b3o$8bo7bo
3bo65bo3bo54bo10bo3bo65bo3bo$7bo7bo4b2o63bo4b2o63bo4b2o63bo4b2o$19bobo
16b3o48bobo16b3o48bobo16b3o48bobo16b3o$38bo69bo69bo69bo$34bo4bo64bo4bo
64bo4bo64bo4bo$13b2o18b2o48b2o18b2o48b2o18b2o48b2o18b2o$12bobo18bobo
46bobo18bobo46bobo18bobo46bobo18bobo$14bo13b3o53bo13b3o53bo13b3o53bo
13b3o$28bo69bo69bo69bo$29bo69bo69bo69bo4$33b2o68b2o68b2o68b2o$32b2o68b
2o68b2o68b2o$34bo69bo69bo69bo20$25b3o67b3o67b3o67b3o$25bo2bo66bo2bo66b
o2bo60b3o3bo2bo$20bo4bo63b3o3bo63bo5bo63bo2bo2bo$19b3o3bo62bo2bo3bo62b
3o4bo63bo5bo$19bob2o2bo65bo3bo62bob2o3bo63bo3bobo$20b3o2bo61bo3bo3bo
63b3o3bo63bo5bo$20b3o2bo65bo3bo63b3o3bo64bobo2bo$20b2o3bo62bobo4bo63b
2o4bo69bo$25bo69bo69bo69bo$25bo69bo69bo69bo$25bo69bo69bo69bo$26bo69bo
69bo69bo24$70bo$71b2o5bo$70b2o7bo$77b3o7$10bo142bo$11bo71bo70bo209bo$
9b3o3bobo66bo10bobo54b3o4bo5bobo61bo5bobo67bobo54bobo10bobo$16b2o64b3o
5bo5b2o62b2o4b2o62bo5b2o61bo6b2o55b2o4bobo4b2o$16bo74bo4bo62b2o5bo61b
3o5bo63bo5bo63b2o4bo$89b3o57bo148b3o69bo$6bo143b2o207bobo$4bobo142b2o
209b2o$5b2o218bo134bo$64bo2bo87bo67bobo69bo$68bo87b2o66b2o67bobo69bobo
$64bo3bo86b2o137b2o70b2o$65b4o297bo2$19b2o$18bo2bo3b2o78b2o68b2o68b2o
68b2o68b2o$18bo2bo4bo79bo62b2o5bo61b2o6bo69bo62b2o5bo$19b2o4bo73b2o4bo
59bo4bo4bo61bo2bo4bo62b2o5bo59bo4bo4bo$25b2o71bobo4b2o58bo3bo5b2o60bo
2bo4b2o60bo2bo4b2o58bo3bo5b2o$98b2o65bo3b2o67b2o67bo2bo64bo3b2o$308b2o
$153b2o208b3o$152bobo210bo$154bo209bo3$b2o$obo4bo$2bo4b2o72b2o137b2o$
6bobo5b3o65b2o2b3o5b3o67b3o52bobo4bo7b3o53b2o12b3o61b2o4b3o$16bo3bo60b
o6bo7bo3bo56b3o6bo3bo50bo4b2o8bo3bo48bobo4bo9bo3bo56bobo6bo3bo$15bo4b
2o65bo7bo4b2o57bo5bo4b2o53bobo7bo4b2o49bo4b2o7bo4b2o57bo5bo4b2o$19bobo
16b3o58bobo16b3o37bo10bobo16b3o48bobo16b3o34bobo11bobo16b3o48bobo16b3o
$38bo79bo69bo69bo69bo69bo$34bo4bo74bo4bo64bo4bo64bo4bo64bo4bo64bo4bo$
13b2o18b2o58b2o18b2o48b2o18b2o48b2o18b2o48b2o18b2o48b2o18b2o$12bobo18b
obo56bobo18bobo46bobo18bobo46bobo18bobo46bobo18bobo46bobo18bobo$14bo
13b3o63bo13b3o53bo13b3o53bo13b3o53bo13b3o53bo13b3o$28bo79bo69bo69bo69b
o69bo$29bo79bo69bo69bo69bo69bo4$33b2o78b2o68b2o68b2o68b2o68b2o$32b2o
78b2o68b2o68b2o68b2o68b2o$34bo79bo69bo69bo69bo69bo19$20bo$19b3o3b3o77b
3o67b3o67b3o67b3o67b3o$19bob2o2bo2bo76bo2bo66bo2bo60bo5bo2bo66bo2bo60b
3o3bo2bo$20b3o2bo74bo4bo63b3o3bo62b3o4bo63bo5bo63bo2bo2bo$20b3o2bo73b
3o3bo62bo2bo3bo62bob2o3bo62b3o4bo63bo5bo$20b3o2bo73bob2o2bo65bo3bo63b
3o3bo62bob2o3bo63bo3bobo$20b2o3bo74b3o2bo61bo3bo3bo63b3o3bo63b3o3bo63b
o3bobo$25bo74b3o2bo61bo3bo3bo63b3o3bo63b3o3bo63bo5bo$25bo74b3o2bo65bo
3bo63b2o4bo63b3o3bo64bobo2bo$25bo74b2o3bo62bobo4bo69bo63b2o4bo69bo$25b
o79bo69bo69bo69bo69bo$25bo79bo69bo69bo69bo69bo$26bo79bo69bo69bo69bo69b
o!

and the right-hand escort syntheses:

Code: Select all

x = 340, y = 295, rule = B3/S23
3bobo$4b2o$4bo$29bo$29bobo$29b2o8$13b2o$14bo$13bo$13b2o5b2o$20b2o10$2b
3o27b2o$4bo3bo22b2o$3bo4b2o23bo$7bobo16b3o$26bo$22bo4bo$b2o18b2o$obo
18bobo$2bo13b3o$16bo$17bo4$21b2o$20b2o$22bo20$13b3o$13bo2bo$13bo6bo$
13bo5b3o$13bo5bob2o$13bo6b3o$13bo6b2o$13bo$13bo$13bo3bo$13bo$14bobo36$
3bobo67bobo57bobo57bobo$4b2o68b2o58b2o58b2o$4bo69bo59bo59bo$29bo130bo$
29bobo128bobo$29b2o67bobo59b2o57bo$98b2o117b2o$99bo118b2o6$13b2o68b2o
58b2o58b2o$14bo69bo59bo59bo$13bo69bo59bo59bo$13b2o5b2o61b2o58b2o6b2o
50b2o$19bobo68b2o58bobo57b2o$20bo68bobo59bo57bobo$90bo119bo7$33bo130bo
56b2o$2b3o27b2o38b3o26b3o28b3o28b2o27b3o26bobo$4bo3bo23bobo39bo3bo22bo
32bo3bo24bobo28bo3bo22bo$3bo4b2o63bo4b2o22bo30bo4b2o53bo4b2o$7bobo16b
3o48bobo16b3o38bobo16b3o38bobo16b3o$26bo69bo59bo59bo$22bo4bo64bo4bo54b
o4bo54bo4bo$b2o18b2o48b2o18b2o38b2o18b2o38b2o18b2o$obo18bobo46bobo18bo
bo36bobo18bobo36bobo18bobo$2bo13b3o53bo13b3o43bo13b3o43bo13b3o$16bo69b
o59bo59bo$17bo69bo59bo59bo4$21b2o68b2o58b2o58b2o$20b2o68b2o58b2o58b2o$
22bo69bo59bo59bo20$13b3o67b3o57b3o57b3o$13bo2bo66bo2bo56bo2bo56bo2bo2b
3o$13bo6bo62bo5b3o51bo7bo51bo5bo2bo$13bo5b3o61bo4bo2bo51bo3bo2b3o50bo
5bo$13bo5bob2o60bo7bo51bo3bo2bob2o49bo5bo3bo$13bo6b3o60bo7bo51bo7b3o
49bo2bo2bo$13bo3bo2b3o60bo7bo51bo7b3o49bo6bobo$13bo6b2o61bo4bobo52bo7b
2o50bo$13bo69bo3bo55bo3bo55bo3bo$13bo69bo3bo55bo3bo55bo3bo$13bo69bo59b
o59bo$14bobo67bobo57bobo57bobo36$3bobo23bo33bobo57bobo57bobo57bobo57bo
bo$4b2o23bobo32b2o58b2o58b2o58b2o58b2o$4bo24b2o33bo59bo24bobo32bo25bo
33bo59bo25bo$89bo59b2o59bobo57bo57b2o$89bobo58bo59b2o58bobo56b2o$34bo
54b2o179b2o$33bo$33b3o119bo59bo$94bo58b2o59bo60bo57bobo$93bo60b2o58b3o
57bo58b2o$93b3o178b3o57bo3$13b2o5b2o51b2o58b2o58b2o58b2o58b2o$14bo4bo
2bo51bo59bo59bo59bo59bo$13bo5bo2bo50bo59bo6b2o51bo7b2o50bo59bo6b2o$13b
2o5b2o51b2o5b2o51b2o4bo2bo50b2o5bo2bo49b2o6b2o50b2o4bo2bo$79bo2bo56bo
2bo57bo2bo56bo2bo55bo2bo$79bo2bo57b2o59b2o57bo2bo56b2o$80b2o179b2o6$
37b3o$32b2o3bo300bo$2b3o26b2o5bo23b3o57b3o33b2o22b3o33b3o21b3o57b3o32b
2o$4bo3bo24bo30bo3bo28b3o24bo3bo23b2o3b2o25bo3bo24b2o3bo25bo3bo29b3o
23bo3bo22b3o3bobo$3bo4b2o53bo4b2o22b2o3bo25bo4b2o22bobo4bo23bo4b2o22b
2o5bo23bo4b2o23b2o3bo24bo4b2o21bo$7bobo16b3o38bobo16b3o2b2o5bo28bobo
16b3o3bo34bobo16b3o5bo32bobo16b3o3b2o5bo27bobo16b3o3bo$26bo59bo6bo52bo
59bo59bo7bo51bo$22bo4bo54bo4bo54bo4bo54bo4bo54bo4bo54bo4bo$b2o18b2o38b
2o18b2o38b2o18b2o38b2o18b2o38b2o18b2o38b2o18b2o$obo18bobo36bobo18bobo
36bobo18bobo36bobo18bobo36bobo18bobo36bobo18bobo$2bo13b3o43bo13b3o43bo
13b3o43bo13b3o43bo13b3o43bo13b3o$16bo59bo59bo59bo59bo59bo$17bo59bo59bo
59bo59bo59bo3$71b2o$21b2o48bobo7b2o58b2o58b2o58b2o58b2o$20b2o49bo8b2o
58b2o58b2o58b2o58b2o$22bo59bo59bo59bo59bo59bo2$89b2o$89bobo$89bo15$20b
o$13b3o3b3o51b3o57b3o57b3o57b3o57b3o$13bo2bo2bob2o50bo2bo56bo2bo56bo2b
o4bo51bo2bo56bo2bo2b3o$13bo6b3o50bo6bo52bo5b3o51bo6b3o50bo7bo51bo5bo2b
o$13bo6b3o50bo5b3o51bo4bo2bo51bo3bo2bob2o49bo3bo2b3o50bo5bo$13bo6b3o
50bo5bob2o50bo7bo51bo7b3o49bo3bo2bob2o49bo5bo3bo$13bo6b2o51bo6b3o50bo
7bo51bo7b3o49bo7b3o49bo2bo2bo3bo$13bo59bo6b3o50bo7bo51bo7b3o49bo7b3o
49bo2bo2bo$13bo59bo6b3o50bo7bo51bo7b2o50bo7b3o49bo6bobo$13bo3bo55bo6b
2o51bo4bobo52bo3bo55bo7b2o50bo$13bo3bo55bo59bo3bo55bo3bo55bo3bo55bo3bo
$13bo59bo3bo55bo59bo59bo59bo$14bobo57bobo57bobo57bobo57bobo57bobo!

Notice that two of the left-hand escort syntheses utilize the following new HWSS synthesis found by Discord user ||potatoes|| based on a partial result by Matthias Merzenich:

Code: Select all

x = 37, y = 28, rule = B3/S23
4bo$5bo$3b3o4bo$11b2o$10b2o$o$b2o$2o2$6bo$7b2o$6b2o$16b2o$4b2o6bo4bo$
3bobo6bo3bo$5bo6bo3b2o6$34b3o$8b3o22bo2bo$10bo25bo$9bo22bo3bo$32bo3bo$
36bo$33bobo!

Re: OWSS synthesis project

Posted: July 24th, 2025, 4:11 pm

by Sokwe

12WSS syntheses
All simple 12WSS flotillas can be synthesized. In this case there are 6 escorts:

Code: Select all

#C 6 Possible escorts for 12WSS (LWSS1, MWSS1, HWSS1-4)
x = 101, y = 53, rule = B3/S23
3o$o2bo$o6bo$o5b3o$o5bob2o$o6b3o$o6b2o$o$o$o3bo$o3bo$o$bobo8$3o$o2bo$o
6bo$o5b3o$o5bob2o$o6b3o$o3bo2b3o$o6b2o$o$o$o3bo$o$bobo8$3o27b3o27b3o
27b3o$o2bo26bo2bo26bo2bo26bo2bo2b3o$o6bo22bo5b3o21bo7bo21bo5bo2bo$o5b
3o21bo4bo2bo21bo3bo2b3o20bo5bo$o5bob2o20bo7bo21bo3bo2bob2o19bo5bo3bo$o
6b3o20bo7bo21bo7b3o19bo2bo2bo3bo$o6b3o20bo7bo21bo7b3o19bo2bo2bo$o6b3o
20bo7bo21bo7b3o19bo6bobo$o6b2o21bo4bobo22bo7b2o20bo$o29bo3bo25bo3bo25b
o3bo$o29bo3bo25bo3bo25bo3bo$o29bo29bo29bo$bobo27bobo27bobo27bobo!

I used QuFince to modify the snake method to synthesize the 12WSS:

Code: Select all

x = 30, y = 46, rule = B3/S23
bobo$2b2o$2bo12$12b2o$13bo$12bo$12b2o12$3o$2bo$bo4b2o$5bobo$7bo$11b2o$
12b2o9bo$11bo10b2o$22bobo$28b2o$27b2o$29bo3$4b2o$5b2o$4bo!

Using this method, all left-hand and right-hand escorts can be synthesized. Here are the left-hand escort syntheses:

Code: Select all

x = 271, y = 277, rule = B3/S23
32bobo$27bo5b2o$28bo4bo$26b3o11$43b2o$44bo$37b2o4bo$37b2o4b2o11$23b2o$
24b2o5b3o$23bo9bo$32bo4b2o$36bobo$38bo$42b2o$43b2o9bo$42bo10b2o$53bobo
$59b2o$58b2o$60bo3$35b2o$36b2o$35bo19$43b3o$43bo2bo$38bo4bo$37b3o3bo$
37bob2o2bo$38b3o2bo$38b2o3bo$43bo$43bo$43bo$43bo$43bo$44bo24$32bobo$
27bo5b2o$28bo4bo$26b3o11$43b2o$44bo$37b2o4bo$36bobo4b2o$36b2o11$23b3o
5b3o$25bo7bo$24bo7bo4b2o$36bobo$38bo$42b2o$43b2o9bo$42bo10b2o$53bobo$
59b2o$58b2o$60bo3$35b2o$36b2o$35bo19$43b3o$43bo2bo$38bo4bo$37b3o3bo$
37bob2o2bo$38b3o2bo$38b3o2bo$38b2o3bo$43bo$43bo$43bo$43bo$44bo12$7bo$
8b2o5bo$7b2o7bo$14b3o7$90bo$20bo70bo139bo$21bo10bobo54b3o4bo5bobo67bob
o54bobo10bobo$19b3o5bo5b2o62b2o4b2o61bo6b2o55b2o4bobo4b2o$28bo4bo62b2o
5bo63bo5bo63b2o4bo$26b3o57bo78b3o69bo$87b2o137bobo$86b2o139b2o$227bo$
92bo69bo$o2bo89b2o65bobo69bobo$4bo87b2o67b2o70b2o$o3bo228bo$b4o3$43b2o
68b2o68b2o68b2o$44bo62b2o5bo69bo62b2o5bo$37b2o4bo59bo4bo4bo62b2o5bo59b
o4bo4bo$36bobo4b2o58bo3bo5b2o60bo2bo4b2o58bo3bo5b2o$36b2o65bo3b2o66bo
2bo64bo3b2o$176b2o2$90b2o138b3o$89bobo140bo$91bo139bo5$18b2o$19b2o2b3o
5b3o67b3o53b2o12b3o61b2o4b3o$18bo6bo7bo60b3o6bo52bobo4bo9bo60bobo6bo$
24bo7bo4b2o57bo5bo4b2o49bo4b2o7bo4b2o57bo5bo4b2o$36bobo56bo10bobo53bob
o11bobo67bobo$38bo69bo69bo69bo$42b2o68b2o68b2o68b2o$43b2o9bo58b2o9bo
58b2o9bo58b2o9bo$42bo10b2o57bo10b2o57bo10b2o57bo10b2o$53bobo67bobo67bo
bo67bobo$59b2o68b2o68b2o68b2o$58b2o68b2o68b2o68b2o$60bo69bo69bo69bo3$
35b2o68b2o68b2o68b2o$36b2o68b2o68b2o68b2o$35bo69bo69bo69bo19$43b3o67b
3o67b3o67b3o$43bo2bo66bo2bo66bo2bo60b3o3bo2bo$38bo4bo63b3o3bo63bo5bo
63bo2bo2bo$37b3o3bo62bo2bo3bo62b3o4bo63bo5bo$37bob2o2bo65bo3bo62bob2o
3bo63bo3bobo$38b3o2bo61bo3bo3bo63b3o3bo63bo3bobo$38b3o2bo61bo3bo3bo63b
3o3bo63bo5bo$38b3o2bo65bo3bo63b3o3bo64bobo2bo$38b2o3bo62bobo4bo63b2o4b
o69bo$43bo69bo69bo69bo$43bo69bo69bo69bo$43bo69bo69bo69bo$44bo69bo69bo
69bo!

and the right-hand escort syntheses:

Code: Select all

x = 242, y = 277, rule = B3/S23
bobo$2b2o$2bo$29bo$29bobo$29b2o9$12b2o$13bo$12bo$12b2o5b2o$19b2o10$33b
o$3o29b2o$2bo29bobo$bo4b2o$5bobo$7bo$11b2o$12b2o9bo$11bo10b2o$22bobo$
28b2o$27b2o$29bo3$4b2o$5b2o$4bo19$12b3o$12bo2bo$12bo6bo$12bo5b3o$12bo
5bob2o$12bo6b3o$12bo6b2o$12bo$12bo$12bo3bo$12bo3bo$12bo$13bobo24$bobo$
2b2o$2bo$29bo$29bobo$29b2o9$12b2o$13bo$12bo$12b2o5b2o$18bobo$19bo9$33b
o$3o29b2o$2bo29bobo$bo4b2o$5bobo$7bo$11b2o$12b2o9bo$11bo10b2o$22bobo$
28b2o$27b2o$29bo3$4b2o$5b2o$4bo19$12b3o$12bo2bo$12bo6bo$12bo5b3o$12bo
5bob2o$12bo6b3o$12bo3bo2b3o$12bo6b2o$12bo$12bo$12bo3bo$12bo$13bobo24$b
obo67bobo67bobo67bobo$2b2o68b2o68b2o68b2o$2bo69bo69bo69bo$29bo$29bobo$
29b2o67bobo138bo$98b2o69bo67b2o$99bo69bobo66b2o$31bo137b2o$31bobo$31b
2o67bobo138bo$100b2o69bo67b2o$101bo69bobo66b2o$171b2o$12b2o68b2o68b2o
68b2o$13bo69bo69bo69bo$12bo69bo69bo69bo$12b2o68b2o68b2o68b2o10$9b2o69b
2o138b3o$10b2o67bobo69b2o69bo$3o6bo60b3o8bo58b3o9b2o56b3o8bo$2bo69bo
69bo8bo60bo$bo4b2o63bo4b2o63bo4b2o63bo4b2o$5bobo67bobo67bobo67bobo$7bo
69bo69bo69bo$11b2o68b2o68b2o68b2o$12b2o9bo58b2o9bo58b2o9bo58b2o9bo$11b
o10b2o57bo10b2o57bo10b2o57bo10b2o$22bobo67bobo67bobo67bobo$28b2o68b2o
68b2o68b2o$27b2o68b2o68b2o68b2o$29bo69bo69bo69bo3$4b2o68b2o68b2o68b2o$
5b2o68b2o68b2o68b2o$4bo69bo69bo69bo19$12b3o67b3o67b3o67b3o$12bo2bo66bo
2bo66bo2bo66bo2bo2b3o$12bo6bo62bo5b3o61bo7bo61bo5bo2bo$12bo5b3o61bo4bo
2bo61bo3bo2b3o60bo5bo$12bo5bob2o60bo7bo61bo3bo2bob2o59bo5bo3bo$12bo6b
3o60bo7bo61bo7b3o59bo2bo2bo3bo$12bo6b3o60bo7bo61bo7b3o59bo2bo2bo$12bo
6b3o60bo7bo61bo7b3o59bo6bobo$12bo6b2o61bo4bobo62bo7b2o60bo$12bo69bo3bo
65bo3bo65bo3bo$12bo69bo3bo65bo3bo65bo3bo$12bo69bo69bo69bo$13bobo67bobo
67bobo67bobo!

13WSS syntheses
All simple 13WSS flotillas can be synthesized. In this case there are 2 escorts, resulting in 3 ships, all of which were originally synthesized by Martin Grant in 2019:

Code: Select all

x = 160, y = 72, rule = B3/S23
16bo59bo59bo$14bobo57bobo57bobo$8bo6b2o51bo6b2o51bo6b2o$6bobo11b2o44bo
bo11b2o44bobo11b2o$7b2o11b2o45b2o11b2o45b2o11b2o$29bo59bo20bobo36bo$5b
o23bobo33bo23bobo19b2o12bo23bobo$6bo22b2o35bo22b2o20bo14bo22b2o$4b3o
57b3o57b3o2$15b2ob2o55b2ob2o14bo40b2ob2o14bo$15b2obo56b2obo14bo25bo15b
2obo14bo$18bo59bo14b3o24bo17bo14b3o$18b2o58b2o38b3o17b2o2$23b2o58b2o
58b2o$10b2o6b2o2bobo45b2o6b2o2bo2bo44b2o6b2o2bo2bo$9bobo6bo4bo45bobo6b
o3bo2bo45bo6bo3bo2bo$9b2o4b2obo50b2o4b2obo4b2o45bo4b2obo4b2o$15b2ob2o
55b2ob2o47bobo5b2ob2o$127b2o2$33bo$b2o29b2o27b2o$obo29bobo25bobo34b3o
57b3o$2bo4b2o53bo4b2o23b2o3bo29b2o23b2o3bo$6bobo57bobo22b2o5bo27bobo
22b2o5bo$8bo59bo24bo34bo24bo3$15b2o58b2o58b2o$14bobo6b2o49bobo6b2o49bo
bo6b2o$16bo6bobo50bo6bobo50bo6bobo$23bo59bo59bo3$18b2o58b2o58b2o$17b2o
58b2o58b2o$19bo59bo59bo20$16b3o57b3o57b3o$16bo2bo56bo2bo56bo2bo$11bo4b
o6bo47bo4bo6bo47bo4bo6bo$10b3o3bo5b3o45b3o3bo5b3o45b3o3bo5b3o$10bob2o
2bo5bob2o44bob2o2bo5bob2o44bob2o2bo5bob2o$11b3o2bo6b3o45b3o2bo6b3o45b
3o2bo6b3o$11b3o2bo3bo2b3o45b3o2bo6b3o45b3o2bo6b3o$11b2o3bo6b2o46b2o3bo
6b3o45b3o2bo6b3o$16bo59bo6b2o46b2o3bo6b2o$16bo59bo59bo$16bo3bo55bo59bo
$16bo3bo55bo3bo55bo3bo$16bo59bo59bo$17bobo57bobo57bobo!

14WSS syntheses
All simple 14WSS flotillas can be synthesized. In this case there is 1 escort, resulting in 1 ship, which was originally synthesized by Martin Grant in 2019:

Code: Select all

x = 50, y = 77, rule = B3/S23
26bo$24bobo$18bo6b2o$16bobo11b2o$17b2o11b2o$obo36bo$b2o12bo23bobo$bo
14bo22b2o$14b3o2$25b2ob2o14bo$9bo15b2obo14bo$10bo17bo14b3o$8b3o17b2o2$
33b2o$20b2o6b2o2bo2bo$21bo6bo3bo2bo$20bo4b2obo4b2o$17bobo5b2ob2o$17b2o
4$47b3o$17b2o23b2o3bo$16bobo22b2o5bo$18bo24bo$21b2o$22b2o$21bo$37b2o$
36b2o$38bo29$26b3o$26bo2bo$21bo4bo6bo$20b3o3bo5b3o$20bob2o2bo5bob2o$
21b3o2bo6b3o$21b3o2bo6b3o$21b3o2bo6b3o$21b2o3bo6b2o$26bo$26bo$26bo3bo$
26bo3bo$26bo$27bobo!

Additionally, Grant found an alternate synthesis for this ship in 2020:

Code: Select all

x = 126, y = 63, rule = B3/S23
54bo$54bobo12bo$54b2o13bobo$69b2o3$74bo$31bo41bo$32b2o39b3o$31b2o5$30b
3o$32bo$31bo$49b2o$48bobo$47bobo$47b2o$53b2o$52bo2bo$24bo27bo2bo$24b2o
27b2o$23bobo$50b2o$50b2o2$30b2o$31b2o$30bo6$16b2o$15bobo$17bo$57bo19b
3o$56b2o14b2o3bo$56bobo12b2o5bo$73bo2$59b3o$59bo$60bo$29bo86b3o$29b2o
85bo2bo$28bobo80bo4bo6bo$110b3o3bo5b3o$2o55bo52bob2o2bo5bob2o$b2o53b2o
53b3o2bo6b3o$o55bobo52b3o2bo6b3o$111b3o2bo6b3o$111b2o3bo6b2o$116bo$
116bo$116bo3bo$116bo3bo$116bo$117bobo!

This completes the proof that all OWSS flotillas consisting of a single OWSS supported on each side by a single standard spaceship can be synthesized.

Re: OWSS synthesis project

Posted: July 28th, 2025, 12:03 pm

by May13

Cheap 9WSS and 10WSS variants:

Code: Select all

x = 170, y = 33, rule = B3/S23
163bo$163bobo$163b2o$93bo$91b2o$92b2o2$96bo68bo$95bo68bo$95b3o66b3o3$
20b3o2$15b2obo56b2obo66b2obo$15bob2o56bob2o66bob2o3$160b3o$160bo$161bo
5$2o58b2o68b2o$b2o28b2o28b2o28b2o38b2o$o30bobo26bo30bobo36bo$31bo59bo
2$96bo70b2o$95b2o70bobo$95bobo69bo!
[[ STOP 48 ]]

I found these when I was trying to synthesise a 38 cell 2c/4 spaceship. Here's the result (see edit of my post):

Code: Select all

x = 132, y = 50, rule = B3/S23
9bo29bobo57bo29bobo$10b2o5bobo19b2o59b2o5bobo19b2o$9b2o7b2o20bo58b2o7b
2o20bo$18bo89bo2$33bo89bo$2bo30bobo56bo30bobo$obo11bobo16b2o55bobo11bo
bo16b2o$b2o12b2o74b2o12b2o$15bo23bobo63bo23bobo$39b2o88b2o$40bo89bo$
12b2o88b2o$12bobo78bo8bobo$13b2o76bobo9b2o$92b2o2$16b2o88b2o$16bobo87b
obo$17bo89bo$91bo$20bo71bo17bo$19bobob2o5b3o57b3o16bobob2o5b3o$20b2ob
2o5bo79b2ob2o5bo$31bo89bo$14b3o2$18bob2o86bob2o$18b2obo86b2obo3$94b3o$
96bo$19b2o74bo13b2o$19b2o88b2o4$35b2o88b2o$4b2o28b2o88b2o$3bobo30bo89b
o$5bo2$88b2o$35bo51bobo35bo$34b2o53bo34b2o$34bobo87bobo$5b2o88b2o$4bob
o87bobo$6bo89bo!

Re: OWSS synthesis project

Posted: July 28th, 2025, 5:59 pm

by Sokwe

May13 wrote: July 28th, 2025, 12:03 pm Cheap 9WSS and 10WSS variants

Nice! That glider+blinker activation is so elegant, I'm annoyed I didn't find it. Here is likewise a slightly cheaper 11WSS synthesis than the one given a few posts back:

Code: Select all

x = 27, y = 40, rule = B3/S23
bobo$2b2o$2bo11$11b2o$12bo$11bo$11b2o11$3o$2bo18b3o$bo5bo13bo$7b2o13bo
$6bobo$25b2o$24b2o$26bo3$5b2o$6b2o$5bo!

Edit:

May13 wrote: July 25th, 2025, 9:40 pm Final steps:

Code: Select all

x = 142, y = 67, rule = B3/S23
10bo$11bo$9b3o4$23bo$21bobo8bo$22b2o8bobo$18bo13b2o$19bo$bo15b3o$2bo$
3o53bo$56bobo$56b2o5$128bo$128b2o$127bobo$23bo$22bobo5bo4bo$21bo2bo5bo
3bobo95b2o$17bo3bobo6bo3bo2bo93b2o$17bo2b2ob2o10bobo3bo91bo$17bo16b2ob
2o2bo$29b2o10bo$23b2o4bo$18bo6bo4bo3b2o79b3o$16b3o3bo5bobo2bo6bo76bo$
15bo7b2o3b2o6bo3b3o73bo$15b2o17b2o7bo$42b2o$18b2o120b2o$17bobo19b2o98b
2o$bo14bobo20bobo99bo$b2o14bo22bobo13b2o$obo38bo13b2o$57bo5$23b2o$18b
3o3b2o$20bo2bo$2b3o14bo34b2o$4bo49bobo$3bo25b3o22bo$29bo92bo13bo$30bo
90b3o11b3o$120b2o2bo3b3o3b2obo$120b2ob3o2bo2bo2bo$120b2o2b2o2bo7b3o$
124b2o2bo4b6o$120b2o6bo5b2obo$125bo2bo4b2o$124bo3bo$124bo3bo$128bo$
128bo3bo$39b3o86bo3bo$39bo88bo$40bo88bobo!

The lengthen-by-3 operation in the last step is quite nice. Is it new? What other XWSS lengthening or shortening operations exist? I know of the following four, but they only really work on the specific spaceships shown, rather than being useful for general conversion:

Code: Select all

x = 187, y = 57, rule = B3/S23
175bobo6bo$140bo34b2o7bobo$138bobo35bo7b2o$139b2o4$141bobo$142b2o$142b
o34bobo$177b2o$49bo115bo12bo$50bo112b2o$48b3o113b2o4bo$168b2o$37bo131b
2o10bo$37b2o8b3o130bo$36bobo10bo112bo17b3o$48bo111bobo$161b2o3$143bo$
143b2o$142bobo6$176b2o$176bobo$176bo2$bo$2bo$3o4bobo$8b2o168b2o$8bo
168b2o$179bo$100bobo$101b2o$101bo2$7b2o93bo$5b2ob2o93bo$5b4o3bobo86b3o
$6b2o5b2o4b3o37b3o47b3o47b3o$13bo5bo2bo36bo2bo46bo2bo46bo2bo$19bo39bo
49bo49bo$19bo3bo35bo3bo45bo3bo45bo$19bo39bo3bo45bo3bo46bobo$11b3o6bobo
36bo49bo$13bo46bobo47bobo$12bo91b2o$103bobo$105bo!

Some of the trickier 7/8/9WSS flotillas can be constructed more efficiently with the lengthen-by-3 converter. Notably, this reduces the one difficult 7WSS flotilla from 25 gliders to 15 gliders:

Code: Select all

x = 129, y = 47, rule = B3/S23
81bobo$81b2o$82bo5$115b2o$48bo65bobo$46bobo67bo$47b2o2$118b3o$118bo$
56b2o2b2o57bo$57b2obobo$56bo3bo$103bo$103b2o$102bobo4$126b3o$126bo$
127bo10$30bo$29bo$29b3o$22b3o$o21bo2bo$obo19bo6b2o43bo4b3o27b3o4bo4b3o
$2o20bo3bo2b2o42b3o3bo2bo26bo2bo2b3o3bo2bo$3b2o17bo3bo6b2o37b2obo3bo
29bo4b2obo3bo$3bobo16bo9b2o38b3o4bo3bo25bo3b4o4bo3bo$3bo19bobo8bo38b2o
4bo3bo25bo3bob2o4bo3bo$79bo29bo11bo$80bobo27bobo9bobo!

While trying to instantiate another flotilla, I accidentally synthesized a variant of blinker puffer 1:

Code: Select all

x = 40, y = 40, rule = B3/S23
10bo$11bo16bo$9b3o16b2o$27bobo3$6bo23b2o$4bobo22b2o$5b2o24bo4$15b3o$
17bo$16bo$20b2o$19bo2bo$19bo2bo15b2o$20b2o15b2o$39bo9$b2o$obo4bo$2bo4b
2o$6bobo2$34bo$27b3o3b3o$27bo2bo2bob2o$27bo6b3o$27bo6b3o$27bo3bo2b3o$
28bo2bo2b2o!

I was intending the following 8WSS flotilla synthesis:

Code: Select all

x = 41, y = 43, rule = B3/S23
10bo$11bo$9b3o2$29bo$29b2o$6bo21bobo$4bobo$5b2o$31b2o$30b2o$32bo4$16b
3o$18bo$17bo3$39b2o$25b2o11b2o$12b2o11bobo12bo$13b2o10bo$12bo6$b2o$obo
4bo$2bo4b2o$6bobo3$35bo$28b3o3b3o$28bo2bo2bob2o$28bo6b3o$28bo6b3o$28bo
3bo2b3o$29bo2bo2b2o!

Re: OWSS synthesis project

Posted: August 4th, 2025, 8:32 am

by pifricted

Syntheses for 11 MWSS on 7WSS on MWSS:

Code: Select all

x = 474, y = 114, rule = B3/S23
8bo$6bobo$7b2o17bo$15bo9bo$16b2o7b3o119bo$15b2o40bo16bo27bo45bo$9b2o44b
obo15bo26bobo43b3o5bobo9bo$9bobo44b2o15b3o25b2o52b2o9bobo21bo65bo25bo
17bo$10bo5b2o6b2o38bo44bo9bo35bo10b2o23bo62b2o24bobo15b2o23bo45bo16bo
62bo$4bo11bobo4bobo39b2o43b2o6bo70b3o46bo16b2o24b2o16b2o20bobo43bobo15b
o24bo39bo$4b2o6b2o3bo6bo39b2o43b2o7b3o76bobo9bo26bobo50bo32b2o17bo26b
2o15b3o20bobo37b3o5bobo9bo$3bobo5bobo15b2o27b2o12b2o29b2o44b2o5b2o40b
2o9bobo25b2o51b2o38bo8b2o35bo32b2o46b2o9bobo$13bo14b2o28bobo10bobo29b
obo43bobo5bo6b2o32bo10b2o34bo43b2o40b2o7b2o35b2o38bo9bo29bo10b2o$19b2o
9bo28bo5b2o5bo31bo5b2o38bo5bo6bobo80b2o5b2o28b2o12b2o31b2o44b2o40b2o6b
o$19bobo31bo11bobo9b2o19bo11bobo4b2o37bobo5bo27b2o51b2o5bobo28bobo10b
obo25b2o44b2o12b2o31b2o7b3o$19bo33b2o6b2o3bo9b2o20b2o6b2o3bo4bobo24b2o
12b2o11bo21bobo4b2o38b2o12bo30bo5b2o5bo26bobo43bobo10bobo25b2o38b2o5b
2o$52bobo5bobo15bo18bobo5bobo9bo26b2o23b2o22bo6bo6b2o30bobo16b2o18bo11b
obo9b2o21bo5b2o5b2o31bo5b2o5bo26bobo37bobo5bo6b2o$62bo44bo14b2o19bo9b
2o6b2o6bobo27bo6bobo31bo5b2o10bobo17b2o6b2o3bo10bobo14bo11bobo3bobo25b
o11bobo9b2o21bo5b2o32bo5bo6bobo$68b2o43b2o6b2o31b2o4b2o24b2o11bobo5bo
26bo11bobo9bo18bobo5bobo14bo16b2o6b2o3bo5bo26b2o6b2o3bo9b2o16bo11bobo
4b2o31bobo5bo$68bobo42bobo7bo29bo8bo24b2o11b2o11bo20b2o6b2o3bo39bo30b
obo5bobo14b2o19bobo5bobo15bo15b2o6b2o3bo4bobo18b2o12b2o11bo$68bo44bo72b
o25b2o19bobo5bobo49b2o33bo14bobo28bo30bobo5bobo9bo20b2o23b2o$196b2o6b
2o6bobo28bo49bobo38b2o7bo36b2o33bo14b2o13bo9b2o6b2o6bobo$197b2o4b2o44b
2o42bo40bobo43bobo38b2o6b2o25b2o4b2o$196bo8bo43bobo82bo45bo40bobo7bo23b
o8bo$249bo171bo19$21bo$6b2o13bobo$6bobo12b2o354bo$7bo5b2o360bobo48bo$
13bobo140b2o135bo76b2o4b2o6b2o40bobo29b2o$14bo4b2o136bo6b2o125bobo40b
o35bobo10bobo25b2o13b2o31bo6b2o$20b2o125bo8bo6bobo83bo6b2o28b2o4b2o6b
2o30bobo36bo12bo26bobo35bo8bo6bobo$19bo127b2o7bobo5bo82bobo5bobo28bob
o10bobo25b2o4b2o77bo5b2o29b2o7bobo5bo$146bobo8b2o41b2o40b2o4b2o6bo30b
o12bo26bobo88bobo27bobo8b2o$64bo44bo81bo9bo6b2o32bobo83bo12b2o37b2o37b
o$56b2o4bobo6b2o28b2o4bobo6b2o25b2o46b2o7bo6bobo33bo96bobo36b2o41b2o21b
2o$56bobo4b2o5bobo28bobo4b2o5bobo24bobo3b2o40bobo7bobo5bo87b2o43bo39b
o41b2o19bobo3b2o$57bo13bo30bo13bo27bo3bobo50b2o92b2o40b2o83bo23bo3bob
o$148bo38b2o63b2o43bo38b2o112bo$65b2o43b2o74bobo3b2o57b2o85bo$64b2o43b
2o77bo3bobo58bo$66bo44bo80bo21$o$b2o$2o4$388bobo$388b2o74bo$260bobo41b
obo82bo74bobo$260b2o42b2o158b2o$6bo70bobo42bobo136bo43bo$4bobo70b2o43b
2o39bo42bo138bobo$5b2o71bo44bo39bobo40bobo136b2o22bo96b3o$163b2o41b2o
138bo20bobo42bo53bo$285bo82b2o40bobo46b2o6bo$56bo44bo181bobo40bo84b2o
6bo38bobo$54bobo42bobo63b3o40b3o30bo42b2o38bobo90bobo40bo$9b2o44b2o43b
2o63bo42bo30bobo83b2o43b2o46b2o48b3o$8b2o148b2o6bo34b2o6bo30b2o127b2o
42b2o53bo$10bo146bobo40bobo83b2o83bo40b2o48b2o5bo$159bo42bo82b2o40b2o
85bo5b2o39b2o$167b3o40b3o29b2o43bo38b2o91b2o42bo$59b2o43b2o61bo42bo30b
2o85bo92bo$58b2o43b2o56b2o5bo35b2o5bo31bo130b2o$60bo44bo54b2o41b2o168b
obo$162bo42bo40b2o42b2o83bo$245bobo41bobo$63b2o43b2o137bo43bo$62bobo42b
obo221b2o$64bo44bo220bobo$332bo$27b3o$27bo$28bo!

Edit: 5 more:

Code: Select all

x = 202, y = 94, rule = B3/S23
3bobo$4b2o$4bo2$45bobo$46b2o45bo$6b2o3bo10bo23bo47b2o$6bobo3b2o7bo71b
2o4bobo9bo26bo39bo$7bo3b2o8b3o29bo10bo35b2o9bobo22bobo40bo$54b2o7bo36b
o10b2o24b2o38b3o4bobo9bo$3o45b2o3b2o8b3o119b2o9bobo$2bo9b2o34bobo44b2o
47bo10bo29bo10b2o$bo10bobo5b2o27bo45bobo3b2o42b2o7bo$8b2o3bo5bobo32b2o
40bo5bo6b2o28b2o3b2o8b3o$7bobo10bo21b3o9bobo5b2o26b2o9bo6bobo28bobo38b
2o4b2o$9bo15b2o17bo5b2o3bo5bobo25bobo9bobo5bo30bo39bobo4bo6b2o$15b2o7b
2o17bo5bobo10bo28bo10b2o11bo18bo10b2o34bo4bo6bobo$15bobo8bo24bo15b2o45b
2o18b2o9bobo5b2o31bobo5bo$15bo41b2o7b2o30b2o6b2o6bobo16bobo5b2o3bo5bo
bo19b2o11b2o11bo$57bobo8bo30b2o4b2o33bobo10bo21b2o22b2o$57bo40bo8bo34b
o15b2o14bo8b2o6b2o6bobo$148b2o7b2o25b2o4b2o$148bobo8bo23bo8bo$148bo15$
152b2o$137bo13bobo32b2o$137b2o13bo34bo6b2o$136bobo39bo7bo6bobo$6b2o137b
2o31b2o6bobo5bo$6bobo40b2o82b2o10bobo29bobo7b2o$7bo41bobo11bo68bobo3b
2o6bo$20bo29bo11bo38b2o31bo3bobo33b2o$19bo35b2o5b3o28bo8bo6b2o27bo34b
obo3b2o$12b2o5b3o33bobo35b2o6bo6bobo64bo3bobo$12bobo41bo5bo29bobo6bob
o5bo69bo$13bo5bo42b2o38b2o$19b2o40bobo25b2o$18bobo67bobo3b2o$90bo3bob
o$94bo12$193bo$193bobo$38bo154b2o$39b2o$38b2o$6bo188b3o$4bobo101bo45b
o40bo$5b2o101bobo43bobo31b2o6bo$108b2o28bo10bo4b2o31bobo$139bo8bo40bo
$137b3o8b3o46b3o$110b3o84bo$8bo44bo56bo33bobo44b2o5bo$9b2o43b2o47b2o6b
o33b2o43b2o$8b2o43b2o47bobo40bo46bo$104bo$5b2o105b3o$4bobo44b2o59bo$6b
o45b2o52b2o5bo$51bo53b2o$107bo2$2b3o$4bo$3bo2$46b2o$47b2o$46bo!

14 left.

Edit 2:
9 more:

Code: Select all

x = 409, y = 95, rule = B3/S23
339bobo43bo$97bobo40bobo145bobo49b2o44b2o$3bobo44bobo45b2o41b2o43bobo
50bobo47b2o15bo33bo44b2o16bobo$4b2o45b2o45bo42bo45b2o16bo34b2o47bo15b
o86bobo8b2o$4bo46bo63bo71bo15b2o35bo64b3o39bo9bo35b2o9bo$22bo91bo89b2o
52bo37bo51b2o6bo36bo$20b2o92b3o77bo52bo8b2o39b2o43b2o3b2o7b3o$21b2o46b
o30b2o3bo37b2o3bo9bo36b2o51b2o7b2o32b2o3b2o44bobo43b2o$6b2o3bo41b2o3b
o8b2o31bobo3b2o35bobo3b2o6bo31b2o3b2o46b2o3b2o42bobo10b2o37bo43bobo4b
2o5b2o$6bobo3b2o39bobo3b2o7b2o31bo3b2o37bo3b2o7b3o29bobo10b2o38bobo47b
o10bobo42b2o37b2o6bo4bobo$7bo3b2o41bo3b2o53b2o75bo10bobo39bo53b2o5bo31b
3o9bobo4b2o37bo6bo$19b2o73b3o15bobo22b3o55b2o5bo45b2o5b2o28b3o9bobo9b
2o27bo5b2o3bo4bobo37bobo$3o15bobo26b3o46bo9b2o5bo25bo9b2o32b3o9bobo9b
2o27b3o9bobo3bobo30bo5b2o3bo9b2o27bo5bobo9bo26b2o11b2o9b3o$2bo9b2o5bo
29bo9b2o5b2o27bo10bobo9b2o18bo10bobo4b2o27bo5b2o3bo10bobo28bo5b2o3bo5b
o30bo5bobo15bo34bo14b2o21b2o21bo$bo10bobo9b2o22bo10bobo3bobo34b2o3bo9b
2o26b2o3bo4bobo26bo5bobo14bo29bo5bobo14b2o32bo56b2o6b2o21bo8b2o6b2o6b
o$8b2o3bo10bobo28b2o3bo5bo34bobo15bo24bobo9bo35bo52bo14bobo37b2o49bob
o7bo30b2o4b2o$7bobo14bo29bobo14b2o30bo42bo14b2o35b2o51b2o7bo39bobo48b
o39bo8bo$9bo46bo14bobo35b2o41b2o6b2o36bobo50bobo46bo$15b2o45b2o7bo37b
obo40bobo7bo35bo52bo$15bobo44bobo44bo42bo$15bo46bo20$381bo$382bo$380b
3o2$100b2o41b2o$6b2o45b2o13bo31bobo40bobo12bo227bo$6bobo44bobo12bobo30b
o42bo13bobo196bo29bo$7bo46bo13b2o88b2o97bo84b2o13bobo25b3o$257bobo31b
2o49bobo12b2o35b2o5b2o$106b2o8bo32b2o38b2o51b2o13b2o32bobo49bo51bo4bo
bo$12b2o8bo36b2o45bobo6b2o32bobo37bobo50bobo47bo55b2o44bo6bo$12bobo6b
2o36bobo45bo7bobo32bo39bo52bo53b2o8bo40bobo43bobo$13bo7bobo36bo134b2o
8bo42b2o47bobo6b2o41bo35bo9b2o$119b2o74bobo6b2o42bobo47bo7bobo76b2o$25b
2o35b2o50b2o3bobo30b2o42bo7bobo42bo134bobo$20b2o3bobo35b2o48bobo3bo33b
2o155b2o39b2o$19bobo3bo36bo52bo36bo55b2o41b2o52b2o3bobo39b2o$21bo181b
2o3bobo41b2o50bobo3bo40bo$202bobo3bo42bo54bo$204bo7$331bo$280bo51b2o$
178bo52bo49b2o48b2o$179b2o51b2o46b2o$178b2o51b2o4$388bo$389b2o$346bo41b
2o$114bo42bo137bo51b2o$20bo46bo46bobo40bobo33bo52bo49b2o48b2o58bo$20b
obo44bobo28bo10bo4b2o25bo10bo4b2o35b2o51b2o46b2o108bo$4bo10bo4b2o29bo
10bo4b2o30bo8bo33bo8bo41b2o51b2o153bo3b3o$5bo8bo37bo8bo35b3o8b3o29b3o
8b3o190b2o54bo$3b3o8b3o33b3o8b3o229b2o50b2o53b3o$104bobo40bobo41b2o51b
2o48b2o48bo$10bobo44bobo45b2o41b2o42b2o51b2o46bo$11b2o45b2o45bo42bo42b
o52bo$11bo46bo340b2o$398b2o$400bo2$339b2o$288b2o50b2o58b3o$186b2o51b2o
48b2o48bo60bo$187b2o51b2o46bo112bo$186bo52bo!

Re: OWSS synthesis project

Posted: August 5th, 2025, 2:58 am

by Chris857

Heads up, some of those syntheses above are not rewindable.

Re: OWSS synthesis project

Posted: August 5th, 2025, 8:39 am

by pifricted

Fixed 5 I found:

Code: Select all

x = 283, y = 106, rule = B3/S23
71bobo55bobo57bobo55bobo$4bobo65b2o56b2o58b2o56b2o$5b2o65bo57bo59bo57b
o$5bo84bo116bo58bo$24bo63b2o116bo58bo$23bo58bobo4b2o49bobo5bo51bobo3b
3o49bobo4b3o$15bobo5b3o48b2o6b2o48b2o6b2o4b2o44b2o6b2o48b2o6b2o$7b2o6b
2o57bobo6bo48bobo6bo5b2o43bobo6bo48bobo6bo$7bobo6bo58bo57bo59bo57bo$8b
o78b2o116b2o$68b3o10b2o3bobo37b3o10b2o45b3o10b2o3bobo37b3o10b2o4b2o$b
3o10b2o5b2o47bo10bo5bo40bo10bo5b2o41bo10bo5bo40bo10bo5bobo$3bo10bo5bo
bo46bo12bo9b2o33bo12bo3bobo40bo12bo9b2o33bo12bo5b2o$2bo12bo5bo58bobo9b
obo43bobo4bo52bobo8b2o45bobo$13bobo64b2o10bo45b2o10b2o46b2o11bo44b2o$
13b2o12b2o121bobo115b3o$26b2o48b2o6b2o48b2o6b2o6bo43b2o6b2o48b2o6b2o6b
o$9b2o6b2o9bo48b2o4b2o50b2o4b2o52b2o4b2o50b2o4b2o8bo$10b2o4b2o58bo8bo
48bo8bo50bo8bo48bo8bo$9bo8bo20$74b2o$60bobo11bobo$61b2o12bo195bo$61bo
25b2o182bobo$86bobo182b2o$87bo2$191b2o57b2o$78b2o2b2o107bobo56bobo13b
obo$77bobob2o49b2o58bo58bo14b2o$79bo3bo48bobo132bo$133bo64b2o57b2o$198b
o58bo$139b2o58bo58bo$5bo133bo57bobo7bo48bobo$5b2o133bo56b2o7b2o48b2o$
4bobo7b2o5b2o115bobo7bo57bobo58b2o$14bo5bobo115b2o7b2o118bobo$b2o12bo
5bo125bobo60b2o55bo$obo3b2o5bobo189b2o3bobo$2bo3bobo4b2o136b2o51bobo3b
o$6bo139b2o3bobo52bo$145bobo3bo$147bo9$51b2o$50bobo$52bo6$195bo58bo$196b
2o57b2o$136bo58b2o57b2o$9bobo125b2o$10b2o124b2o$10bo$5bobo$6b2o$6bo3$
70bo$71bo132bo7bo3bobo44bo7bo3bobo$69b3o132b2o7b2ob2o45b2o7b2ob2o$145b
o7bo3bobo33b2o8bobo6b2o3bo34b2o8bobo6b2o3bo$19bo125b2o7b2ob2o35b2o57b
2o$18b2o114b2o8bobo6b2o3bo34bo58bo$18bobo58bo7b2o46b2o$78b2o6bobo45bo
$16bo61bobo6bo$10b2o3b2o$11b2o2bobo$10bo210b2o57b2o$221bobo56bobo$162b
2o57bo58bo$162bobo$162bo!