Smallest Spaceships Supporting Specific Speeds (5s) Project

[Aleph]

Double post, but (8,1)c/9:

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(...)

This and the (7,1)c/8 look so...different from other relativistic oblique spaceships. What was the search methodology used to find it?

[LaundryPizza03]

Double post, but (8,1)c/9:

Code: Select all

(...)

This and the (7,1)c/8 look so...different from other relativistic oblique spaceships. What was the search methodology used to find it?

They used LLS to find promising frontends and backends. Then they searched those rules with LLSSS using a custom search orientation.

[NimbleRogue]

Double post, but (8,1)c/9:

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(...)

This and the (7,1)c/8 look so...different from other relativistic oblique spaceships. What was the search methodology used to find it?

I found some p1 orthogonal backends and then thought about extending the concept to obliques. May13's OT (2,1)c/3s were the inspiration for these specific backend. Me and Ampere have been working on finding completions for a bit now.
Here are some preliminary results
https://conwaylife.com/forums/viewtopic ... 98#p235398

There were a bunch of things that were tried but what ended up planning out was doing LLS searches for frontends while forcing the trailing edge to be completely filled while also requiring a partial backend to work. I have attached the LLS search where the precurser rule to the (7,1)c/8 was found. After finding a frontend the key was running LLSSS on a bunch of related rules to see if any ships pop out

[NimbleRogue]

Me and Ampere are working on finding (9,1)c/10 there are some worries about finding period 1 backends and signals that will work, but I expect something will turn up soon

If this rule had B8 this would be an incredibly small (8,1)c/9

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x = 22, y = 23, rule = B2-ik3-aiky4cqtw5-ijy67/S012i3cjky4acejkry5-ac6-i78
4b3ob3ob3obo$2b2o4b6obob3o$2bob5ob5obobo$b4ob10ob4o$bo4b14o$19o$2b16o$
2b15o$2b14o$2b13o$2b12o$2b11o$2b10o$2b9o$2b8o$2b7o$2b6o$2b5o$2b4o$2b3o
$2b2o$3o$bo!

Edit 1:

1 cell off

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x = 21, y = 24, rule = B2ace3-aiky4cqtw5-ijy67/S012in3cjky4-inqwz5-ac6-i78
8bobo$3b3o2bobo2b3obo$b2obob2ob2ob3o3bo$2b2o2bob2ob2obobob2o$2o2b12obo
$b19o$2b17o$3b16o$4b15o$5b14o$6b13o$7b12o$8b11o$9b10o$10b9o$11b8o$12b
7o$13b6o$14b5o$15b4o$16b3o$17b2o$18b3o$19bo!

New smallest (8,1)c/9 minpop 427

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x = 36, y = 39, rule = B2-ik3-aiky4ejtwyz5-ciry67e8/S012i3cjky4-intwz5-ace678
8b3o$2bob2o4b4ob3o$bo4bobobo4bo2bo$2b4o2b3obo3b2o$11obob4o$b15obo2bo$
2b6ob10obo$3b18o$4b15obo$5b14o2b4o$6b17o$7b19o$8b18o$9b16o$10b17o$11b
15o$12b14o$13b13o$14b12o$15b13o$16b11obo$17b13o$18b11obo$19b12o$20b10o
$21b11o$22b9obo$23b7o4bo$24b12o$25b10o$26b6ob2o$27b8o$28b7o$29b7o$30b
4o$31b3o$32b2o$33b3o$34bo!

Edit 2:

Smallest known (7,1)c/8 (minpop 354) from a relative of the minpop 427 (8,1)c/9

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x = 30, y = 32, rule = B2ace3cejny4qtyz5-k6ace78/S01c2ikn3-einr4ajkr5ijknq678
6bobobobob3o$4b2obo4bob2ob2o$bobob3obob4o2b2o$2ob12obobo$b10ob3ob4o$2b
10ob3ob3obo$3b9o2b5o2bo$4b12o2b3o$5b12o4bo$6b15obo$7b15o$8b13o$9b13o$
10b18o$11b16o$12b14o$13b14o$14b14o$15b13o$16b13o$17b12o$18b11o$19b10o$
20b9o$21b8o$22b7o$23b7o$24b4o$25b3o$26b2o$27b3o$28bo!

[yyh_baboon]

With recent progress I’m somewhat positive about the existence of lightspeed spaceships with a clean backend and signal emitters in the front that sends signals which either extends or collapses the side.
Maybe you can find it

[AforAmpere]

(9,1)c/10:

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x = 125, y = 128, rule = B2aci3ceqry4-cejrz5-eikq6aek78/S01e2-ai3cnq4-nw5-ajy6-e78
110bo3bo$103bob3o2b5o2b2o$100b2o2b2o2b5o2b2o$99b4o2b8o2b2o4b2o$100b4o
2b19o$99bob3o2b5o3b2ob7o$98bob6ob16o$96b10o2b14o$94b2o2b8ob14o$92b28o$
93b26o$90b28o$89bob26o$90b26o$89b26o$88b26o$84b3ob25o$86bob24o$84b3ob
23o$82bobo2b23o$83b4ob21o$82bobobob20o$81b3ob22o$79bo2b2ob21o$80b2o2b
21o$79b25o$78b25o$77b2ob22o$77bob22o$78bob20o$74b3obob19o$75b23o$75b
22o$72b3ob20o$74b21o$72b3ob18o$70bobobobob15o$69b2o3b18o$70b21o$69bob
19o$68b2ob18o$63b3o3bob17o$62bo2bo2bob17o$62bobobob18o$65b20o$62b2ob
19o$62bob19o$58b2ob2ob18o$57bo4b19o$57bob21o$57b22o$58bob18o$57b20o$
52b2ob21o$51bob2ob6ob12o$51b7ob15o$51bob5ob14o$53b5ob13o$50b21o$50b20o
$42bobo4bob18o$42bo6b19o$42b2ob22o$42b2o2bo2b17o$37b2o2b4o3b17o$36b28o
$34b3ob25o$33b2obob24o$33b3o2b23o$34b3ob22o$33b4ob21o$36b22o$32bob23o$
32b24o$29bobob22o$28bob24o$28b25o$27b25o$27bob22o$27b2ob20o$27bo3b18o$
27b2ob18o$25b22o$22bob22o$20b25o$20b24o$20b2o2b19o$23b19o$19b22o$19b
12ob8o$21b9ob8o$18b20o$16bob19o$18b18o$15b2ob17o$14b3o2b15o$14b19o$13b
19o$12bob17o$14b16o$14b15o$12b16o$13b14o$10b16o$10b15o$8b16o$8b15o$5b
2o2b13o$6bob13o$5b2ob12o$4b15o$b6ob10o$2b6ob8o$bob13o$2b2ob10o$4b10o$
3b10o$b11o$2b9o$ob8o$2b7o$3b5o$bob4o$3b3o$2b3o$3bo$bo$2bo!

With that, all possible (n,1)c/(n+1) ships have been found, as very's proof extended to obliques eliminates the possibility of any others.

[WhiteHawk]

(9,1)c/10:

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With that, all possible (n,1)c/(n+1) ships have been found, as very's proof extended to obliques eliminates the possibility of any others.

What happens in an (10,1)c/11 ship search?

[AforAmpere]

What happens in an (10,1)c/11 ship search?

You end up getting nothing out. Frontends at that speed can't exist, so LLS searches for them UNSAT (very quickly, too).

Also, smaller (9,1)c/10:

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x = 71, y = 71, rule = B2aci3eqr4ainqtwy5ajnry6aei78/S01e2-ai3nq4-cnw5-ajy6-ei78
67bo$66b2o$65b4o$64b5o$63b5o$62b5o$61b6ob3o$60b11o$59b10o$58b13o$57b
12o$56b10ob4o$55b11ob3o$54b12o3b2o$53b14o2bo$52b16ob2o$51b19o$50b19obo
$49b21o$48b16o2b3obo$47b21o2bo$46b18o2b3o$45b23o$44b23ob2o$43b24ob2o$
42b19o2b2obobo$41b20o2bo$40b18o4b3o$39b19o2b4o$38b23o2bo$37b19o2b5o$
36b20o3b2o$35b25ob2o$34b19ob2o2bob3o$33b20ob3o3bo$32b19o2bo5bo$31b17ob
o$30b23o$29b19o2bobo$28b20ob2obo$27b22o2bo$26b22o$25b22o$24b21o2bo$23b
25o$22b19obob3o$21b18ob6o$20b21ob3o$19b24obo$18b18ob4ob2o$17b18o3b2o$
16b19ob2ob2o$15b20o4bo$14b20obobobo$13b22o$12b17o2b3obo$11b17o2b5o$10b
17o2bobo2bo$9b18o3b4o$8b22obo$7b19ob4ob2o$6b18ob2ob2ob3o$5b22o4bo$4b
23o3bo$3b19ob4obo$2b21ob2ob2o$o2bo3b16o3bo$bo3bo4bo3bo3b5o$8bo3bo3bo3b
2o2$20bo!

[NimbleRogue]

Even smaller (7,1)c/8 minpop 223

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x = 21, y = 24, rule = B2-ik3cejny4ktyz5-jry67e8/S01c2ik3-einr4-wy5cinqr678
3bo2b3obo$2bo2b2ob5ob3o$2b4o3bo3bo2bo$2b4o4b3obobo$9obo4bobo$b8o3bo6bo
$2b10ob6o$3b18o$4b16o$5b15o$6b14o$7b13o$8b12o$9b11o$10b10o$11b9o$12b8o
$13b7o$14b7o$15b4o$16b3o$17b2o$18b3o$19bo!

[NimbleRogue]

2 clean 10c/11 wickstretchers

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x = 41, y = 19, rule = B23acek4-ceqy5aciky6-in78/S01e2en3-aikr4-enrty5-aqr678
15bob3ob3obo$7b2obob2obo2b5o2bob2obob2o$3b3ob7o2bob5obo2b7ob3o$b3o2b5o
bo2bob7obo2bob5o2b3o$o2b2o2b5o3bob7obo3b5o2b2o2bo$b11obob11obob11o$b
39o$b39o$b39o$b39o$b39o$b39o$b39o$b11obob11obob11o$o2b2o2b5o3bob7obo3b
5o2b2o2bo$b3o2b5obo2bob7obo2bob5o2b3o$3b3ob7o2bob5obo2b7ob3o$7b2obob2o
bo2b5o2bob2obob2o$15bob3ob3obo!

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x = 41, y = 30, rule = B2-e3aceqy4ceiqrw5-eikq6-a7c8/S12ck3acejq4-aejrz5-kny6-e78
20bo$8bo2b2obob2o2bo2b2obob2o2bo$5b2o3b2o2b2ob7ob2o2b2o3b2o$b2o2bo2b2o
bo3b4obob4o3bob2o2bo2b2o$b2o2bo2b2ob2obob3obob3obob2ob2o2bo2b2o$7o3bo
4b4obob4o4bo3b7o$b10ob2o3bob3obo3b2ob10o$b6o2b3ob15ob3o2b6o$b5ob5ob3o
2b5o2b3ob5ob5o$b10o2b15o2b10o$b12ob13ob12o$b9obob15obob9o$b5ob27ob5o$b
4ob29ob4o$b39o$b39o$b39o$b39o$b39o$b39o$b39o$b39o$b39o$b39o$b39o$b39o$
b39o$b39o$b39o$o39bo!

Edit 1:
50c/55 wickstretcher

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x = 41, y = 35, rule = B2ack3aejqr4cekyz5-cjkn6ci7/S01e2i3jny4-cijk5-j6-in78
11b3ob3ob3ob3ob3o$5b3ob3o2b2obo2bo2bob2o2b3ob3o$bob4o3bo2b2o3b5o3b2o2b
o3b4obo$3obobob4ob2o3bobobo3b2ob4obobob3o$b3ob6o3b3o3bo3b3o3b6ob3o$b3o
b6o4bo2b5o2bo4b6ob3o$b8ob2obobobob3obobobob2ob8o$b6obob2o2bo3b5o3bo2b
2obob6o$b4o5b4o2b9o2b4o5b4o$b5o2b9o7b9o2b5o$b16o3bo3b16o$b16obo3bob16o
$b16ob5ob16o$b39o$b19ob19o$b39o$b39o$b39o$b39o$b39o$b19ob19o$b39o$b16o
b5ob16o$b16obo3bob16o$b16o3bo3b16o$b5o2b9o7b9o2b5o$b4o5b4o2b9o2b4o5b4o
$b6obob2o2bo3b5o3bo2b2obob6o$b8ob2obobobob3obobobob2ob8o$b3ob6o4bo2b5o
2bo4b6ob3o$b3ob6o3b3o3bo3b3o3b6ob3o$3obobob4ob2o3bobobo3b2ob4obobob3o$
bob4o3bo2b2o3b5o3b2o2bo3b4obo$5b3ob3o2b2obo2bo2bob2o2b3ob3o$11b3ob3ob
3ob3ob3o!

Not only is there an asymmetric 50c/55 wickstretcher in the rule, and the same edge extensions in the first 9c/10 wickstretcher rule work here too

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x = 45, y = 92, rule = B2ack3aejqr4cekyz5-cjkn6ci7/S01e2i3jny4-cijk5-j6-in78
11bob3ob3ob3ob3obo$5bob3obo3bo2bo3bo2bo3bob3obo$2b2ob2o4bob4o7b4obo4b
2ob2o$o2bob2obo2b4ob2ob3ob2ob4o2bob2obo2bo$b2ob3ob3ob6o2bo2b6ob3ob3ob
2o$b2obob5ob3o3bobobo3b3ob5obob2o$b10ob2obo2b5o2bob2ob10o$b12o3bob5o2b
o2b12o$b7ob3o4bob5obobo2b4ob8o$b4o3bob3o3b9obob5o3b5o$b5o2b15o2b9ob6o$
b16o2b4obob15o$b16ob6o2b17o$b41o$b41o$b41o$b27ob15o$b42o$b15ob7ob18o$b
4ob37o$b44o$b14ob6ob21o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b34ob8o$b
43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b
43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b
43o$b43o$b43o$b43o$b34ob8o$b43o$b43o$b43o$b43o$b43o$b43o$b43o$b14ob6ob
21o$b44o$b4ob37o$b15ob7ob18o$b42o$b27ob15o$b41o$b41o$b41o$b16ob6o2b17o
$b16o2b4obob15o$b5o2b15o2b9ob6o$b4o3bob3o3b9obob5o3b5o$b7ob3o4bob5obob
o2b4ob8o$b12o3bob5o2bo2b12o$b10ob2obo2b5o2bob2ob10o$b2obob5ob3o3bobobo
3b3ob5obob2o$b2ob3ob3ob6o2bo2b6ob3ob3ob2o$o2bob2obo2b4ob2ob3ob2ob4o2bo
b2obo2bo$2b2ob2o4bob4o7b4obo4b2ob2o$5bob3obo3bo2bo3bo2bo3bob3obo$11bob
3ob3ob3ob3obo!

There also is a 1 cell removing edgesignal in the rule

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x = 15, y = 9, rule = B2ack3aejqr4cekyz5-cjkn6ci7/S01e2i3jny4-cijk5-j6-in78
4bo$5b10o$15o$15o$15o$15o$15o$15o$15o!