Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 7th, 2026, 1:26 pm
This and the (7,1)c/8 look so...different from other relativistic oblique spaceships. What was the search methodology used to find it?
ConwayLife.com
Forums for Conway's Game of Life
https://conwaylife.com/forums/
Smallest Spaceships Supporting Specific Speeds (5s) Project
Page 58 of 58
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 7th, 2026, 4:17 pm
They used LLS to find promising frontends and backends. Then they searched those rules with LLSSS using a custom search orientation.Aleph wrote: October 7th, 2026, 1:26 pmThis and the (7,1)c/8 look so...different from other relativistic oblique spaceships. What was the search methodology used to find it?
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 7th, 2026, 6:26 pm
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.Aleph wrote: October 7th, 2026, 1:26 pmThis and the (7,1)c/8 look so...different from other relativistic oblique spaceships. What was the search methodology used to find it?
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
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 9th, 2026, 4:24 am
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
Edit 1:
1 cell off
New smallest (8,1)c/9 minpop 427
Edit 2:
Smallest known (7,1)c/8 (minpop 354) from a relative of the minpop 427 (8,1)c/9
If this rule had B8 this would be an incredibly small (8,1)c/9
Code: Select all
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!1 cell off
Code: Select all
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!
Code: Select all
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!
Smallest known (7,1)c/8 (minpop 354) from a relative of the minpop 427 (8,1)c/9
Code: Select all
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!Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 9th, 2026, 8:06 am
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
Maybe you can find it
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 10th, 2026, 12:00 am
(9,1)c/10:
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.
Code: Select all
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!Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 10th, 2026, 12:28 am
What happens in an (10,1)c/11 ship search?AforAmpere wrote: October 10th, 2026, 12:00 am (9,1)c/10: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.Code: Select all
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 10th, 2026, 1:27 am
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:
Code: Select all
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!
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 12th, 2026, 11:41 pm
Even smaller (7,1)c/8 minpop 223
Code: Select all
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!Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 20th, 2026, 12:03 am
2 clean 10c/11 wickstretchers
Edit 1:
50c/55 wickstretcher
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
There also is a 1 cell removing edgesignal in the rule
Code: Select all
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!Code: Select all
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!
50c/55 wickstretcher
Code: Select all
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!Code: Select all
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!Code: Select all
x = 15, y = 9, rule = B2ack3aejqr4cekyz5-cjkn6ci7/S01e2i3jny4-cijk5-j6-in78
4bo$5b10o$15o$15o$15o$15o$15o$15o$15o!
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 24th, 2026, 2:08 pm
(47,42)c/344 (new speed)
Code: Select all
x = 44, y = 33, rule = B2in3-ekny4e6cin/S2aek3-acy4iz5ae6cin
b3o$o2bo$o2bo$3o18$39bobo$12b2o24bobobo$13bo23bo5bo$7b3o2bo2bo20b3obo
$7bo8b2o19bo2bobo$7bobo3bo26b3o$8b2o2$30bo$28bo$25bob2o$28bo!
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 25th, 2026, 11:31 pm
10c/11!!!
This is the fastest non C speed achievable in INT
This is the fastest non C speed achievable in INT
Code: Select all
x = 39, y = 24, rule = B2ac3aer4aceikqw56-en7c8/S012-ac3ky4aceikwz5-enq6-en78
10bob3ob3ob3ob3obo$4bob3obob3ob2obob2ob3obob3obo$2b5o3bobobobob3obobo
bobo3b5o$b4o2b3ob17ob3o2b4o$2b2ob29ob2o$b7o2b19o2b7o$ob5ob23ob5obo$bo
b6ob5o2b5o2b5ob6obo$3bob6ob4o7b4ob6obo$4bob11obobob11obo$5bob25obo$6b
ob23obo$7bob21obo$8bob19obo$9bob17obo$10bob15obo$11bob13obo$12bob11ob
o$14bob7obo$15bob5obo$16bob3obo$17bobobo$18bobo$19bo!
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 26th, 2026, 12:01 am
...That we know of.NimbleRogue wrote: October 25th, 2026, 11:31 pm 10c/11!!!
This is the fastest non C speed achievable in INTCode: Select all
x = 39, y = 24, rule = B2ac3aer4aceikqw56-en7c8/S012-ac3ky4aceikwz5-enq6-en78 10bob3ob3ob3ob3obo$4bob3obob3ob2obob2ob3obob3obo$2b5o3bobobobob3obobo bobo3b5o$b4o2b3ob17ob3o2b4o$2b2ob29ob2o$b7o2b19o2b7o$ob5ob23ob5obo$bo b6ob5o2b5o2b5ob6obo$3bob6ob4o7b4ob6obo$4bob11obobob11obo$5bob25obo$6b ob23obo$7bob21obo$8bob19obo$9bob17obo$10bob15obo$11bob13obo$12bob11ob o$14bob7obo$15bob5obo$16bob3obo$17bobobo$18bobo$19bo!
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 26th, 2026, 12:06 am
There's a proof some time back.
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 26th, 2026, 12:21 am
This is the proof from a few weeks ago. It shows by extension that 10c/11 is the fastest period which can occur orthogonally below lightspeedOogaBooga_ wrote: October 26th, 2026, 12:01 am...That we know of.NimbleRogue wrote: October 25th, 2026, 11:31 pm 10c/11!!!
This is the fastest non C speed achievable in INTCode: Select all
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 29th, 2026, 9:22 am
Woah. What was the search methodology for this?
Re: Smallest Spaceships Supporting Specific Speeds (5s) Project
Posted: October 29th, 2026, 11:13 am
NimbleRogue constructed a plausible stable backend and then used LLS for a triangle-shaped solution with this backend.