## Slow 2-state spaceships

For discussion of other cellular automata.

### Slow 2-state spaceships

A thread to document all extremely slow spaceships that exist in 2-state rules, have speeds equal to or slower than c/10^3, and do not belong to any adjustable-speed families. The only one of these thus far which is one of my findings is the absolute slowest ship.

c/2068:
`x = 10, y = 9, rule = B34578/S4564bobo\$4b3o\$2b2o3b2o\$2b2o3b2o\$2o6bo\$bo7bo\$2o2bo3bo\$2b4ob2o\$2bobobo!`

c/5648: (Slowest range-1 outer-totalistic known)
`x = 12, y = 14, rule = B3457/S45684bo2bo\$4b4o\$2b8o\$2b2ob2ob2o\$obobo2bobobo\$2ob6ob2o\$ob3o2b3obo\$3ob4ob3o\$2ob6ob2o\$b3o4b3o\$b3o4b3o\$3b2o2b2o\$3bo4bo\$5b2o!`

c/40368:
`x = 81, y = 78, rule = R39,C0,M1,S2174..3710,B1884..3748,NM28bobo19bobo\$24bobob2o21b2obobo\$26b3o23b3o\$21bo2b4o6b13o6b4o2bo\$20bob5o4b19o4b5obo\$19bob5o3b23o3b5obo\$18b8ob27ob8o\$17b47o\$16b49o\$15b51o\$14b53o\$13b55o\$12b57o\$11b59o\$10b61o\$9b63o\$8b65o\$7bob63obo\$8b65o\$7b67o\$7b67o\$6b69o\$5b71o\$5b4ob61ob4o\$4b4ob63ob4o\$4b2o3b63o3b2o\$3b2o3b65o3b2o\$3bo4b65o4bo\$7b67o\$2bo4b67o4bo\$6b69o\$6b69o\$6b69o\$6b69o\$6b69o\$6b69o\$5b71o\$5b71o\$5b71o\$5b71o\$5b71o\$6b69o\$6b69o\$o5b69o5bo\$6b69o\$6b69o\$7b67o\$b2o4b67o4b2o\$3bo3b67o3bo\$2b3o3b65o3b3o\$3b3o2b65o2b3o\$3b4o2b63o2b4o\$4b4o2b61o2b4o\$4b73o\$5b71o\$5b71o\$6b69o\$7b67o\$8b65o\$8b65o\$9b63o\$10b61o\$11b59o\$12b57o\$13b55o\$14b53o\$15b51o\$16b49o\$17b47o\$18b8ob27ob8o\$19b7o3b23o3b7o\$21b6o4b19o4b6o\$22b6o9b7o9b6o\$25b4o23b4o\$25bob3o21b3obo\$27bob2o19b2obo\$29bo2bo15bo2bo\$32bo15bo!`

2c/2262:
`x = 61, y = 60, rule = R29,C0,M1,S1216..2068,B1050..2092,NM22b7o\$19b8o\$18b7o\$16b8o\$15b7o2b8o8bo\$14b21o6b2o\$13b25o4b3o\$12b28o2b4o\$12b30ob5o\$11b38o\$10b40o\$9b43o\$8b45o\$8b46o\$7b48o\$6b50o\$6b51o\$5b3ob49o\$5b2o2b49o\$4b2o2b51o\$8b51o\$7b53o\$7b48ob4o\$6b50ob3o\$6b50o2b2o\$6b50o2b3o\$5b51o3b2o\$5b51o3b2o\$5b51o4bo\$4b52o\$4b52o\$o3b52o\$o3b51o\$2o2b51o\$2o2b51o\$3ob51o\$4ob49o\$54o\$b52o\$b52o\$2b50o3bo\$2b50o2bo\$3b48ob3o\$3b51o\$4b50o\$5b48o\$6b46o\$7b45o\$9b42o\$10b40o\$11b39o\$12b5o2b30o\$14b4o3b27o\$16b3o4b24o\$17b3o5b21o\$19bo8b9ob7o\$37b7o\$35b8o\$34b7o\$31b8o!`

4c/273954: (SLOWEST KNOWN SHIP)
`x = 100, y = 100, rule = R45,C0,M1,S2885..4923,B2500..4973,NM40b20o\$36b9o10b9o\$34b7o5b8o5b7o\$32b6o6b12o6b6o\$30b6o6b16o6b6o\$28b6o5b22o5b6o\$27b5o5b26o5b5o\$25b6o3b32o3b6o\$24b5o4b34o4b5o\$22b6o3b38o3b6o\$21b6o2b42o2b6o\$20b6o2b44o2b6o\$19b6o2b46o2b6o\$18b6ob50ob6o\$16b7ob52ob7o\$15b7ob54ob7o\$15b6ob56ob6o\$14b6ob58ob6o\$13b6ob60ob6o\$12b6ob62ob6o\$11b6ob64ob6o\$10b6ob66ob6o\$9b6ob68ob6o\$9b82o\$8b84o\$7b5ob74ob5o\$7b4ob76ob4o\$6b4ob78ob4o\$5b90o\$5b43o4b43o\$4b4ob34o14b34ob4o\$4b37o18b37o\$3b37o20b37o\$3b3ob32o22b32ob3o\$3b34o26b34o\$2b4ob29o28b29ob4o\$2b33o30b33o\$2b32o32b32o\$b33o32b33o\$b32o34b32o\$b31o36b31o\$b31o36b31o\$31o38b31o\$31o38b31o\$31o38b31o\$30o40b30o\$30o40b30o\$30o40b30o\$30o40b30o\$31o38b31o\$31o38b31o\$31o38b31o\$31o38b31o\$3ob27o38b27ob3o\$3ob28o36b28ob3o\$b3ob27o36b27ob3o\$b3ob27o36b27ob3o\$b2o3b27o34b27o3b2o\$b3o2b28o32b28o2b3o\$b3o3b27o32b27o3b3o\$2b2o3b28o30b28o3b2o\$2b3o2b29o28b29o2b3o\$2b3o3b29o26b29o3b3o\$3b3o2b30o24b30o2b3o\$3b3o3b30o22b30o3b3o\$4b3o2b32o18b32o2b3o\$4b3o3b32o16b32o3b3o\$5b3o2b34o12b34o2b3o\$5b3o3b78o3b3o\$6b3o3b76o3b3o\$6b4o2b76o2b4o\$7b4o2b74o2b4o\$7b4o3b72o3b4o\$8b4o2b72o2b4o\$9b4o2b70o2b4o\$9b5o2b68o2b5o\$10b5o2b66o2b5o\$11b6ob64ob6o\$12b6ob62ob6o\$13b6ob60ob6o\$13b7ob58ob7o\$14b7ob56ob7o\$15b7ob54ob7o\$16b7ob52ob7o\$17b7ob50ob7o\$18b7ob48ob7o\$19b7ob46ob7o\$20b8ob42ob8o\$22b7ob40ob7o\$23b8ob36ob8o\$24b8o2b32o2b8o\$26b8o2b28o2b8o\$27b9o2b24o2b9o\$29b10o2b18o2b10o\$31b10o2b14o2b10o\$33b34o\$35b30o\$38b24o\$41b18o\$48b4o!`

8c/63194:
`x = 101, y = 103, rule = R50,C0,M1,S3563..6059,B3078..6129,NM47b7o\$41b4o11b4o\$38b4o17b4o\$35b4o23b4o\$33b4o27b4o\$31b5o29b5o\$30b4o2bo27bo2b4o\$28b7o14b3o14b7o\$27b7o10b13o10b7o\$25b8o7b21o7b8o\$24b9o5b25o5b9o\$23b9o4b29o4b9o\$22b9o3b33o3b9o\$21b9o2b37o2b9o\$20b9o2b39o2b9o\$19b9ob43ob9o\$18b9ob45ob9o\$17b67o\$16b69o\$15b71o\$14b73o\$13b75o\$12b77o\$11b79o\$10bo2b75o2bo\$11b79o\$11b79o\$11b79o\$10b81o\$9b83o\$9b83o\$8b85o\$7b5ob75ob5o\$7b3o2b77o2b3o\$6b3o3b77o3b3o\$6b2o3b79o3b2o\$5b2o3b81o3b2o\$5bo4b81o4bo\$bo2bo4b83o4bo2bo\$9b83o\$8b85o\$8b85o\$8b85o\$7b87o\$7b87o\$7b87o\$7b87o\$7b87o\$7b87o\$7b87o\$6b89o\$6b89o\$6b89o\$6b89o\$6b89o\$6b89o\$6b89o\$7b87o\$7b87o\$7b87o\$o6b87o6bo\$7b87o\$bo5b87o5bo\$2o6b85o6b2o\$obo5b85o5bobo\$b3o4b85o4b3o\$bob2o4b83o4b2obo\$2b4o3b83o3b4o\$2b5o3b81o3b5o\$2b6o2b81o2b6o\$3b6o2b79o2b6o\$3b7o2b77o2b7o\$4b7ob77ob7o\$5b7ob75ob7o\$5b8ob73ob8o\$6b89o\$7b87o\$7b87o\$8b85o\$9b83o\$10b81o\$11b79o\$12b77o\$13b75o\$14b73o\$15b71o\$17b67o\$18b65o\$19b63o\$19b63o\$20b9o2b39o2b9o\$21b9o3b35o3b9o\$23b8o3b33o3b8o\$24b8o4b29o4b8o\$25b8o5b25o5b8o\$26b8o7b19o7b8o\$28b7o14b3o14b7o\$30b6o29b6o\$31b6o27b6o\$33b5o25b5o\$36b4o21b4o\$38b3o19b3o\$41b2o15b2o!`

9c/121716:
`x = 89, y = 88, rule = R43,C0,M1,S2657..4491,B2268..4554,NM39b11o\$35bo3bo9bo3bo\$32bo4bo13bo4bo\$30bo3b2o17b2o3bo\$28bo3b3o19b3o3bo\$26bo3b3o23b3o3bo\$28b4o12bo12b4o\$23bo2b5o8b11o8b5o2bo\$22bo2b5o5b19o5b5o2bo\$21bob6o4b23o4b6obo\$22b6o3b27o3b6o\$21b6o2b31o2b6o\$18bob49obo\$17b55o\$16b57o\$15b59o\$14b61o\$13b63o\$12bob61obo\$11bob63obo\$10bob65obo\$11b67o\$10b69o\$10b69o\$9b71o\$8b73o\$8b4ob63ob4o\$7b4o2b63o2b4o\$6b4o2b65o2b4o\$6b3o3b65o3b3o\$5b3o3b67o3b3o\$5b2o3b69o3b2o\$4b2o4b69o4b2o\$4bo4b71o4bo\$9b71o\$9b71o\$8b73o\$8b73o\$8b73o\$8b73o\$8b73o\$7b75o\$7b75o\$7b75o\$7b75o\$7b75o\$7b75o\$o6b75o6bo\$o6b75o6bo\$o6b75o6bo\$2o5b75o5b2o\$2o5b75o5b2o\$b2o4b75o4b2o\$b2o5b73o5b2o\$b3o4b73o4b3o\$2b3o4b71o4b3o\$2b4o3b71o3b4o\$2b5o2b71o2b5o\$3b5o2b69o2b5o\$3b6ob69ob6o\$4b6ob67ob6o\$4b7ob65ob7o\$5b79o\$5b79o\$6b77o\$7b75o\$7b75o\$8b73o\$9b71o\$10b69o\$11b67o\$12b65o\$13b63o\$14b61o\$15b59o\$16b57o\$17b55o\$18b9ob33ob9o\$19b9o2b29o2b9o\$20b9o3b25o3b9o\$22b8o4b21o4b8o\$24b7o7b13o7b7o\$25b7o25b7o\$27b6o23b6o\$29b5o21b5o\$31b4o19b4o\$33b3o17b3o\$36b2o13b2o!`
Last edited by muzik on February 6th, 2019, 9:20 pm, edited 3 times in total.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3301
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Slow 2-state spaceships

Here are the slow diagonal spaceships, with otherwise the same restrictions:

c/1000 diagonal:
`x = 3, y = 4, rule = B2k3acijr4ejkqr5ajry6cin/S1c2aek3-acy4ciryz5acek6an7c8o\$2o\$b2o\$2o!`

c/1018 diagonal:
`x = 3, y = 3, rule = B2kn3aijkr4cqyz5acr6in7e8/S2aek3-aey4cinrty5aejkn6in7ebo\$3o\$o!`

c/1060 diagonal:
`x = 3, y = 5, rule = B2ik3aijry4eiktz5cenr7c/S02-cn3-aek4eqt5ainqr6-n7e2bo\$b2o\$2o\$bo\$2bo!`

c/1534 diagonal:
`x = 3, y = 3, rule = B2-ac3aikqy4ikqwy5eq6-an7e8/S2-cn3ijkry4aceiqr5ai6-c7ebo\$b2o\$2o!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3301
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Slow 2-state spaceships

Great LTL Solids!
How long did it take for you to find them?
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

Posts: 2903
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Slow 2-state spaceships

Saka wrote:Great LTL Solids!
How long did it take for you to find them?

The only solid I did find might have taken a few hours; I just left the computer running (with your script, btw) on the range-39 rule that I then manually converted to range 45.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3301
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Slow 2-state spaceships

muzik wrote:
Saka wrote:Great LTL Solids!
How long did it take for you to find them?

The only solid I did find might have taken a few hours; I just left the computer running (with your script, btw) on the range-39 rule that I then manually converted to range 45.

Hmm, cool!
To post something helpful, here's the slowest ship I've found, c/1842d:
`x = 50, y = 51, rule = R24,C0,M1,S838..1426,B724..1443,NM26b4o\$28b5o\$30b5o\$17bo13b6o\$15b2o6b8ob6o\$13b3o4b19o\$12b3o2b22o\$10b4o2b24o\$9b32o\$8b34o\$7b36o\$5b39o\$4b40o\$3b38ob3o\$2b40ob3o\$2b41ob2o\$b42o3bo\$b43o\$44o\$3ob41o\$2o2b41o\$2ob43o\$o2b43o\$3b43o\$3b43o\$3b44o\$3b44o\$4b43o\$4b43o2bo\$4b43ob2o\$5b41o2b2o\$5b41ob3o\$6b44o\$3bo2b43o\$3b2o2b42o\$4b2ob41o\$5b2ob39o\$5b42o\$6b40o\$7b38o\$7b36o\$8b34o\$9b27ob4o\$10b25ob3o\$10b23o2b3o\$11b20o3b3o\$12b6ob8o6b2o\$13b6o\$15b5o\$17b5o\$19b6o!`

I'm running a search on Range 66 right now.
Last edited by Saka on February 7th, 2019, 3:57 am, edited 1 time in total.
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

Posts: 2903
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Slow 2-state spaceships

Saka wrote:
muzik wrote:To post something helpful, here's the slowest ship I've found, c/1842o:
`x = 50, y = 51, rule = R24,C0,M1,S838..1426,B724..1443,NM26b4o\$28b5o\$30b5o\$17bo13b6o\$15b2o6b8ob6o\$13b3o4b19o\$12b3o2b22o\$10b4o2b24o\$9b32o\$8b34o\$7b36o\$5b39o\$4b40o\$3b38ob3o\$2b40ob3o\$2b41ob2o\$b42o3bo\$b43o\$44o\$3ob41o\$2o2b41o\$2ob43o\$o2b43o\$3b43o\$3b43o\$3b44o\$3b44o\$4b43o\$4b43o2bo\$4b43ob2o\$5b41o2b2o\$5b41ob3o\$6b44o\$3bo2b43o\$3b2o2b42o\$4b2ob41o\$5b2ob39o\$5b42o\$6b40o\$7b38o\$7b36o\$8b34o\$9b27ob4o\$10b25ob3o\$10b23o2b3o\$11b20o3b3o\$12b6ob8o6b2o\$13b6o\$15b5o\$17b5o\$19b6o!`

Isn't that c/1842d?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3301
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Slow 2-state spaceships

Is there any range-1 non-totalistic isotropic ones?
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1032
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Slow 2-state spaceships

All four of the ships in muzik's second post are in range-1 isotropic non-totalistic rules.

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Slow 2-state spaceships

77topaz wrote:All four of the ships in muzik's second post are in range-1 isotropic non-totalistic rules.

But no orthogonal.
This post was brought to you by the Element of Magic.

Plz correct my grammar mistakes. I'm still studying English.

Working on:

Nothing.

Favorite gun ever:
`#C Favorite Gun. Found by me.x = 4, y = 6, rule = B2e3i4at/S1c23cijn4ao2bo\$4o3\$4o\$o2bo!`
Hunting

Posts: 1032
Joined: September 11th, 2017, 2:54 am
Location: Ponyville, Equestria

### Re: Slow 2-state spaceships

c/40002o (I also posted in LTL thread but I guess it fits here as well)
`x = 117, y = 116, rule = R49,C0,M1,S3423..5823,B2956..5889,NM52b12o\$49b18o\$47b22o\$45b26o\$44b28o\$42b8o19b5o\$41b5o26b3o\$40b3o8b9o15bo\$39b2o7b15o\$38bo6b21o\$43b24o\$41b28o\$39b31o\$37b6ob28o\$36b5o2b30o\$35b4o3b32o\$34b4o3b34o\$32b4o4b36o\$32b3o4b38o\$31b2o5b40o\$29b3o5b42o\$29b2o5b44o\$28b2o6b45o\$27bo7b46o\$26bo7b48o\$25bo7b50o\$24bo7b52o\$23bo7b54o\$22bo7b56o\$21bo7b58o\$20bo7b60o9bo\$19b2o6b62o9bo\$19bo6b64o8b2o\$18bo6b66o8b2o\$17bo6b68o8b2o\$16b2o4b72o7bo\$16bo4b74o6b2o\$15bo4b76o6b2o\$14b2o3b78o6bo\$8bo5bo3b80o5b2o\$7bo5b2o2b39o3b40o3bobo3bo\$6b2o5bo2b37o9b38o4b2o3bo\$5b3o4b2ob37o12b37o2bob2o2b2o\$5b2o5bob37o14b37o3b2o3bo\$4b3o4bob36o17b37obobo3b2o\$4b3o4bob35o20b37ob2o2b3o\$3b3o5b36o22b35o2b2o3b2o\$3b3o4b36o24b35o2b2o2b3o\$2b4o4b35o26b35ob2o2b3o\$2b3o5b35o26b35o2bo2b4o\$b4o4b35o28b35ob2ob4o\$b4o4b34o30b34ob2ob5o\$b4o4b33o32b36ob5o\$b4o3b34o32b36ob5o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$b4o3b34o32b36ob5o\$b4o4b33o32b36ob5o\$b4o4b34o30b34ob2ob5o\$b4o4b35o28b35ob2ob4o\$2b3o5b35o26b35o2bo2b4o\$2b4o4b35o26b35ob2o2b3o\$3b3o4b36o24b35o2b2o2b3o\$3b3o5b36o22b35o2b2o3b2o\$4b3o4bob35o20b37ob2o2b3o\$4b3o4bob36o17b37obobo3b2o\$5b2o5bob37o14b37o3b2o3bo\$5b3o4b2ob37o12b37o2bob2o2b2o\$6b2o5bo2b37o9b38o4b2o3bo\$7bo5b2o2b39o3b40o3bobo3bo\$8bo5bo3b80o5b2o\$14b2o3b78o6bo\$15bo4b76o6b2o\$16bo4b74o6b2o\$16b2o4b72o7bo\$17bo6b68o8b2o\$18bo6b66o8b2o\$19bo6b64o8b2o\$19b2o6b62o9bo\$20bo7b60o9bo\$21bo7b58o\$22bo7b56o\$23bo7b54o\$24bo7b52o\$25bo7b50o\$26bo7b48o\$27bo7b46o\$28b2o6b45o\$29b2o5b44o\$29b3o5b42o\$31b2o5b40o\$32b3o4b38o\$32b4o4b36o\$34b4o3b34o\$35b4o3b32o\$36b5o2b30o\$37b6ob28o\$39b31o\$41b28o\$43b24o\$38bo6b21o\$39b2o7b15o\$40b3o8b9o15bo\$41b5o26b3o\$42b8o19b5o\$44b28o\$45b26o\$47b22o\$49b18o\$52b12o!`
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

Posts: 2903
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Slow 2-state spaceships

Saka wrote:c/40002o (I also posted in LTL thread but I guess it fits here as well)
`Slower than slow`

That thing is like the gems one, but it just looks like an oscillator with a very very long period.
Of course, it does move. It’s just funny how there are roomba bugs that become oscillators and then there are very slow bugs that look like oscillators.
My rules:
They can be found here

Also, the tree game
Bill Watterson once wrote: "How do soldiers killing each other solve the world's problems?"

Moosey

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Location: A house, or perhaps the OCA board.