## Slow 2-state spaceships

For discussion of other cellular automata.
muzik
Posts: 3783
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### 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:

Code: Select all

``````x = 10, y = 9, rule = B34578/S456
4bobo\$4b3o\$2b2o3b2o\$2b2o3b2o\$2o6bo\$bo7bo\$2o2bo3bo\$2b4ob2o\$2bobobo!
``````
c/5648: (Slowest range-1 outer-totalistic known)

Code: Select all

``````x = 12, y = 14, rule = B3457/S4568
4bo2bo\$4b4o\$2b8o\$2b2ob2ob2o\$obobo2bobobo\$2ob6ob2o\$ob3o2b3obo\$3ob4ob3o\$
2ob6ob2o\$b3o4b3o\$b3o4b3o\$3b2o2b2o\$3bo4bo\$5b2o!
``````
c/40368:

Code: Select all

``````x = 81, y = 78, rule = R39,C0,M1,S2174..3710,B1884..3748,NM
28bobo19bobo\$24bobob2o21b2obobo\$26b3o23b3o\$21bo2b4o6b13o6b4o2bo\$20bob
5o4b19o4b5obo\$19bob5o3b23o3b5obo\$18b8ob27ob8o\$17b47o\$16b49o\$15b51o\$14b
53o\$13b55o\$12b57o\$11b59o\$10b61o\$9b63o\$8b65o\$7bob63obo\$8b65o\$7b67o\$7b
67o\$6b69o\$5b71o\$5b4ob61ob4o\$4b4ob63ob4o\$4b2o3b63o3b2o\$3b2o3b65o3b2o\$3b
o4b65o4bo\$7b67o\$2bo4b67o4bo\$6b69o\$6b69o\$6b69o\$6b69o\$6b69o\$6b69o\$5b71o\$
5b71o\$5b71o\$5b71o\$5b71o\$6b69o\$6b69o\$o5b69o5bo\$6b69o\$6b69o\$7b67o\$b2o4b
67o4b2o\$3bo3b67o3bo\$2b3o3b65o3b3o\$3b3o2b65o2b3o\$3b4o2b63o2b4o\$4b4o2b
61o2b4o\$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:

Code: Select all

``````x = 61, y = 60, rule = R29,C0,M1,S1216..2068,B1050..2092,NM
22b7o\$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\$5b
48o\$6b46o\$7b45o\$9b42o\$10b40o\$11b39o\$12b5o2b30o\$14b4o3b27o\$16b3o4b24o\$
17b3o5b21o\$19bo8b9ob7o\$37b7o\$35b8o\$34b7o\$31b8o!
``````
4c/273954: (SLOWEST KNOWN SHIP)

Code: Select all

``````x = 100, y = 100, rule = R45,C0,M1,S2885..4923,B2500..4973,NM
40b20o\$36b9o10b9o\$34b7o5b8o5b7o\$32b6o6b12o6b6o\$30b6o6b16o6b6o\$28b6o5b
22o5b6o\$27b5o5b26o5b5o\$25b6o3b32o3b6o\$24b5o4b34o4b5o\$22b6o3b38o3b6o\$
21b6o2b42o2b6o\$20b6o2b44o2b6o\$19b6o2b46o2b6o\$18b6ob50ob6o\$16b7ob52ob7o
\$15b7ob54ob7o\$15b6ob56ob6o\$14b6ob58ob6o\$13b6ob60ob6o\$12b6ob62ob6o\$11b
6ob64ob6o\$10b6ob66ob6o\$9b6ob68ob6o\$9b82o\$8b84o\$7b5ob74ob5o\$7b4ob76ob4o
\$6b4ob78ob4o\$5b90o\$5b43o4b43o\$4b4ob34o14b34ob4o\$4b37o18b37o\$3b37o20b
37o\$3b3ob32o22b32ob3o\$3b34o26b34o\$2b4ob29o28b29ob4o\$2b33o30b33o\$2b32o
32b32o\$b33o32b33o\$b32o34b32o\$b31o36b31o\$b31o36b31o\$31o38b31o\$31o38b31o
\$31o38b31o\$30o40b30o\$30o40b30o\$30o40b30o\$30o40b30o\$31o38b31o\$31o38b31o
\$31o38b31o\$31o38b31o\$3ob27o38b27ob3o\$3ob28o36b28ob3o\$b3ob27o36b27ob3o\$
b3ob27o36b27ob3o\$b2o3b27o34b27o3b2o\$b3o2b28o32b28o2b3o\$b3o3b27o32b27o
3b3o\$2b2o3b28o30b28o3b2o\$2b3o2b29o28b29o2b3o\$2b3o3b29o26b29o3b3o\$3b3o
2b30o24b30o2b3o\$3b3o3b30o22b30o3b3o\$4b3o2b32o18b32o2b3o\$4b3o3b32o16b
32o3b3o\$5b3o2b34o12b34o2b3o\$5b3o3b78o3b3o\$6b3o3b76o3b3o\$6b4o2b76o2b4o\$
7b4o2b74o2b4o\$7b4o3b72o3b4o\$8b4o2b72o2b4o\$9b4o2b70o2b4o\$9b5o2b68o2b5o\$
10b5o2b66o2b5o\$11b6ob64ob6o\$12b6ob62ob6o\$13b6ob60ob6o\$13b7ob58ob7o\$14b
7ob56ob7o\$15b7ob54ob7o\$16b7ob52ob7o\$17b7ob50ob7o\$18b7ob48ob7o\$19b7ob
46ob7o\$20b8ob42ob8o\$22b7ob40ob7o\$23b8ob36ob8o\$24b8o2b32o2b8o\$26b8o2b
28o2b8o\$27b9o2b24o2b9o\$29b10o2b18o2b10o\$31b10o2b14o2b10o\$33b34o\$35b30o
\$38b24o\$41b18o\$48b4o!``````
8c/63194:

Code: Select all

``````x = 101, y = 103, rule = R50,C0,M1,S3563..6059,B3078..6129,NM
47b7o\$41b4o11b4o\$38b4o17b4o\$35b4o23b4o\$33b4o27b4o\$31b5o29b5o\$30b4o2bo
27bo2b4o\$28b7o14b3o14b7o\$27b7o10b13o10b7o\$25b8o7b21o7b8o\$24b9o5b25o5b
9o\$23b9o4b29o4b9o\$22b9o3b33o3b9o\$21b9o2b37o2b9o\$20b9o2b39o2b9o\$19b9ob
43ob9o\$18b9ob45ob9o\$17b67o\$16b69o\$15b71o\$14b73o\$13b75o\$12b77o\$11b79o\$
10bo2b75o2bo\$11b79o\$11b79o\$11b79o\$10b81o\$9b83o\$9b83o\$8b85o\$7b5ob75ob5o
\$7b3o2b77o2b3o\$6b3o3b77o3b3o\$6b2o3b79o3b2o\$5b2o3b81o3b2o\$5bo4b81o4bo\$b
o2bo4b83o4bo2bo\$9b83o\$8b85o\$8b85o\$8b85o\$7b87o\$7b87o\$7b87o\$7b87o\$7b87o\$
7b87o\$7b87o\$6b89o\$6b89o\$6b89o\$6b89o\$6b89o\$6b89o\$6b89o\$7b87o\$7b87o\$7b
87o\$o6b87o6bo\$7b87o\$bo5b87o5bo\$2o6b85o6b2o\$obo5b85o5bobo\$b3o4b85o4b3o\$
bob2o4b83o4b2obo\$2b4o3b83o3b4o\$2b5o3b81o3b5o\$2b6o2b81o2b6o\$3b6o2b79o2b
6o\$3b7o2b77o2b7o\$4b7ob77ob7o\$5b7ob75ob7o\$5b8ob73ob8o\$6b89o\$7b87o\$7b87o
\$8b85o\$9b83o\$10b81o\$11b79o\$12b77o\$13b75o\$14b73o\$15b71o\$17b67o\$18b65o\$
19b63o\$19b63o\$20b9o2b39o2b9o\$21b9o3b35o3b9o\$23b8o3b33o3b8o\$24b8o4b29o
4b8o\$25b8o5b25o5b8o\$26b8o7b19o7b8o\$28b7o14b3o14b7o\$30b6o29b6o\$31b6o27b
6o\$33b5o25b5o\$36b4o21b4o\$38b3o19b3o\$41b2o15b2o!
``````
9c/121716:

Code: Select all

``````x = 89, y = 88, rule = R43,C0,M1,S2657..4491,B2268..4554,NM
39b11o\$35bo3bo9bo3bo\$32bo4bo13bo4bo\$30bo3b2o17b2o3bo\$28bo3b3o19b3o3bo\$
26bo3b3o23b3o3bo\$28b4o12bo12b4o\$23bo2b5o8b11o8b5o2bo\$22bo2b5o5b19o5b5o
2bo\$21bob6o4b23o4b6obo\$22b6o3b27o3b6o\$21b6o2b31o2b6o\$18bob49obo\$17b55o
\$16b57o\$15b59o\$14b61o\$13b63o\$12bob61obo\$11bob63obo\$10bob65obo\$11b67o\$
10b69o\$10b69o\$9b71o\$8b73o\$8b4ob63ob4o\$7b4o2b63o2b4o\$6b4o2b65o2b4o\$6b3o
3b65o3b3o\$5b3o3b67o3b3o\$5b2o3b69o3b2o\$4b2o4b69o4b2o\$4bo4b71o4bo\$9b71o\$
9b71o\$8b73o\$8b73o\$8b73o\$8b73o\$8b73o\$7b75o\$7b75o\$7b75o\$7b75o\$7b75o\$7b
75o\$o6b75o6bo\$o6b75o6bo\$o6b75o6bo\$2o5b75o5b2o\$2o5b75o5b2o\$b2o4b75o4b2o
\$b2o5b73o5b2o\$b3o4b73o4b3o\$2b3o4b71o4b3o\$2b4o3b71o3b4o\$2b5o2b71o2b5o\$
3b5o2b69o2b5o\$3b6ob69ob6o\$4b6ob67ob6o\$4b7ob65ob7o\$5b79o\$5b79o\$6b77o\$7b
75o\$7b75o\$8b73o\$9b71o\$10b69o\$11b67o\$12b65o\$13b63o\$14b61o\$15b59o\$16b57o
\$17b55o\$18b9ob33ob9o\$19b9o2b29o2b9o\$20b9o3b25o3b9o\$22b8o4b21o4b8o\$24b
7o7b13o7b7o\$25b7o25b7o\$27b6o23b6o\$29b5o21b5o\$31b4o19b4o\$33b3o17b3o\$36b
2o13b2o!
``````
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: 3783
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:

Code: Select all

``````x = 3, y = 4, rule = B2k3acijr4ejkqr5ajry6cin/S1c2aek3-acy4ciryz5acek6an7c8
o\$2o\$b2o\$2o!``````
c/1018 diagonal:

Code: Select all

``````x = 3, y = 3, rule = B2kn3aijkr4cqyz5acr6in7e8/S2aek3-aey4cinrty5aejkn6in7e
bo\$3o\$o!``````
c/1060 diagonal:

Code: Select all

``````x = 3, y = 5, rule = B2ik3aijry4eiktz5cenr7c/S02-cn3-aek4eqt5ainqr6-n7e
2bo\$b2o\$2o\$bo\$2bo!``````
c/1534 diagonal:

Code: Select all

``````x = 3, y = 3, rule = B2-ac3aikqy4ikqwy5eq6-an7e8/S2-cn3ijkry4aceiqr5ai6-c7e
bo\$b2o\$2o!``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Saka
Posts: 3409
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X
Contact:

### Re: Slow 2-state spaceships

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

Code: Select all

``````o3b2ob2obo3b2o2b2o\$bo3b2obob3o3bo2bo\$2bo2b3o5b3ob4o\$3o3bo2bo2b3o3b3o\$
4bo4bobo4bo\$2o2b2o2b4obo2bo3bo\$2ob4o3bo2bo2bo2bo\$b2o3bobob2o\$3bobobo5b
obobobo\$3bobobob2o3bo2bobo!
``````
(Check gen 3)

muzik
Posts: 3783
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### 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!

Saka
Posts: 3409
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X
Contact:

### 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:

Code: Select all

``````x = 50, y = 51, rule = R24,C0,M1,S838..1426,B724..1443,NM
26b4o\$28b5o\$30b5o\$17bo13b6o\$15b2o6b8ob6o\$13b3o4b19o\$12b3o2b22o\$10b4o2b
24o\$9b32o\$8b34o\$7b36o\$5b39o\$4b40o\$3b38ob3o\$2b40ob3o\$2b41ob2o\$b42o3bo\$b
43o\$44o\$3ob41o\$2o2b41o\$2ob43o\$o2b43o\$3b43o\$3b43o\$3b44o\$3b44o\$4b43o\$4b
43o2bo\$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.

Code: Select all

``````o3b2ob2obo3b2o2b2o\$bo3b2obob3o3bo2bo\$2bo2b3o5b3ob4o\$3o3bo2bo2b3o3b3o\$
4bo4bobo4bo\$2o2b2o2b4obo2bo3bo\$2ob4o3bo2bo2bo2bo\$b2o3bobob2o\$3bobobo5b
obobobo\$3bobobob2o3bo2bobo!
``````
(Check gen 3)

muzik
Posts: 3783
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Slow 2-state spaceships

Saka wrote:
muzik wrote:To post something helpful, here's the slowest ship I've found, c/1842o:

Code: Select all

``````x = 50, y = 51, rule = R24,C0,M1,S838..1426,B724..1443,NM
26b4o\$28b5o\$30b5o\$17bo13b6o\$15b2o6b8ob6o\$13b3o4b19o\$12b3o2b22o\$10b4o2b
24o\$9b32o\$8b34o\$7b36o\$5b39o\$4b40o\$3b38ob3o\$2b40ob3o\$2b41ob2o\$b42o3bo\$b
43o\$44o\$3ob41o\$2o2b41o\$2ob43o\$o2b43o\$3b43o\$3b43o\$3b44o\$3b44o\$4b43o\$4b
43o2bo\$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!

Hunting
Posts: 3000
Joined: September 11th, 2017, 2:54 am

### Re: Slow 2-state spaceships

Is there any range-1 non-totalistic isotropic ones?
MLP will live on forever, so does John Horton Conway.
Moosey wrote:
February 5th, 2019, 7:51 pm
“New knightship tagalong!”
“Quick, hide it!”
My TODO list

LeapLife - DirtyLife - LispLife

I could make a rule in ten seconds flat

77topaz
Posts: 1497
Joined: January 12th, 2018, 9:19 pm

### Re: Slow 2-state spaceships

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

Hunting
Posts: 3000
Joined: September 11th, 2017, 2:54 am

### 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.
MLP will live on forever, so does John Horton Conway.
Moosey wrote:
February 5th, 2019, 7:51 pm
“New knightship tagalong!”
“Quick, hide it!”
My TODO list

LeapLife - DirtyLife - LispLife

I could make a rule in ten seconds flat

Saka
Posts: 3409
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X
Contact:

### Re: Slow 2-state spaceships

c/40002o (I also posted in LTL thread but I guess it fits here as well)

Code: Select all

``````x = 117, y = 116, rule = R49,C0,M1,S3423..5823,B2956..5889,NM
52b12o\$49b18o\$47b22o\$45b26o\$44b28o\$42b8o19b5o\$41b5o26b3o\$40b3o8b9o15bo
\$39b2o7b15o\$38bo6b21o\$43b24o\$41b28o\$39b31o\$37b6ob28o\$36b5o2b30o\$35b4o
3b32o\$34b4o3b34o\$32b4o4b36o\$32b3o4b38o\$31b2o5b40o\$29b3o5b42o\$29b2o5b
44o\$28b2o6b45o\$27bo7b46o\$26bo7b48o\$25bo7b50o\$24bo7b52o\$23bo7b54o\$22bo
7b56o\$21bo7b58o\$20bo7b60o9bo\$19b2o6b62o9bo\$19bo6b64o8b2o\$18bo6b66o8b2o
\$17bo6b68o8b2o\$16b2o4b72o7bo\$16bo4b74o6b2o\$15bo4b76o6b2o\$14b2o3b78o6bo
\$8bo5bo3b80o5b2o\$7bo5b2o2b39o3b40o3bobo3bo\$6b2o5bo2b37o9b38o4b2o3bo\$5b
3o4b2ob37o12b37o2bob2o2b2o\$5b2o5bob37o14b37o3b2o3bo\$4b3o4bob36o17b37ob
obo3b2o\$4b3o4bob35o20b37ob2o2b3o\$3b3o5b36o22b35o2b2o3b2o\$3b3o4b36o24b
35o2b2o2b3o\$2b4o4b35o26b35ob2o2b3o\$2b3o5b35o26b35o2bo2b4o\$b4o4b35o28b
35ob2ob4o\$b4o4b34o30b34ob2ob5o\$b4o4b33o32b36ob5o\$b4o3b34o32b36ob5o\$5o
3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b
33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$5o3b33o34b35ob6o\$b4o3b
34o32b36ob5o\$b4o4b33o32b36ob5o\$b4o4b34o30b34ob2ob5o\$b4o4b35o28b35ob2ob
4o\$2b3o5b35o26b35o2bo2b4o\$2b4o4b35o26b35ob2o2b3o\$3b3o4b36o24b35o2b2o2b
3o\$3b3o5b36o22b35o2b2o3b2o\$4b3o4bob35o20b37ob2o2b3o\$4b3o4bob36o17b37ob
obo3b2o\$5b2o5bob37o14b37o3b2o3bo\$5b3o4b2ob37o12b37o2bob2o2b2o\$6b2o5bo
2b37o9b38o4b2o3bo\$7bo5b2o2b39o3b40o3bobo3bo\$8bo5bo3b80o5b2o\$14b2o3b78o
6bo\$15bo4b76o6b2o\$16bo4b74o6b2o\$16b2o4b72o7bo\$17bo6b68o8b2o\$18bo6b66o
8b2o\$19bo6b64o8b2o\$19b2o6b62o9bo\$20bo7b60o9bo\$21bo7b58o\$22bo7b56o\$23bo
7b54o\$24bo7b52o\$25bo7b50o\$26bo7b48o\$27bo7b46o\$28b2o6b45o\$29b2o5b44o\$
29b3o5b42o\$31b2o5b40o\$32b3o4b38o\$32b4o4b36o\$34b4o3b34o\$35b4o3b32o\$36b
5o2b30o\$37b6ob28o\$39b31o\$41b28o\$43b24o\$38bo6b21o\$39b2o7b15o\$40b3o8b9o
15bo\$41b5o26b3o\$42b8o19b5o\$44b28o\$45b26o\$47b22o\$49b18o\$52b12o!
``````

Code: Select all

``````o3b2ob2obo3b2o2b2o\$bo3b2obob3o3bo2bo\$2bo2b3o5b3ob4o\$3o3bo2bo2b3o3b3o\$
4bo4bobo4bo\$2o2b2o2b4obo2bo3bo\$2ob4o3bo2bo2bo2bo\$b2o3bobob2o\$3bobobo5b
obobobo\$3bobobob2o3bo2bobo!
``````
(Check gen 3)

Moosey
Posts: 3280
Joined: January 27th, 2019, 5:54 pm
Location: A house, or perhaps the OCA board. Or [click to not expand]
Contact:

### Re: Slow 2-state spaceships

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

Code: Select all

``````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.
I am a prolific creator of many rather pathetic googological functions

My CA rules can be found here

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