## Perfect Diagonal Speeds in Life-like CA

For discussion of other cellular automata.

### Perfect Diagonal Speeds in Life-like CA

Rules follow the orthogonal thread as closely as possible. Glide reflective allowed if the overall period still matches the speed.

c/2: (Impossible in Life)
`x = 3, y = 4, rule = B2ac/S1o\$b2o2\$2bo!`

c/3: (Impossible in Life)
`x = 3, y = 3, rule = B2-ai3-in4w/S1c2aei3-ajobo\$bo\$2bo!`

c/4: (glider)
`x = 3, y = 3, rule = B3/S23b2o\$obo\$2bo!`

c/5: (Unnamed)
`x = 23, y = 23, rule = B3/S23b2o\$b2o\$o2bo\$o2bob2o\$o\$o2bo3b2o\$bo5b2o\$b5obo\$6bo3\$7b3o\$9bo\$10b2o\$11bo4b2o\$11bo3b3o\$14bo4bo\$15bo3bo\$15bo\$15bobob2o\$15bo5b2o\$15b2o4b2o\$17b4o!`

c/6: (Unnamed)
`x = 36, y = 36, rule = B3/S23bo\$obo\$o2b2o2\$5bo\$3b2o2b2o\$7b2o\$8bo\$8bobo\$9b2o\$9bo2bo\$8bo4bo\$8bo5bo\$13bo3bo\$11b2o3bobo\$15b2ob2o\$12bobo4b2o\$12bo7b2o\$12bo9bo\$20b2o\$20bo\$19bo3bo\$22bobo\$17b3obo3bo\$21bo\$26b2o\$25b2o\$23b2o2b4o\$29b2o2\$31bo\$30bo2bo\$30bo2bo\$34bo\$35bo\$33b2o!`

c/7: (Lobster)
`11b3o\$13bo\$8b2o2bo\$8b2o\$12b2o\$11b2o\$10bo2bo2\$8bo2bo\$7bo3bo\$6bob3o\$5bo\$5bo13bobo2b2o\$6bo13b2obobo\$b2o13b2o2bo4bo\$o2b2o2b2o6bo3bo\$5bo2bo6bo6b2o\$9b2o4bobo4b2o\$2bo3bo3bo5bo\$6b2o4bo2bo\$bobo5bo3b2o\$2o8bo\$5bo4bo\$7bo3bo\$4b2o5bo\$4bo5bo!`

c/8:
`x = 5, y = 4, rule = B36/S1253o2\$2bobo\$bo!`

c/9:
`x = 4, y = 4, rule = B347/S3567obo\$ob2o\$2o\$4o!`

c/10:
`x = 3, y = 3, rule = B34-air/S234-airb2o\$b2o\$o!`

c/11:
`x = 5, y = 5, rule = B2n3-r4ew5cky6n/S023-rbo\$3bo\$o\$4bo\$2bo!`

c/12: (Known in Life, but not at this period)
`x = 4, y = 4, rule = B2cek3acijr5c6cik/S2-ck3inrobo\$3bo2\$3bo!`

c/13:
`x = 5, y = 9, rule = B35c6-k78/S234-aqrwy3\$b3o\$3bo\$bobo!`

c/14:
`x = 3, y = 3, rule = B2ek3-qy6cik/S2aein3inr4ai5i2bo\$o\$bo!`

c/15:
`x = 5, y = 5, rule = B3457/S355o\$bo2bo\$b2obo\$2b3o\$4bo!`

c/16:
`x = 3, y = 4, rule = B2ek3-ajny4aw/S02-ei3n4aqo\$2bo2\$o!`

c/17:
`x = 6, y = 6, rule = B3457/S14572b3o\$6o\$o3b2o\$b2ob2o\$b2obo\$3b2o!`

c/18:
`x = 3, y = 4, rule = B2in34r/S1e2-e3-a4ijtb2o\$obo\$obo\$bo!`

c/19:
`x = 6, y = 6, rule = B3/S145684b2o\$2b4o\$2b3o\$b4o\$b2o\$o!`

c/20:
`x = 5, y = 5, rule = B34/S04578bo\$4o\$4o\$5o\$b3o!`

c/21:
`x = 3, y = 3, rule = B2n34-a7/S2-in33o\$2bo\$2bo!`

c/22:
`x = 4, y = 3, rule = B2c3ajk4/S1c23bo\$2bo\$2obo!`

c/23:
`x = 4, y = 4, rule = B3567/S02467bo2\$o2bo\$2o!`

c/24:
`x = 7, y = 7, rule = B3467/S045685bo\$4b3o\$2b4o\$2bobo\$ob3o2\$obo!`

c/25:
`x = 6, y = 6, rule = B2-a3-ik4-aik/S23b2o\$b2o\$o2bo\$4b2o\$4b2o\$3bo!`

c/30:
`x = 4, y = 4, rule = B38/S234wzbobo\$o2bo\$o2bo\$b2o!`

c/42:
`x = 5, y = 3, rule = B2cei3-i/S235a2o\$o\$2b3o!`

c/66:
`x = 4, y = 4, rule = B34e/S23-ebobo\$o2bo\$o2bo\$2o!`

c/118:
`x = 8, y = 8, rule = B347/S3562b3o\$bo2b3o\$ob2o2bo\$obo3b2o\$b2o2bobo\$3b3obo\$3bo2bo\$4b2o!`

c/125:
`x = 9, y = 9, rule = B34568/S184b3obo\$5bo\$2b5obo\$3o3b3o\$3obobobo\$obo3bo\$ob5o\$o3b2o\$6o!`

c/129:
`x = 8, y = 8, rule = B34578/S458bobo\$b2o\$4obo\$5o\$3ob2obo\$7o\$8o\$6o!`

c/132: (B0)
`x = 5, y = 4, rule = B01348/S142o\$obobo\$b2o\$3o!`

c/156: (B0)
`x = 6, y = 6, rule = B0138/S01235b2o\$o\$2b2o\$bobobo\$b2o2bo\$4bo!`

c/161:
`x = 9, y = 7, rule = B34568/S4582b6o\$2b7o\$obo2b2o\$2bo2b3o\$o3bo\$2b4o\$b3o!`

c/177:
`x = 11, y = 11, rule = B34568/S45786bo\$4b3o\$4b2ob2o\$2b3ob3o\$2b2ob3ob2o\$7ob2o\$6ob3o\$ob6o\$bob5o\$b2ob2o\$3b3o!`

c/178: (B0)
`x = 9, y = 9, rule = B0124/S01362b2o\$4bo\$6bo\$4obo\$2b3o2bo\$3b3o2bo\$4b2o2bo\$5bo\$5bo!`

c/180: (B0)
`x = 7, y = 5, rule = B016/S0124b3o\$3bob2o\$2o3b2o\$3bo\$b2o!`

c/195:
`x = 9, y = 9, rule = B3458/S4563b4o\$3b4o\$b2o4b2o\$b5ob2o\$3o2bob2o\$4obob2o\$7o\$2b5o\$2b3o!`

c/230:
`x = 4, y = 5, rule = B34568/S268b3o\$3bo\$3o\$b3o\$bo!`

c/245:
`x = 11, y = 11, rule = B3457/S4565b5o\$3bob2obobo\$3bobobob2o\$b5o2bobo\$b5o3b2o\$5ob5o\$bob5o\$10o\$b3ob3o\$b7o\$3bobo!`

c/368:
`x = 8, y = 8, rule = B3457/S4562bobo\$7o\$3ob3o\$4ob3o\$5obo\$b7o\$b6o\$3b4o!`

c/723:
`x = 10, y = 10, rule = B34578/S45683bobobo\$3b2o2bo\$b3ob2ob2o\$2b2ob3o\$2obob3obo\$b3o4bo\$2ob7o\$bo2bob2o\$b5obo\$3bobo!`

work in progress
Last edited by muzik on June 30th, 2017, 10:07 am, edited 9 times in total.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3467
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Perfect Diagonal Speeds in Life-like CA

No non-tot. rules?
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: 3119
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Perfect Diagonal Speeds in Life-like CA

Saka wrote:No non-tot. rules?

not yet, no
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3467
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Perfect Diagonal Speeds in Life-like CA

Smaller c/10
`x = 3, y = 3, rule = B34-air/S234-airobo\$o\$3o!`
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Rhombic

Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Perfect Diagonal Speeds in Life-like CA

c/22
`x = 4, y = 3, rule = B2c3ajk4/S1c232obo\$2bo\$bo!`

c/3
`x = 3, y = 3, rule = B2-ai3-in4w/S1c2aei3-aj2bo\$bo\$obo!`

c/30
`x = 4, y = 4, rule = B38/S234wzb2o\$o2bo\$o2bo\$bobo!`

c/25
`x = 6, y = 6, rule = B2-a3-ik4-aik/S233bo\$4b2o\$4b2o\$o2bo\$b2o\$b2o!`

c/14
`x = 3, y = 3, rule = B2ek3-qy6cik/S2aein3inr4ai5ibo\$o\$2bo!`

c/12
`x = 4, y = 4, rule = B2cek3acijr5c6cik/S2-ck3inr3bo2\$3bo\$obo!`

c/16
`x = 3, y = 4, rule = B2ek3-ajny4aw/S02-ei3n4aqo2\$2bo\$o!`

c/2
`x = 3, y = 4, rule = B2ac/S12bo2\$b2o\$o!`

Also, what's with the enormous c/4-c/7 ships?
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

toroidalet

Posts: 1004
Joined: August 7th, 2016, 1:48 pm
Location: my computer

### Re: Perfect Diagonal Speeds in Life-like CA

c/21, fewer cells
`x = 3, y = 3, rule = B2n34-a7/S2-in33o\$o\$o!`

Amusingly closely related c/18
`x = 3, y = 3, rule = B2n34-a7/S2-in34q3o\$o\$o!`
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Rhombic

Posts: 1056
Joined: June 1st, 2013, 5:41 pm

### Re: Perfect Diagonal Speeds in Life-like CA

A c/66:
`x = 4, y = 4, rule = B34e/S23-e2b2o\$o2bo\$o2bo\$obo!`
Rocknlol

Posts: 83
Joined: April 15th, 2012, 9:06 am

### Re: Perfect Diagonal Speeds in Life-like CA

Rhombic wrote:Smaller c/10
`x = 3, y = 3, rule = B34-air/S234-airobo\$o\$3o!`
`x = 8, y = 10, rule = B3/S233b2o\$3b2o\$2b3o\$4bobo\$2obobobo\$3bo2bo\$2bobo2bo\$2bo4bo\$2bo4bo\$2bo!`

No football of any dui mauris said that.

83bismuth38

Posts: 453
Joined: March 2nd, 2017, 4:23 pm
Location: Still sitting around in Sagittarius A...

### Re: Perfect Diagonal Speeds in Life-like CA

83bismuth38 wrote:
Rhombic wrote:Smaller c/10
`x = 3, y = 3, rule = B34-air/S234-airobo\$o\$3o!`

Yeah, I'm pretty sure that's where it's from.
Also, the preboat phase is the minimal one so that should be used.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Posts: 1891
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: Perfect Diagonal Speeds in Life-like CA

NSWSS
I didnt check if these have been posted.
C/14
`x = 4, y = 4, rule = B2k3-j/S2-i32bo\$o2bo\$obo\$2o!`

C/10
`x = 3, y = 3, rule = B2k3-e/S2-i32bo\$3o\$3o!`

C/8
`x = 4, y = 4, rule = B2-a3i/S1c278obo\$bobo\$3bo\$bo!`

C/30
`x = 4, y = 4, rule = B38/S234wzb2o\$o2bo\$3bo\$3o!`

C/28 (Glide-Symmetric)
`x = 6, y = 5, rule = B35in/S236n7c4b2o\$4b2o\$bo2b2o\$obo\$b2o!`

C/13
`x = 5, y = 9, rule = B35c6-k78/S234-aqrwy3\$b3o\$3bo\$bobo!`

C/11
`x = 5, y = 5, rule = B2n3-r4ew5cky6n/S023-r3bo\$bo\$4bo\$o\$2bo!`

C/18 (Glide symmetric)
`x = 3, y = 4, rule = B2in34r/S1e2-e3-a4ijtbo\$obo\$obo\$b2o!`

C/42
`x = 5, y = 3, rule = B2cei3-i/S235a2b3o\$o\$2o!`

C/19
`x = 5, y = 5, rule = B2ein3aeijnq4ceiw5iy6n/S2ae3-a4ctyz5a2bo\$3b2o\$obo\$bo\$bo!`
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: 3119
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: Perfect Diagonal Speeds in Life-like CA

We now have speeds from c/2 to c/25!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3467
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Perfect Diagonal Speeds in Life-like CA

Better ships:
3-cell c/3
`x = 3, y = 3, rule = B2cei3a/S02i3i2bo2\$obo!`

3-cell c/4
`x = 2, y = 3, rule = B2-a/S12-kbo\$bo\$o!`

3-cell c/5
`x = 3, y = 3, rule = B2ein3acein4r5i/S02-ck3a2bo2\$obo!`

3-cell c/6
`x = 2, y = 3, rule = B2-a/S12bo\$bo\$o!`

3-cell c/7
`x = 3, y = 3, rule = B2cen3eqry4aeijnrt5eny6-n7e/S012ae3ejknq4eijknqt5ckry6-i72bo2\$obo!`

3-cell c/8
`x = 4, y = 3, rule = B2-an3aijy4-eirz5ikqr6acn8/S05q3bo\$o\$2bo!`

3-cell c/9
`x = 3, y = 3, rule = B2eik3-jky4aeikryz5-cqry6-cn7e/S02k3e4c2bo2\$obo!`

From the 5S diagonal ships file.
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

toroidalet

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