## Superluminary orthogonal speeds

For discussion of other cellular automata.
muzik
Posts: 3522
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Superluminary orthogonal speeds

Aiming for lowest possible populations. All ships with periods of 23 or below that move 24 or less cells per iteration, which are faster than c, will be included within this post. All rules must be two-state.

2c/1: 9

Code: Select all

``````x = 4, y = 7, rule = R3,C0,M0,S3..3,B5..5,NM
2o\$2bo\$3bo\$3bo\$3bo\$2bo\$2o!
``````
3c/2: 8

Code: Select all

``````x = 5, y = 6, rule = R2,C0,M0,S3..3,B4..4,NM
obo\$4bo\$4bo\$4bo\$4bo\$obo!``````
4c/2: 8

Code: Select all

``````x = 9, y = 7, rule = R2,C0,M0,S15..15,B3..3,NM
3bobo2\$8bo\$o7bo\$8bo2\$3bobo!
``````
5c/2: 18

Code: Select all

``````x = 11, y = 10, rule = R4,C0,M1,S7..7,B8..8,NM
3bo2bo\$2bo7bo\$10bo\$10bo\$10bo\$o9bo\$10bo\$bo8bo\$10bo\$4bobo!
``````
5c/4: 44

Code: Select all

``````x = 9, y = 8, rule = R5,C0,M1,S31..43,B27..36,NM
2b3o\$b8o\$o3b5o\$o4b4o\$o4b4o\$o3b5o\$b8o\$2b3o!
``````
6c/2: 14

Code: Select all

``````x = 14, y = 12, rule = R4,C0,M1,S7..9,B7..8,NM
2bo7bo\$12bo\$o\$13bo\$13bo\$13bo\$13bo\$13bo\$13bo\$o\$12bo\$2bo7bo!``````
6c/4: 9

Code: Select all

``````x = 5, y = 6, rule = R2,C0,M0,S4..4,B4..4,NM
b2o\$o3bo\$4bo\$4bo\$4bo\$obo!``````
7c/4: 20

Code: Select all

``````x = 10, y = 10, rule = R4,C0,M1,S7..8,B8..8,NM
3b3o\$o\$o8bo\$o8bo\$o8bo\$o8bo\$o8bo\$o8bo\$o\$3b3o!``````
7c/5: 65

Code: Select all

``````x = 12, y = 13, rule = R5,C0,M1,S34..50,B29..38,NM
3bo\$4b2obo\$3b6o\$2b9o\$bo4b5o\$o7b4o\$o7b4o\$o7b4o\$bo4b5o\$2b9o\$3b6o\$4b2obo\$
3bo!
``````
7c/6: 200

Code: Select all

``````x = 19, y = 18, rule = R10,C0,M1,S124..211,B121..166,NM
6b4o\$5b7o\$4b10o\$3b14o\$2b3ob12o\$b3o4b11o\$b3o5b10o\$3o7b9o\$3o8b8o\$3o8b8o\$
3o7b9o\$b3o5b10o\$b3o4b11o\$2b3ob12o\$3b14o\$4b10o\$5b7o\$6b4o!
``````
8c/2: 12

Code: Select all

``````x = 17, y = 13, rule = R4,C0,M1,S50..50,B5..5,NM
5bo5bo4\$16bo\$o15bo\$o15bo\$o15bo\$16bo4\$5bo5bo!``````
8c/4: 9

Code: Select all

``````x = 10, y = 9, rule = R4,C0,M1,S4..6,B7..7,NM
8bo\$o\$9bo\$9bo\$9bo\$9bo\$9bo\$o\$8bo!``````
8c/7: 220

Code: Select all

``````x = 20, y = 19, rule = R10,C0,M1,S123..212,B123..167,NM
7b4o\$6b6o\$5b9o\$3b14o\$2b16o\$b18o\$b3o5b10o\$3o7b9o\$3o8b9o\$3o8b9o\$3o8b9o\$
3o7b9o\$b3o5b10o\$b18o\$2b16o\$3b14o\$5b9o\$6b6o\$7b4o!``````
9c/6: 12

Code: Select all

``````x = 6, y = 8, rule = R3,C0,M0,S5..5,B6..6,NM
b2o\$o3bo\$5bo\$5bo\$5bo\$5bo\$o3bo\$b2o!
``````
10c/4: 16

Code: Select all

``````x = 10, y = 10, rule = R4,C0,M1,S6..6,B8..8,NM
obo2bo\$bo7bo\$9bo\$9bo\$9bo\$9bo\$9bo\$9bo\$bo7bo\$obo2bo!``````
12c/4: 46

Code: Select all

``````x = 27, y = 25, rule = R3,C0,M0,S3..6,B4..4,NM
17bo3bo2\$17b2o6bo2\$26bo\$15bo10bo\$26bo\$4bo21bo\$17bo\$4bo19bo\$4bo\$4o13bo
4bo\$4o\$4o13bo4bo\$4bo\$4bo19bo\$17bo\$4bo21bo\$26bo\$15bo10bo\$26bo2\$17b2o6bo
2\$17bo3bo!``````
12c/6: 15

Code: Select all

``````x = 11, y = 16, rule = R2,C0,M0,S15..15,B3..3,NM
5bobo2\$10bo\$2bo7bo\$10bo\$o\$7bo2\$5bo3\$8bo\$o7bo\$8bo2\$3bobo!
``````
12c/10: 30

Code: Select all

``````x = 6, y = 15, rule = R3,C0,M0,S3..6,B5..5,NM
4o\$4o\$4o\$4o\$4o\$4o5\$5bo\$5bo\$5bo\$4b2o\$5bo!``````
12c/11: 220

Code: Select all

``````x = 19, y = 19, rule = R10,C0,M1,S123..212,B123..170,NM
7b3o\$5b7o\$4b9o\$3b13o\$2b15o\$b17o\$4o4b11o\$3o6b10o\$3o7b9o\$3o7b9o\$3o7b9o\$
3o6b10o\$4o4b11o\$b17o\$2b15o\$3b13o\$4b9o\$5b7o\$7b3o!
``````
14c/8: 20

Code: Select all

``````x = 10, y = 10, rule = R4,C0,M1,S7..9,B8..8,NM
3b3o\$o\$o8bo\$o8bo\$o8bo\$o8bo\$o8bo\$o8bo\$o\$3b3o!``````
15c/6: 16

Code: Select all

``````x = 10, y = 10, rule = R4,C0,M1,S5..6,B8..8,NM
obo2bo\$bo7bo\$9bo\$9bo\$9bo\$9bo\$9bo\$9bo\$bo7bo\$obo2bo!
``````
16c/4: 16

Code: Select all

``````x = 17, y = 13, rule = R5,C0,M0,S3..6,B9..9,NM
3bobo4bo2\$16bo\$16bo\$16bo\$16bo\$o15bo\$16bo\$16bo\$16bo\$16bo2\$3bobo4bo!
``````
16c/8: 12

Code: Select all

``````x = 9, y = 8, rule = R3,C0,M0,S4..4,B6..6,NM
4b2o\$8bo\$o7bo\$8bo\$8bo\$8bo\$o7bo\$o4bo!``````
17c/12: 237

Code: Select all

``````x = 21, y = 21, rule = R10,C0,M1,S124..211,B121..166,NM
8b3o\$7b5o\$5b9o\$5b11o\$3b15o\$2b17o\$2b18o\$b3o7b10o\$b2o9b9o\$3o10b8o\$3o10b
8o\$3o10b8o\$b2o9b9o\$b3o7b10o\$2b18o\$2b17o\$3b15o\$5b11o\$5b9o\$7b5o\$8b3o!
``````
18c/4: 22

Code: Select all

``````x = 26, y = 20, rule = R5,C0,M0,S2..3,B8..8,NM
14bo3\$18bo\$21b2o2\$25bo\$25bo\$3o22bo\$25bo\$25bo\$3o22bo\$25bo\$25bo2\$21b2o\$
18bo3\$14bo!``````
18c/12: 26

Code: Select all

``````x = 22, y = 10, rule = R2,C0,M0,S4..4,B4..4,NM
2bo\$2bo2b2o\$bo4bo\$6bo10b2o\$o18b3o\$o18b3o\$6bo10b2o\$bo4bo\$2bo2b2o\$2bo!``````
20c/19: 224

Code: Select all

``````x = 20, y = 20, rule = R10,C0,M1,S123..212,B123..167,NM
7b3o\$6b5o\$5b9o\$4b12o\$3b14o\$2b17o\$b5o3b10o\$b3o6b10o\$3o8b9o\$3o8b9o\$3o8b
9o\$3o8b9o\$b3o6b10o\$b5o3b10o\$2b17o\$3b14o\$4b12o\$5b9o\$6b5o\$7b3o!``````
21c/12: 16

Code: Select all

``````x = 7, y = 4, rule = R4,C0,M1,S7..11,B8..8,NM
4bo\$7o\$7o\$4bo!``````
23c/17: 220

Code: Select all

``````x = 21, y = 21, rule = R10,C0,M1,S124..211,B121..166,NM
8b3o\$6b5o\$5b8o\$4b11o\$4b13o\$3b16o\$2b3o4b11o\$b3o7b9o\$3o9b9o\$3o10b8o\$2o
11b8o\$3o10b8o\$3o9b9o\$b3o7b9o\$2b3o4b11o\$3b16o\$4b13o\$4b11o\$5b8o\$6b5o\$8b
3o!
``````
Last edited by muzik on February 11th, 2019, 8:50 am, edited 10 times in total.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

AforAmpere
Posts: 1052
Joined: July 1st, 2016, 3:58 pm

### Re: Superluminary orthogonal speeds

That 13c/11 is actually 12c/11

3c/2:

Code: Select all

``````x = 5, y = 6, rule = R2,C0,M0,S3..3,B4..4,NM
obo\$4bo\$4bo\$4bo\$4bo\$obo!
``````
18c/12:

Code: Select all

``````x = 22, y = 10, rule = R2,C0,M0,S4..4,B4..4,NM
2bo\$2bo2b2o\$bo4bo\$6bo10b2o\$o18b3o\$o18b3o\$6bo10b2o\$bo4bo\$2bo2b2o\$2bo!
``````
36c/24:

Code: Select all

``````x = 243, y = 50, rule = R2,C0,M0,S4..4,B4..4,NM
73bobo36bo\$73bobo33bo3bobo\$74b2o37bobo21bob2o\$73bo2bo37bo\$73bo2bo34b3o
b2o\$114b3o18bo7bo\$144bo2\$109bo4bo17bo\$70b3o36bo33b2o\$129bo12b2o\$109bo
32bo\$70b3o37bo4bo13bo11bo\$41bobo30bo54bo\$70bob2o65bo\$44bo11bo12bob3o
63b2o33b2o\$40bo2b2o8b2o14b4o59bo3b2o34b2o\$39bo2bo9bo80bo2bo40bo\$4bo13b
o22bo50bo78bo\$4obobo7bobob4o68bo\$6bobo5bobo78bo76bo3b2o15bo21b2o6b2o\$
4b2ob2o5b2ob2o33bo4bo34bo77bo23bo20b2o6b2o\$9b5o39b3o119bo15bo3bobo2bo
14bo8bo14bo\$6bo9bo76b4o75b2o16bo5bo18b2o6b2o\$8bo5bo175bo7b2o2b2o8b2ob
2o6b2ob2o8b2o2b3o\$8bo5bo175bo7b2o2b2o8b2ob2o6b2ob2o8b2o2b3o\$6bo9bo76b
4o75b2o16bo5bo18b2o6b2o\$9b5o39b3o119bo15bo3bobo2bo14bo8bo14bo\$4b2ob2o
5b2ob2o33bo4bo34bo77bo23bo20b2o6b2o\$6bobo5bobo78bo76bo3b2o15bo21b2o6b
2o\$4obobo7bobob4o68bo\$4bo13bo22bo50bo78bo\$39bo2bo9bo80bo2bo40bo\$40bo2b
2o8b2o14b4o59bo3b2o34b2o\$44bo11bo12bob3o63b2o33b2o\$70bob2o65bo\$41bobo
30bo54bo\$70b3o37bo4bo13bo11bo\$109bo32bo\$129bo12b2o\$70b3o36bo33b2o\$109b
o4bo17bo2\$144bo\$114b3o18bo7bo\$73bo2bo34b3ob2o\$73bo2bo37bo\$74b2o37bobo
21bob2o\$73bobo33bo3bobo\$73bobo36bo!
``````
C d:

Code: Select all

``````x = 5, y = 5, rule = R2,C0,M0,S5..5,B4..4,NM
4bo2\$3b2o\$2bobo\$ob2o!
``````
12c/10:

Code: Select all

``````x = 6, y = 15, rule = R3,C0,M0,S3..6,B5..5,NM
4o\$4o\$4o\$4o\$4o\$4o5\$5bo\$5bo\$5bo\$4b2o\$5bo!
``````
12c/4:

Code: Select all

``````x = 27, y = 25, rule = R3,C0,M0,S3..6,B4..4,NM
17bo3bo2\$17b2o6bo2\$26bo\$15bo10bo\$26bo\$4bo21bo\$17bo\$4bo19bo\$4bo\$4o13bo
4bo\$4o\$4o13bo4bo\$4bo\$4bo19bo\$17bo\$4bo21bo\$26bo\$15bo10bo\$26bo2\$17b2o6bo
2\$17bo3bo!
``````
16c/8:

Code: Select all

``````x = 9, y = 8, rule = R3,C0,M0,S4..4,B6..6,NM
4b2o\$8bo\$o7bo\$8bo\$8bo\$8bo\$o7bo\$o4bo!
``````
28c/14:

Code: Select all

``````x = 8, y = 13, rule = R3,C0,M0,S2..2,B5..5,NM
b2o\$o2bo\$o3bo\$bo3bo\$6bo\$7bo\$7bo\$7bo\$6bo\$bo3bo\$o3bo\$o2bo\$b2o!
``````
38c/30:

Code: Select all

``````x = 95, y = 20, rule = R3,C0,M0,S3..5,B6..6,NM
88b3o2\$21b3o61bo\$20bo3bo15bo18bo34bo\$20bo3bo15bo18bo34bo\$19bo6bo13bo
18bo34bo\$19bo8bo11bo18bo34bo\$22bo4b2o56bo\$21bo5b2o\$27b2o59b3o\$23bob2o
21b3o\$o23bo\$o44bo\$6bo12bo34bo\$19bo34bo\$19bo34bo\$19bo34bo\$o44bo\$bo\$48b
3o!
``````
Smaller 2c:

Code: Select all

``````x = 4, y = 7, rule = R3,C0,M0,S3..3,B5..5,NM
2o\$2bo\$3bo\$3bo\$3bo\$2bo\$2o!
``````
57c/45:

Code: Select all

``````x = 143, y = 23, rule = R3,C0,M0,S3..5,B6..6,NM
27bo\$26bo29bo\$26bo29bo8bo\$56bo9bo\$24bo31bo10bo\$32bo35bo67bo\$57bo10bo
16bo18bo31bo5bo\$30bo26bo9bo17bo18bo31bo5bo\$20bo45bo18bo18bo31bo5bo\$2bo
54bo7bo19bo18bo31bo5bo\$5o52bo78bo\$2bo18bo4bo23bo\$5o41b2o6bo9bo\$bo42bo
13b2o3bo\$bo6bo32bo3bo14bo\$bo39bo3bo\$41bo4b5o9bo2bo29bo\$41bo4bo10bo5bo
29bo5bo\$57bo3bo2bo28bo5bo\$2bo53b4o2bobo28bo5bo\$3bo52b4obobo29bo5bo\$58b
obo32bo\$59bo!
``````
64c/32:

Code: Select all

``````x = 149, y = 10, rule = R3,C0,M0,S5..5,B6..6,NM
4b3o\$2bo4b7o3bo122bo4bo\$o19bo116bo10bo\$20bo116bo10bo\$20bo116bo10bo\$20b
o116bo10bo\$20bo116bo10bo\$o19bo116bo10bo\$2bo4b7o3bo122bo4bo\$4b3o!
``````
68c/34:

Code: Select all

``````x = 25, y = 17, rule = R3,C0,M0,S3..3,B7..8,NM
14bo\$13bo4bo\$12bo6bo\$12bo\$4b3o5bo7b2o\$4bo2bo13b2o\$2bo3bo16bo\$2o21b2o\$
2o5b2o15bo\$2o21b2o\$2bo3bo16bo\$4bo2bo13b2o\$4b3o5bo7b2o\$12bo\$12bo6bo\$13b
o4bo\$14bo!
``````
6c/6 d:

Code: Select all

``````x = 8, y = 8, rule = R3,C0,M0,S5..6,B7..8,NM
6bo\$3b3obo\$7bo\$bo4bo\$bo3b2o\$bo2b2o\$o2b2o\$b2o!
``````
10c/4 d:

Code: Select all

``````x = 27, y = 17, rule = R4,C0,M1,S20..20,B4..4,NM
3bo17bo\$bo19bo\$22bo\$o22bo\$24bo\$25bo\$26bo4\$o3\$3bo22bo\$14bo10bo\$15bo8bo\$
16bo6bo!
``````
8c/2:

Code: Select all

``````x = 17, y = 13, rule = R4,C0,M1,S50..50,B5..5,NM
5bo5bo4\$16bo\$o15bo\$o15bo\$o15bo\$16bo4\$5bo5bo!
``````
96c/86:

Code: Select all

``````x = 20, y = 19, rule = R10,C0,M1,S123..212,B123..167,NM
6b5o\$5b8o\$3b13o\$2b15o\$b17o\$b18o\$3o3bo4b9o\$3o8b9o\$2o10b8o\$2o10b8o\$2o10b
8o\$3o8b9o\$3o3bo4b9o\$b18o\$b17o\$2b15o\$3b13o\$5b8o\$6b5o!
``````
29c/34 d:

Code: Select all

``````x = 20, y = 20, rule = R10,C0,M1,S123..212,B123..167,NM
7b5o\$5b8o\$4b10o\$3b12o\$3b13o\$2b15o\$b17o\$b18o\$7o4b9o\$6o6b8o\$5o7b8o\$3o9b
8o\$3o9b8o\$b2o8b8o\$b3o6b9o\$2b3o4b9o\$3b3o3b8o\$4b11o\$5b9o\$7b5o!
``````
30c/29:

Code: Select all

``````x = 19, y = 18, rule = R10,C0,M1,S123..212,B123..167,NM
6b5o\$5b7o\$3b12o\$2b15o\$b17o\$b3ob14o\$3o7b9o\$3o8b8o\$3o8b8o\$3o8b8o\$3o8b8o\$
3o7b9o\$b3ob14o\$b17o\$2b15o\$3b12o\$5b7o\$6b5o!
``````
20c/19:

Code: Select all

``````x = 20, y = 20, rule = R10,C0,M1,S123..212,B123..167,NM
7b3o\$6b5o\$5b9o\$4b12o\$3b14o\$2b17o\$b5o3b10o\$b3o6b10o\$3o8b9o\$3o8b9o\$3o8b
9o\$3o8b9o\$b3o6b10o\$b5o3b10o\$2b17o\$3b14o\$4b12o\$5b9o\$6b5o\$7b3o!
``````
8c/7:

Code: Select all

``````x = 20, y = 19, rule = R10,C0,M1,S123..212,B123..167,NM
7b4o\$6b6o\$5b9o\$3b14o\$2b16o\$b18o\$b3o5b10o\$3o7b9o\$3o8b9o\$3o8b9o\$3o8b9o\$
3o7b9o\$b3o5b10o\$b18o\$2b16o\$3b14o\$5b9o\$6b6o\$7b4o!
``````
66c/64:

Code: Select all

``````x = 19, y = 19, rule = R10,C0,M1,S123..212,B123..167,NM
6b5o\$5b7o\$3b11o\$2b15o\$b17o\$b17o\$3o4b12o\$3o7b9o\$2o8b9o\$2o8b9o\$2o8b9o\$3o
7b9o\$4o3b12o\$b17o\$b17o\$2b14o\$4b10o\$5b7o\$6b4o!
``````
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

muzik
Posts: 3522
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Superluminary orthogonal speeds

A for awesome wrote:
AforAmpere wrote:Fastest ship for R<=50, at 200c/4:

Code: Select all

``````x = 101, y = 89, rule = R50,C0,M0,S50..90,B51..51,NM
3o\$3b2o\$5b2o\$7b2o\$9b2o\$11b2o\$13b2o\$15b2o\$17b2o\$19b2o\$21b2o\$23b2o\$25b2o
\$27b2o\$29b2o\$31b2o\$33b36o\$69b16o\$85b14o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$
50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$
50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$
101o\$101o\$101o\$101o\$101o\$101o\$101o\$101o\$101o\$101o\$101o\$101o\$101o\$101o\$
101o\$101o\$101o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo
48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo
48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$50bo48b2o\$85b14o\$69b16o\$33b36o\$31b
2o\$29b2o\$27b2o\$25b2o\$23b2o\$21b2o\$19b2o\$17b2o\$15b2o\$13b2o\$11b2o\$9b2o\$7b
2o\$5b2o\$3b2o\$3o!
``````
1000c/20 based on that:

Code: Select all

``````x = 186, y = 287, rule = R50,C0,M0,S50..90,B51..51,NM
35bo67bo\$35bo83bo\$35bo97bo2\$137bo\$139bo\$141bo\$143bo\$145bo\$147bo\$149bo\$
151bo\$153bo\$155bo\$157bo\$159bo\$161bo\$163bo\$165bo\$167bo2\$bo32\$185bo\$185b
o\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$
185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185b
o\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$
185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185bo\$185b
o\$185bo\$185bo\$185bo30\$181bo3\$180bo3\$179bo3\$178bo3\$177bo3\$176bo3\$175bo
3\$174bo\$174bo2\$9bo2\$o175bo6\$182bo18\$184bo\$184bo\$184bo\$184bo\$184bo\$184b
o\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$
184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184b
o\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$
184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo\$184bo32\$o
2\$166bo\$164bo\$162bo\$160bo\$158bo\$156bo\$154bo\$152bo\$150bo\$148bo\$146bo\$
144bo\$142bo\$140bo\$138bo\$136bo2\$34bo97bo\$34bo83bo\$34bo67bo!
``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Apple Bottom
Posts: 1027
Joined: July 27th, 2015, 2:06 pm
Contact:

### Re: Superluminary orthogonal speeds

I'm not even sure these deserve to be called "superluminal" (or "superluminary", if you prefer) -- by definition the speed of light in a CA is equivalent to its range. A range-5 LtL rule has a higher speed of light than, say, Conway Life, and the existence of ships with period n and displacement 5n in the former is not a priori surprising.

Put more succinctly, "speed of light" != "1 cell/generation". The wiki is, sadly, a bit unclear on the matter, first stating (correctly) that "[s]peeds are almost always measured in reference to the speed of light (or speed of life), denoted by c which, for first neighbor neighborhoods, is a rate of one cell per generation", but then conflating the two anyway. (Which is not surprising, as it was initially written to cover just Life).

Just something I wanted to point out -- best to nip confusion in the bud before it spreads.
If you speak, your speech must be better than your silence would have been. — Arabian proverb

Catagolue: Apple Bottom • Life Wiki: Apple Bottom • Twitter: @_AppleBottom_

Proud member of the Pattern Raiders!

muzik
Posts: 3522
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Superluminary orthogonal speeds

Then what name should we give to "speeds of form dc/g where d/g > 1"?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

AforAmpere
Posts: 1052
Joined: July 1st, 2016, 3:58 pm

### Re: Superluminary orthogonal speeds

Apple Bottom wrote:I'm not even sure these deserve to be called "superluminal" (or "superluminary", if you prefer) -- by definition the speed of light in a CA is equivalent to its range. A range-5 LtL rule has a higher speed of light than, say, Conway Life, and the existence of ships with period n and displacement 5n in the former is not a priori surprising.
However, the norm now seems to be to call say a ship that moves forward 2 cells in 1 generation '2c', which kind of indicates faster-than-light travel, even though that is technically not the case according to some definitions. I don't know what to call these ships, but slower-than-light seems off too.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

muzik
Posts: 3522
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Superluminary orthogonal speeds

Should we redefine one cell per generation as "true lightspeed", and any range's maximum possible speed as "relative lightspeed", or something along those lines?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Macbi
Posts: 706
Joined: March 29th, 2009, 4:58 am

### Re: Superluminary orthogonal speeds

We could use "c" to refer to whatever the maximal speed that information can travel at, and then write cell/gen if we mean something different?

AforAmpere
Posts: 1052
Joined: July 1st, 2016, 3:58 pm

### Re: Superluminary orthogonal speeds

Macbi wrote:We could use "c" to refer to whatever the maximal speed that information can travel at, and then write cell/gen if we mean something different?
But that would just add an extra layer of confusion, as 2c, and the like are already used to represent those speeds. The current method is also Range-independent, which makes visualization easier as well.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

77topaz
Posts: 1395
Joined: January 12th, 2018, 9:19 pm

### Re: Superluminary orthogonal speeds

Maybe we could use c as we currently do, and use a larger-than-normal c, C, for the Larger than Life speeds of information?

AforAmpere
Posts: 1052
Joined: July 1st, 2016, 3:58 pm

### Re: Superluminary orthogonal speeds

77topaz wrote:Maybe we could use c as we currently do, and use a larger-than-normal c, C, for the Larger than Life speeds of information?
Yeah, or maybe we could use RC, for Relative C. Capital C is used interchangeably with c in other places, so another level of distinguishing should be added.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

muzik
Posts: 3522
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Superluminary orthogonal speeds

This 9c/6 breaks no records:

Code: Select all

``````x = 16, y = 20, rule = R2,C0,M0,S3..3,B4..4,NM
3b2o\$2bob2o\$2bob2o\$o4bo\$4o\$bo2b2o3bo\$2bo2bo5bo\$2bo2bo6bo\$4b2o7bo\$6bo7b
2o\$6bo7b2o\$4b2o7bo\$2bo2bo6bo\$2bo2bo5bo\$bo2b2o3bo\$4o\$o4bo\$2bob2o\$2bob2o
\$3b2o!
``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
Posts: 3522
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Superluminary orthogonal speeds

Not superluminary, but a 4c/8 wave:

Code: Select all

``````x = 8, y = 270, rule = R2,C0,M0,S3..3,B4..4,NM
b2obo\$o\$o\$o6bo\$2bo4bo\$6bo\$3b3o5\$3b3o\$6bo\$2bo4bo\$o6bo\$o\$o\$b2obo11\$b2obo
\$o\$o\$o6bo\$2bo4bo\$6bo\$3b3o5\$3b3o\$6bo\$2bo4bo\$o6bo\$o\$o\$b2obo11\$b2obo\$o\$o\$
o6bo\$2bo4bo\$6bo\$3b3o5\$3b3o\$6bo\$2bo4bo\$o6bo\$o\$o\$b2obo11\$b2obo\$o\$o\$o6bo\$
2bo4bo\$6bo\$3b3o5\$3b3o\$6bo\$2bo4bo\$o6bo\$o\$o\$b2obo11\$b2obo\$o\$o\$o6bo\$2bo4b
o\$6bo\$3b3o5\$3b3o\$6bo\$2bo4bo\$o6bo\$o\$o\$b2obo11\$b2obo\$o\$o\$o6bo\$2bo4bo\$6bo
\$3b3o5\$3b3o\$6bo\$2bo4bo\$o6bo\$o\$o\$b2obo11\$b2obo\$o\$o\$o6bo\$2bo4bo\$6bo\$3b3o
5\$3b3o\$6bo\$2bo4bo\$o6bo\$o\$o\$b2obo11\$b2obo\$o\$o\$o6bo\$2bo4bo\$6bo\$3b3o5\$3b
3o\$6bo\$2bo4bo\$o6bo\$o\$o\$b2obo11\$b2obo\$o\$o\$o6bo\$2bo4bo\$6bo\$3b3o5\$3b3o\$6b
o\$2bo4bo\$o6bo\$o\$o\$b2obo11\$b2obo\$o\$o\$o6bo\$2bo4bo\$6bo\$3b3o5\$3b3o\$6bo\$2bo
4bo\$o6bo\$o\$o\$b2obo!
``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

AforAmpere
Posts: 1052
Joined: July 1st, 2016, 3:58 pm

### Re: Superluminary orthogonal speeds

If someone can tame it, this will be a 32c/8:

Code: Select all

``````x = 14, y = 21, rule = R4,C0,M1,S0..0,B5..5,NM
2o\$2o\$2o\$2o\$2o3\$5b4o\$10b4o\$5b4ob4o\$5b4ob4o\$5b4ob4o\$10b4o\$5b4o3\$2o\$2o\$
2o\$2o\$2o!
``````
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

muzik
Posts: 3522
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Superluminary orthogonal speeds

Admittedly suboptimal and at the wrong period:

Code: Select all

``````x = 54, y = 63, rule = R4,C0,M1,S0..0,B5..5,NM
21bo5bo4\$16bo24bo\$16bo24bo\$o15bo24bo\$o15bo\$16bo25bo5bo\$9bo\$9bo\$9bo\$9bo
22bo20bo\$4bo32bo15bo\$6bo8bo21bo15bo\$37bo15bo\$53bo2\$20bo\$4bo15bo\$4bo15b
o21bo5bo\$4bo15bo\$20bo3\$42bo5bo\$9bo5bo3\$53bo\$37bo15bo\$37bo15bo\$37bo15bo
\$53bo3\$9bo5bo\$42bo5bo3\$20bo\$4bo15bo\$4bo15bo21bo5bo\$4bo15bo\$20bo2\$53bo\$
37bo15bo\$6bo8bo21bo15bo\$4bo32bo15bo\$9bo22bo20bo\$9bo\$9bo\$9bo\$16bo25bo5b
o\$o15bo\$o15bo24bo\$16bo24bo\$16bo24bo4\$21bo5bo!
``````
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

Bullet51
Posts: 543
Joined: July 21st, 2014, 4:35 am

### Re: Superluminary orthogonal speeds

AforAmpere wrote:If someone can tame it, this will be a 32c/8:

Code: Select all

``````code
``````
A 32c/8 is possible in this rule:

Code: Select all

``````x = 30, y = 26, rule = R4,C0,M1,S0..0,B5..5,NM
15bo5bo4\$o5bo19bo\$o5bo19bo\$26bo\$26bo\$26bo2\$10bo2\$13bo11bo\$o5bo10bo7bo\$
o5bo10bo9bo3\$29bo\$29bo\$29bo\$29bo\$29bo4\$18bo5bo!
``````
Still drifting.

AforAmpere
Posts: 1052
Joined: July 1st, 2016, 3:58 pm

### Re: Superluminary orthogonal speeds

6c/2:

Code: Select all

``````x = 14, y = 12, rule = R4,C0,M1,S7..9,B7..8,NM
2bo7bo\$12bo\$o\$13bo\$13bo\$13bo\$13bo\$13bo\$13bo\$o\$12bo\$2bo7bo!
``````
16c/4:

Code: Select all

``````x = 17, y = 24, rule = R4,C0,M1,S0..0,B5..5,NM
5bo5bo2\$o2\$16bo\$16bo\$16bo\$16bo\$o15bo7\$o15bo\$16bo\$16bo\$16bo\$16bo2\$o2\$5b
o5bo!
``````
Almost a 14c/4:

Code: Select all

``````x = 9, y = 13, rule = R4,C0,M1,S8..10,B7..9,NM
o\$4o\$5o\$6o\$8o\$9o\$9o\$9o\$8o\$6o\$5o\$4o\$o!
``````
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

AforAmpere
Posts: 1052
Joined: July 1st, 2016, 3:58 pm

### Re: Superluminary orthogonal speeds

7c/4:

Code: Select all

``````x = 10, y = 10, rule = R4,C0,M1,S7..8,B8..8,NM
3b3o\$o\$o8bo\$o8bo\$o8bo\$o8bo\$o8bo\$o8bo\$o\$3b3o!
``````
10c/4:

Code: Select all

``````x = 10, y = 10, rule = R4,C0,M1,S6..6,B8..8,NM
obo2bo\$bo7bo\$9bo\$9bo\$9bo\$9bo\$9bo\$9bo\$bo7bo\$obo2bo!
``````
15c/6:

Code: Select all

``````x = 10, y = 10, rule = R4,C0,M1,S5..6,B8..8,NM
obo2bo\$bo7bo\$9bo\$9bo\$9bo\$9bo\$9bo\$9bo\$bo7bo\$obo2bo!
``````
40c/16:

Code: Select all

``````x = 11, y = 10, rule = R4,C0,M1,S6..6,B8..8,NM
bobo2bo\$2bo7bo\$10bo\$o9bo\$10bo\$o9bo\$o9bo\$10bo\$10bo\$4bobo!
``````
45c/18:

Code: Select all

``````x = 11, y = 10, rule = R4,C0,M1,S7..7,B8..8,NM
3bo2bo\$2bo7bo\$bo8bo\$o9bo\$10bo\$10bo\$o9bo\$bo8bo\$2bo7bo\$3bo2bo!
``````
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

muzik
Posts: 3522
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Superluminary orthogonal speeds

Finally updated the OP with some more findings.

How long until someone finds a superluminary 3-cell ship?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

AforAmpere
Posts: 1052
Joined: July 1st, 2016, 3:58 pm

### Re: Superluminary orthogonal speeds

Smaller 5c/2:

Code: Select all

``````x = 11, y = 10, rule = R4,C0,M1,S7..7,B8..8,NM
3bo2bo\$2bo7bo\$10bo\$10bo\$10bo\$o9bo\$10bo\$bo8bo\$10bo\$4bobo!
``````
15 cells

6c/2:

Code: Select all

``````x = 14, y = 12, rule = R4,C0,M1,S7..9,B7..8,NM
2bo7bo\$12bo\$o\$13bo\$13bo\$13bo\$13bo\$13bo\$13bo\$o\$12bo\$2bo7bo!
``````
14 cells

8c/2:

Code: Select all

``````x = 15, y = 17, rule = R5,C0,M0,S6..8,B7..7,NM
bo7bo4\$12bo\$13bo\$o13bo\$14bo\$14bo\$14bo\$o13bo\$13bo\$12bo4\$bo7bo!
``````
15 cells

Smaller 5c/4:

Code: Select all

``````x = 9, y = 8, rule = R5,C0,M1,S31..43,B27..36,NM
2b3o\$b8o\$o3b5o\$o4b4o\$o4b4o\$o3b5o\$b8o\$2b3o!
``````
44 cells

6c/4:

Code: Select all

``````x = 5, y = 6, rule = R2,C0,M0,S4..4,B4..4,NM
b2o\$o3bo\$4bo\$4bo\$4bo\$obo!
``````
9 cells

8c/4:

Code: Select all

``````x = 10, y = 9, rule = R4,C0,M1,S4..6,B7..7,NM
8bo\$o\$9bo\$9bo\$9bo\$9bo\$9bo\$o\$8bo!
``````
9 cells

10c/4:

Code: Select all

``````x = 10, y = 10, rule = R4,C0,M1,S6..6,B8..8,NM
obo2bo\$bo7bo\$9bo\$9bo\$9bo\$9bo\$9bo\$9bo\$bo7bo\$obo2bo!
``````
16 cells

12c/4:

Code: Select all

``````x = 27, y = 25, rule = R3,C0,M0,S3..6,B4..4,NM
17bo3bo2\$17b2o6bo2\$26bo\$15bo10bo\$26bo\$4bo21bo\$17bo\$4bo19bo\$4bo\$4o13bo
4bo\$4o\$4o13bo4bo\$4bo\$4bo19bo\$17bo\$4bo21bo\$26bo\$15bo10bo\$26bo2\$17b2o6bo
2\$17bo3bo!
``````
46 cells

16c/4:

Code: Select all

``````x = 17, y = 13, rule = R5,C0,M0,S3..6,B9..9,NM
3bobo4bo2\$16bo\$16bo\$16bo\$16bo\$o15bo\$16bo\$16bo\$16bo\$16bo2\$3bobo4bo!
``````
16 cells

18c/4:

Code: Select all

``````x = 26, y = 20, rule = R5,C0,M0,S2..3,B8..8,NM
14bo3\$18bo\$21b2o2\$25bo\$25bo\$3o22bo\$25bo\$25bo\$3o22bo\$25bo\$25bo2\$21b2o\$
18bo3\$14bo!
``````
22 cells

Smaller 7c/5:

Code: Select all

``````x = 12, y = 13, rule = R5,C0,M1,S34..50,B29..38,NM
3bo\$4b2obo\$3b6o\$2b9o\$bo4b5o\$o7b4o\$o7b4o\$o7b4o\$bo4b5o\$2b9o\$3b6o\$4b2obo\$
3bo!
``````
65 cells
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

muzik
Posts: 3522
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Superluminary orthogonal speeds

Should we be trying to minimise the range for the rules that contain these? It seems to make more sense that we'd be looking for a 2c ship in a range-2 rule, rather than a range-5 one.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

AforAmpere
Posts: 1052
Joined: July 1st, 2016, 3:58 pm

### Re: Superluminary orthogonal speeds

muzik wrote:Should we be trying to minimise the range for the rules that contain these? It seems to make more sense that we'd be looking for a 2c ship in a range-2 rule, rather than a range-5 one.
That's way, way harder to find. I think just having Nc/1 ships for all N now is good for now.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)