User:AforAmpere/HighLife: Difference between revisions

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Also no C/6 at w10a
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| style="background: #ffa0a0;" | 16
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| (2,0)c/7
| (2,0)c/7

Revision as of 01:41, 19 August 2026

where entries are bifurcated in twain vertically, the lower one is strict (must not be of a subsymmetry or comprised of disjoint objects)

diagonal spaceship speeds are measured in half-diagonal

Known spaceships by width

Velocity Asymmetric Symmetric Glide-symmetric
odd even odd even
(1,0)c/2 9[n 1] 17 20
(1,0)c/3 10[n 2] 15 12
(1,0)c/4 10[n 3] 15[n 4] 16[n 5]
(2,0)c/4 5 11 12 5[n 6] 12
10 15 18[n 7] 14[n 8]
(1,1)c/4 4 11 4[n 9]
10 13
(1,0)c/5 10[3] 17[3] 16
(2,0)c/5 12[n 10] 19[n 11] 22[n 12]
(1,1)c/5 11
12 (LLSSS)
15 < w ≤ 17
(rlifesrc)[n 13] 		27[n 14]
(1,0)c/6 10 17[7] 18[8]
(2,0)c/6 10 13[4] 16[5] 15[n 15] 12[n 16]
(3,0)c/6 9 17 18
(1,1)c/6 10[9]
13 (rlifesrc) 		19[9]
21 (rlifesrc)[n 17] 		22[9][10]
(1,0)c/7 9 17 18
(2,0)c/7 10[n 18] 19[11] 20[n 19]
(3,0)c/7 11 21 22
(1,1)c/7 11 (rlifesrc) 21 (rlifesrc)
(1,0)c/8 7 13 16[12]
(2,0)c/8 8 15 16 13 14
(3,0)c/8 10[13] 19[13] 20[13]
(4,0)c/8 8 15 18 13[n 20] 18
(1,1)c/8 6
9 (rlifesrc) 		11
15 (rlifesrc) 		12
14 (rlifesrc)
(1,0)c/9 7 13 14
(2,0)c/9 8[n 21] 15[n 22] 16[n 23]
(3,0)c/9 8 13 14
(4,0)c/9 10 19 20
(4,0)c/10 9 15 16 15 16
(5,0)c/10 8 15 14
(2,0)c/12 6 9 10 9 8
(4,0)c/12 7 13 14 9 8
(6,0)c/12 8 15 14 13 12
(1,0)c/98 w ≤ 25
x = 577, y = 96, rule = B36/S23 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#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 2920 HEIGHT 530 ZOOM 5 ]]
(click above to open LifeViewer)

Credits to Matthias Merzenich, Josh Ball and Arie Paap for some of these searches.

Known spaceships by height

using Matthias Merzenich's definition,

note that the 'strict' criterion from the lower subcells above pertains to all entries

Velocity Asymmetric Symmetric Glide-symmetric
odd even odd even
(1,0)c/2 10 10 10
(1,0)c/3 7[n 24] 7 7
(1,0)c/4 6[n 25] 7[14] 6[n 26] < w ≤ 9
(1,0)c/5 8[n 27] 8 8
(2,0)c/5 9[n 28] 9 9
(2,0)c/6 6 6 6 6 6
(3,0)c/6 7 7 7
(2,0)c/7 7[n 29] 7 < h ≤ 10 7
(3,0)c/7 8[n 30] 8 8
x = 98, y = 25, rule = B36/S23 9b3o3b2o20b3o32b4o$5b3ob3ob2o2b2obo12b3ob3ob3o24b3ob4ob3o$5bo3bobo8b2o11bo3bobo3bo24bo3bo2bo3bo$4b2obo5bo3bob2o11b2obo5bob2o22b2obo6bob2o$14b2o4b3o$2b3obo13bo9b3obo7bob3o18b3obo8bob3o$b2o20b3o3b2o15b2o16b2o16b2o$bo23bo3bo17bo16bo18bo$2o26b2o17b2o14b2o18b2o$25b2o2$4b2ob3o3b2o20b3ob3o27b3o4b3o$2b2obob3o2bo2bob3ob2obo6bo3bobobobo3bo10b3o6bo5b2o2b2o5bo6b3o$4bo2b2o2bo3bo5b2ob2o4bo2bobo5bobo2bo5bob2o3bob3obob2obo6bob2obob3obo3b2obo$b2o2bo5b2o4bobobobo2bo2b2o2b2o2bobo2b2o2b2o3b3o3bob2o3bobobob2o4b2obobobo3b2obo3b3o$bo5bo3b2o3b2obo5bo5b2o5bo5b2o4bo3bo3bobo2bo4bo2b6o2bo4bo2bobo3bo3bo$bobobo10bo14bo13bo5bo10b2o3bobo3b2o3bobo3b2o10bo$17bo14bo11bo2$25b3o7b2obob2o7b3o$26bo3b2ob3o2bo2b3ob2o3bo$28b3obobobobobobobob3o$32bo11bo$34bo7bo$34bo7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 840 HEIGHT 240 ZOOM 8 ]]
(click above to open LifeViewer)

Notes

  1. ↑ 46 cells, only other at w9a is a 48-cell backend variant
  2. ↑ found in [1], 43 cells; see also shortest w11a (40 cells), shortest w12a (40 cells, same frontend as the turtle)
  3. ↑ 84 cells, shortest/smallest w11a is 47 cells, both were first found in [2]
  4. ↑ 157 cells
    shortest/smallest w17o is 69 cells, w19o is 60, w27o is 43
  5. ↑ 168 cells
    shortest/smallest w18e is 124 cells, w20e is 32
  6. ↑ unique second-thinnest nontrivial (after xWSS's) is a width 11
  7. ↑ see https://catagolue.hatsya.com/census/xq4_wgkr996w699rkgzwonm03y030mnozk44c3buy0ub3c44kz0evgge968869eggvezxdt3fa44af3tdzy0ev5sws5ve/b36s23 (cannot be directly linked inline due to substring)
  8. ↑ 74 cells
    second-shortest w14 is 98 cells
  9. ↑ unique second-thinnest nontrivial is a width 14
  10. ↑ found in [5]; 160 cells and 12 × 62, shortest at w13a is 156 cells (13 × 55)
  11. ↑ shortest at w21o (and w23o) is thinner version of the w22e
  12. ↑ found in [6]; is also shortest w24e
  13. ↑
    the w17a is probably not at all minimal, since it filled up most of the 128 × 128 search region's length; however, note that it took 879 hours running in WASM on my laptop
    longest w15a partial:
    ........
    .........
    ..........
    ......ooo..
    ..oo..oo....
    .o..o........
    oo.oo...oo....
    .o.o....ooo....
     ooo.......o....
      .....oo..o.o...
       ...........o...
        ..oo...o.oo....
         o..o.oooo......
          o.o.ooo...o.o..
           ooo...o.o..o...
            .oo.oo.ooo.o...
             .........oooo..
              ..o.oooo..oo...
               .o.....o.oo..o.
                .....oo.ooooo..
                 ..oo..ooo..o.o.
                  ....o....oo..o.
                   ..ooo.oo.....o.
                    ...o.o...o..oo.
                     ..o.oo.o.o..ooo
                      ....ooo.....oo.
                       ...o....o...o..
                        ...o.oo........
                         ..o.....oooo...
                          .......ooo.oo.o
                           ....o....o.o.o.
                            ..ooooo...oo.??
                             oo.oo.oo..o???
                              .ooo.oo.o???
                               .....oo.??
                                .o.o...?
                                 o.ooo?
                                  .???
                                   ??
  14. ↑ found by Sokwe in 2010
    disproof of w25 was via 5561s rlifesrc search; longest partial:
    .............
    .......ooo....
    .....oo.oo.....
    .....oo.o.......
    ....o.o..........
    ..oo.o..oo...o....
    ..ooo..oo.o.oooo...
    .o....o.....oo..o...
    .ooo.oo.o.o....o.....
    .oo..o......o....o....
    ......o.o...oo..o..o...
    ...........oo...o..o....
    ......oo.ooo.......o.....
     ....ooo..o.........oo....
      ....o..........o....oooo.
       ...o.o........ooo.oo..oo.
        ...o..oo.....oo...o......
         ....o....ooo.oooo....o...
          .........ooo.oooo.o.o....
           ...ooo..o.oo..oo..ooo....
            .....o...oo....o..oo.....
             ....o.o.ooo.....ooo......
              ....ooo.oo...............
               ...o.....o.......ooo.....
                ..o...o.........oooo.....
                 .oo...o.o....o....oo....o
                  .o.ooooo...o.oooo.o..oo.o
                   ....ooo....oooo.ooooo....
                    .......oo.oo....oooo...o.
                     ......oo.oo.......o...oo.
                      .....oo.o........o...o..o
                       .....oo.o.......oo.....o.
                        .....oooo......o.....ooo.
                         ......oo.....oo.o.oo.o...
                          .....oo....o..oo.oo......
                           ...oooooooo....oo........
                            ..o....o..o....o.o.......
                             o.......oo...o..oo.......
                              o........o.ooo.o.o.o.o...
                               .ooo..oooo.oo.o...oo.oo..
                                .o...oo.......o.oo.......
                                 ...o...oooo...oooo..o.oo.
                                  oooo...o..o......o...oo..
                                   .o.....o..o..o.....oo....
                                    ........oo.o.....ooo.....
                                     .....oooo.........oo.....
                                      .....o.o......o..........
                                       ...o...o......oo.ooo.....
                                        ...o......o...oo.o..o....
                                         ..o.o..o..o....ooo.......
                                          .....oo..oo..oo.o......oo
                                           ..ooooo..o.o.o.oo.o..oo..
                                            .oo..o.o.ooo.o...o...o.o.
                                             ......ooo..o....oo.......
                                              .....o.ooo......o...o.o..
                                               ........o.....o.ooo.oo...
                                                ....o........o...oo...o..
                                                 ......ooo.oo..ooo.o.oo.o.
                                                  .......oo....oo...o....o.
                                                   ........o.ooo....ooo.o...
                                                    ...o...o.oo..oo.o........
                                                     .ooo..ooo..o....o........
                                                      o...o.o...o....o.....o...
                                                       .o..o.o........ooo.oo....
                                                        ..oo..ooo......ooo....ooo
                                                         ....o.o.oo..o..o..oo.o???
                                                          ..oo.o...o......o...o??
                                                           ........oo..o.o.o????
                                                            .o.o...ooo....o.???
                                                             .o.....o..o..oo??
                                                              .....o..o.oo.o?
                                                               ...oo.o.o.ooo
                                                                .....o.????
                                                                 ......???
                                                                  ..ooo??
                                                                   .o???
                                                                    o??
                                                                     ?
  15. ↑ 65 cells, next two shortest w15's are tagalongs of the w15o c/3, both at 287 cells despite considerable variation
  16. ↑ 94 cells, only other at w12 is a 102-cell variant with a longer and thinner backend
  17. ↑
    longest partial:
    ...........
    ......oo....
    ..oooo..o....
    ..ooo.o.......
    ..oo..o...oo.o.
    ..o..........o..
    .o.oo..o..ooo....
    .o....o.o..o.oo...
    ..o....o..o...oo.oo
    .........oo..ooo.oo.
    ....o.o.oo...ooo.....
     ...o.oo....oo.o......
      ....o....o.o.oo......
       .oo.o.oooo..oo..oo...
        ...oooo.....oo.......
         ...oooooo.......o.o..
          ......ooo...oo.o.o...
           .oo....o...o..oo.o...
            oo......oo...oooo....
             ....o..o.....o.o.....
              ...o.................
               ....oooo......oo.....
                .....ooo....oooo.....
                 ..oo.o....ooo..o.....
                  ...ooo..oo...oo......
                   ......ooo..o.oo......
                    .....oo..oo.o..o.oo..
                     .....o.o..o.o.ooo.oo.
                      .....oooo....o.......
                       ......o.o....oo.oo...
                        ..............oooo...
                         .....ooo.......o.....
                          .....o.o....oooooo...
                           ...oo.o....o...ooo..o
                            ..o...o.oo....o.oo.o.
                             ..o.oo.o.....o....o?
                              .o.oooo...o..o.oo.?
                               ...o.o....oo....o?
                                ....oooo.o.ooooo?
                                 ...oo..o.oo.oo??
                                  ...oo...o.????
                                   ...o.o.oo???
                                    ....o.oo??
                                     ooo.oo??
                                      .?????
  18. ↑ 9*40 partial (9-cell-wide phase of 10-cell-wide spaceship)
    5bo$4b3o$3b5o$3b5o$4bob2o$5b2o2$7bo$6b2o$5b4o$6bo$8bo$b2ob4o$b2o5bo$o$5bob2o$4b2o$5bob2o$2b2o3b2o$5bo$bobo3bo$2o2b
    3o2$4bo$5b2o$bo3b2o$4bo$2b3obo$3bobobo$3b2o2bo$2bo2bob2o$2bo5bo$2b3o$3o2b3o$3o$bo3bobo$3o2bo2bo$6bobo$5b3o$2bo2bo!
  19. ↑ 20*79 partial
    7b6o$5b2o2b2o2b2o$4bo3bo2bo3bo$2b3o10b3o$2b2obob6obob2o$bob2o10b2obo$2o4bo2b2o2bo4b2o$2bo3b2o4b2o3bo$5bo2bo2bo2bo2$4bo3bo2bo3bo$3b2o10b
    2o$6bo6bo$7b2o2b2o$3b2o10b2o$4b2o2bo2bo2b2o$6b8o$8bo2bo$4bob3o2b3obo$4bobobo2bobobo$3bo12bo$4b2o8b2o2$3bo2bo6bo2bo2$3bob2o6b2obo$4bo10b
    o3$3bo2bo6bo2bo$3bo2bo6bo2bo$3bo2bo6bo2bo$3bo2bo6bo2bo$4b5o2b5o$4bo10bo$5b2obo2bob2o$5b3o4b3o2$4bob3o2b3obo$4bo10bo$4bobo6bobo$7b2o2b2o
    2$6b8o$6b8o$7bo4bo$6b2o4b2o$8bo2bo$4b2o8b2o$3b3o3b2o3b3o$3bobo8bobo$3bo3b2o2b2o3bo$7bob2obo$7bo4bo2$5bo8bo$3bob2o2b2o2b2obo$3bo3bob2obo
    3bo$4b3o6b3o$7bob2obo$2b4o2bo2bo2b4o$2bobo3bo2bo3bobo$2bobobo6bobobo$2b2o3bo4bo3b2o$3bo3bo4bo3bo$3bo4bo2bo4bo$6b8o$2b5ob4ob5o$2b2o12b2o
    $4bo10bo$b2o14b2o$obo2b2o2b2o2b2o2bobo$2o4bo6bo4b2o$8bo2bo$3o4b2o2b2o4b3o$b2o4bo4bo4b2o$bobob2o6b2obobo$b2o2b2o6b2o2b2o$2bo3b2o4b2o3bo!
  20. ↑ 32 cells, only other one found by gfind at w13glide is this 40-cell variation
  21. ↑ 8*37 partial
    3b3o$2b2o$2bo2bo$2b3o$6bo$bo2b2o$bob2o2bo$o3bobo$4bobo$2bo2bo$3b4o$3bo$3b2o$2b2o$2bobo$2b3o2$5b2o$4b3o$6bo
    $5bo$2bo2bo$3b5o$3bo2b2o$3bob2o$2bob2o$2bob2o$b2ob2o$b2o$b2o$2bobo$3bob2o$5bo$2b2o3bo$bo5bo$2o3bo$3bobobo!
  22. ↑ 15*50 partial
    4b2o3b2o$3bo2bobo2bo$3bobo3bobo$3bo7bo$3bob5obo$4b7o$5b5o$3bo7bo$2bobo5bobo3$2b3o5b3o$3b3o3b3o2$3bobo3bobo$3b2o
    5b2o$2bo2bo3bo2bo$2bo9bo$b5o3b5o$ob2o7b2obo$obo9bobo$2bo9bo$2bo9bo$2bobo5bobo$2bo3b3o3bo$4b2o3b2o2$4bo5bo$4bo2b
    o2bo$3bo2bobo2bo$3b4ob4o$4bo2bo2bo$2b2o7b2o$b2o9b2o$bobobobobobobo$2bo2b5o2bo$5bobobo$4b3ob3o$5b5o$2o4b3o4b2o$
    bo11bo$2bob2o3b2obo$bobo2bobo2bobo$4b3ob3o$b3o2b3o2b3o$obo3b3o3bobo$2b2o2bobo2b2o$3b2o5b2o$2obo7bob2o$2ob9ob2o!
  23. ↑ 16*45 partial
    5bo4bo$4bob4obo$5bo4bo$3b4o2b4o$3b2o6b2o$4bobo2bobo$bo12bo$b2o10b2o$5bo4bo$5bo4bo$5bo4bo$5b2o2b2o$5bob2obo$4bo6bo$2b2o8b2o$3bob2o2b2obo$2b2ob2
    o2b2ob2o$3bo2bo2bo2bo$4b3o2b3o$4b3o2b3o2$3b3o4b3o$5bo4bo$3b2obo2bob2o$3bo8bo$7b2o$3bo8bo$3bo8bo$3bo3b2o3bo$b2o2bob2obo2b2o$b2ob3o2b3ob2o$3b10o
    $bo2bo6bo2bo$bo12bo$6b4o$2bo2b2o2b2o2bo$2bob2o4b2obo$3bo8bo$2b3obo2bob3o$6b4o$obo2b6o2bobo$5b2o2b2o$2bobobo2bobobo$obob2o4b2obobo$o4bob2obo4bo!
  24. ↑ is 7 cells high in all phases, whereas this one is 6 cells high in two
  25. ↑ if h=7, w>42; if h=8, w>14
  26. ↑ if h=7, w>74; if h=8, w>20
  27. ↑ specified part of widest rlifesrc partial at height 7
    ..o..oo.o........o........
    .oooo.....o......ooo...o.o
    o...o..o......oo...ooo.o..
    .o..o.oooo.oo.oooo...o....
    .....o.oo..oooo..o.oooooo.
    ........o.ooo.....oo..oooo
    ........o...o......o.....o
    and 8 (took 5 hours to disprove)
    ..........o...........o......o.......oo.
    .........oo.......o...o.o...o.oo.oo.ooo
    .oo......o.oo.....oo..o.o..oo..o.oo.oo
    .ooo.....oo.oo..oo..ooo..o.oo.o.oo....
    .oo.....ooo..o..o.oo.o.ooo..o......oo.
    ....oo..oo....oo.o.oo.....o.o....o..o.
    .....oooo...oo.oo.......o.o.oo..o...ooo
    .........................o...........oo.
  28. ↑ widest rlifesrc partial at height 9 (took 5 hours)
    ...........................
    ......o.....o.....ooo....o
    .....ooo...ooo...oo.o...oo.
    ...oo.o.o.o..o....o..ooooo.
    ..o.oooo.ooo..oooooo.oo....
    ..o..ooo..o..oooo.o....o..o.
    .o.oo.....o.oo.o....oooo.oo.
    ............o..o....oo.ooo..
    ............o.o...........o.
  29. ↑ widest rlifesrc partial at h7 (took 52 hours)
    ..ooooo.....o
    .....ooooooo.
    ..oooo.o..o.o
    .o.oo.ooooooo
    o..o....oooo.
    ....o.....ooooo
    o...........oo.
  30. ↑ widest rlifesrc partial at h8 (took 30 hours)
    ...........o....
    ..o.......ooo.oo
    .ooo....oo..o...
    .o.oo.ooooo.ooo
    .ooooo...o.o.o.
    ....o...o..ooo.
    .....o.....oooo
    ..............o

other such tables alike this

References

  1. ↑ 400spartans (April 30, 2020). Re: HighLife , in which the smallest c/3 (at w10a) was found
  2. ↑ velcrorex (April 23, 2018). Re: HighLife , in which the smallest c/4 w10a and w11a were found
  3. ↑ 3.0 3.1 Sokwe (April 24, 2018). Re: HighLife , in which the shortest minimal-width c/5's at w10a and w17o were found
  4. ↑ 4.0 4.1 praosylen (September 12, 2016). Re: HighLife , in which the smallest w13o 2c/6 (thinnest odd) was found, also seemingly the first 2c/6 in general
  5. ↑ 5.0 5.1 AforAmpere (April 23, 2018). Re: HighLife , in which the thinnest 2c/5 at w12a was found, and the thinnest even-symmetric 2c/6 (odd was a rediscovery, initially found in [4])
  6. ↑ velcrorex (April 23, 2018). Re: HighLife , in which the thinnest even-width 2c/5 at w22e was found, as well as a w21o from deduplicating its central column
  7. ↑ velcrorex (November 19, 2015). Re: Thread for Your Accidental Discoveries that Aren't in CGOL , in which the first c/6 was found at w17o
  8. ↑ AforAmpere (April 23, 2018). Re: HighLife , in which the second c/6 was found at w18e
  9. ↑ 9.0 9.1 9.2 apgoucher (May 31, 2021). Message in #naturalistic on the Conwaylife Lounge Discord server , in which c/6d's were disproven up to logical width 10
  10. ↑ LaundryPizza03 (September 1, 2023). Re: HighLife , in which the first true-period c/6d was found at w22glide (thinnest possible)
    the program used to find this wasn't stated, if it was ikpx2 it may not be the shortest example
  11. ↑ wildmyron (October 6, 2018). Re: HighLife , in which the first and only known 2c/7 was found at w19o (28 cells!)
  12. ↑ velcrorex (April 22, 2018). Re: HighLife , in which the first c/8 was found at w16e with zfind
  13. ↑ 13.0 13.1 13.2 LaundryPizza03 (November 16, 2021). Re: HighLife , in which 3c/8 spaceships of logical width ≤10 were disproven
  14. ↑ JP21 (September 26, 2020). Re: HighLife , in which the shortest possible c/4 was found at h7 (also only 43 cells, a record at the time)
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