User:AforAmpere/Day&Night

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This page is an equivalent to the Spaceship Search Status Page for Day & Night (B3678/S34678) instead of Life.

Known spaceships by width

Width is measured laterally; diagonal spaceships' widths are measured in half-diagonals, knightwises in third-knight-moves, etc.

Velocity Asymmetric Symmetric Gutter Glide-symmetric
odd even odd even
(1,0)c/2 8 9 10
(1,0)c/3 8 9 10
(1,1)c/3 9 9 21
13[n 1]
(1,0)c/4 9[n 2] 13 12[2]
(1,1)c/4 8 11 19 8[n 3]
(2,0)c/4 7 7 8 7 8
(1,0)c/5 9[n 4] 13[n 5] 12[n 6]
(1,1)c/5 9[n 7] 11[n 8] 21
(2,0)c/5 15[5] 19[n 9] 24[n 10]
(2,1)c/5 w ≤ 45
(1,0)c/6 9 13[n 11] 14[n 12]
(1,1)c/6 12[n 13] 15 17 14
(2,0)c/6 8[n 14] 9[n 15] 10[n 16] 9[n 17] 10
(2,1)c/6 w ≤ 45
(2,2)c/6 9 13 21
(3,0)c/6 9 9[n 18] 10[n 19]
(1,0)c/7 9 13 12[n 20]
(1,1)c/7 9 15[10] 15
(2,0)c/7 10 17[n 21] 16
(2,2)c/7 16 (llsss-ng)[n 22] 23[n 23] 21
(3,0)c/7 12
14 (llsss-ng)[n 24] 		23[n 25] 20[n 26]
(1,0)c/8 7 11 14[n 27]
(1,1)c/8 9[n 28] 15[n 29] 13 14[n 30]
(2,0)c/8 7 11 12[n 31] 11 10
(3,0)c/8 10 19 20
(4,0)c/8 8 9[n 32] 12[n 33] 9 10[n 34]
(1,0)c/9 6 13 14
(2,0)c/9 8 15 14
(3,0)c/9 7 11 10
(4,0)c/9 11 19 20
(1,0)c/10 6 11 12
(2,0)c/10 6 9 10 7 8
(3,0)c/10 8 13 14
(4,0)c/10 8 15 16 13 14
(5,0)c/10 8 9[n 35] 12
(1,0)c/11 6 9 12
(6,0)c/12 6 9 10 9 10
(2,0)c/14 5 5 8
5

non-orthogonal ships by orthogonal width and height

(width and height defined as being along the axis through which they move most slowly and quickly respectively)

Velocity Asymmetric Symmetric Glide
width height
(1,1)c/3 6 6
(1,1)c/4 8 11 8
(1,1)c/5 9[n 36] 16[n 37]
(2,1)c/5 16[n 38] 11
(1,1)c/6 9[n 39] < w ≤ 14 14 9
(2,1)c/6 12[18] 7
(2,1)c/7 10
(3,1)c/7 12
(2,1)c/8 8
(3,1)c/8 10
(3,1)c/9 9
(4,1)c/9 10
(4,1)c/10 9
x = 830, y = 171, rule = B3678/S34678 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#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 2560 HEIGHT 560 ZOOM 3 ]]
(click above to open LifeViewer)

Known spaceships by height

measured perpendicularly to travel direction; lower bounds determined by rlifesrc

Velocity Asymmetric Symmetric Glide-symmetric
odd even odd even
(1,0)c/2 5 4 < h ≤ 6 4 < h ≤ 6
(1,0)c/3 7[n 40] 7 7
(1,0)c/4 7[n 41] 8 8[19]
(1,1)c/4 7 7 8
(1,0)c/5 6 7 6
(2,0)c/5 10[n 42] 10 10
(1,1)c/5 9 9
(2,0)c/7 6 6 6
(3,0)c/7 7 7 7
(2,2)c/7 9 9

B1e2cn3acjkr4cny5einqy6ei7c/S01e2-ei3acjkr4-ejr5einqy6-cn7c8 (known chequercrawlers by width)

lower bounds found with qfind for orthogonals and rlifesrc for diagonals unless otherwise specified

Velocity Asymmetric Symmetric Glide-symmetric
odd even odd even
(1,0)c/1[20] 7 13 14
(1,0)c/2[20] 13[n 43] 25 24
(1,0)c/3 10 19 20
(1,1)c/3 19 25[n 44]
(1,0)c/4 10 19 20
(2,0)c/4 10 19 20 15 16
(1,1)c/4 17
18 (LLSSS) 		23[n 45] 28
(1,1)c/5 15 21
(1,1)c/6 13 19 18
(2,1)c/6
16 (ikpx2)
(1,1)c/8 9
(3,1)c/8
16 (ikpx2)
(1,0)c/11 6 11 12

Notes

  1. ↑ 51 cells, see also cool 55-cell w20a from [1] and the results by orthogonal width
  2. ↑ 97 cells; shortest w10a is 46 cells
  3. ↑ 61 cells; at w10glide is a 29-cell one, then at w12glide is a 24-cell one (which LLSSS proves is the smallest possible by minpop)
  4. ↑ also supports a tagalong
  5. ↑ 105 cells, first found in [3]
    is also the shortest at w15o, but beaten at w17o by the shortest possible c/5 (40 cells)
  6. ↑ 406 cells; also known as the totem pole; first known was longer variant found in [2]
    shortest at w14e is 116 cells, at w16e is 58 cells
  7. ↑ 83 cells, per gfind it is the unique w9a and per LLSSS it is also the shortest w10a; none at w11a in 21 × 21, a 104-cell one in 21 × 22
  8. ↑ 134 cells; smallest known symmetrical was formerly an 87-cell w17s from [4] until the discovery of the 46-cell unique 16 × 16 which happens to be w25s (shown in #non-orthogonal ships by orthogonal width and height)
  9. ↑ 365 cells; shortest w21o is 310, shortest w23o is 254, shortest w25o is 308
  10. ↑ first found in [6], 5008s to verify shortestness via LLSSS
    276 cells, [7] found the shortest w26e (as verified (in 5416s and 37.43GB RAM) by LLSSS) which is 164 cells
  11. ↑ shortest w15o is 81 cells, second-shortest is 93 (however its frontend has only one engine instead of two and its maxpop is only 1 greater)
  12. ↑ 250 cells; shortest w16e is 78
  13. ↑ 11 was disproven in [8]; after discovering it unexpectedly (two copies packed tightly into 32 × 32 bounding box), it took 95019s in rlifesrc to show that it is the unique w13a (as well as 12a) that can fit in a 18 × 18 bounding box
  14. ↑ 53 cells with a glide-symmetric p6 backend; AforAmpere originally included a 70-cell one with a fully asymmetric p6 backend; is shortest and smallest at w9 also
  15. ↑ 147 cells, shortest w11o is 115, shortest w13o is 149
  16. ↑ 110 cells, shortest w12e is 92, at w14e there are (in increasing order of height) 114, 108, 86
  17. ↑ 130 cells, shortest w11glide is 136
  18. ↑ 170 cells, shortest w11o is 64, shortest w13o is 92
  19. ↑ 56 cells, also shortest w12e, shortest w14e is 52
    see also this more interesting w10e
  20. ↑ found in [9], 380 cells; note shortest w14e is 174
  21. ↑ 1061 cells; shortest w19o is 273
  22. ↑ took a few weeks on-and-off and 206975773557 bytes of backups, longest partial (flattened width 180, population 385)
    previously, via rlifesrc: 537s for 13, 47573s for 15, longest partial:
    ........
    .........
    ..........
    ..oooo.oo..
    .o.oo.ooo...
    .ooo.....oo..
    .oo.ooo.o..oo.
    .o..ooooooo.oo.
     .....o.oo..o...
      ......oo.o.ooo.
       ....oo.oo..o.o.
        ...ooooooo.oo..
         ....o.o.ooooo..
          ...ooooooooo...
           ..oo...ooooo...
            .......ooo.o...
             ....o.ooooooo..
              .oo.oooooo.o...
               .o.o.ooooooo...
                .oo.ooooo..oooo
                 .oooooo........
                  .oooooo..oo.o..
                   oooo.oooo....o.
                    ...o.ooo..oo...
                     ..oooo..ooooo.o
                      ooo..o.o.oo.o.o
                       .oooo.ooo..ooo.
                        ....ooo.ooo...o
                         .oooooo.ooooo.o
                          ..o.oo.oo..oo.o
                           ...ooo.ooo?????
                            .oooo.o.o????
                             .o.o..oo???
                              ....o.o??
                               .oo????
                                .????
                                 ???
  23. ↑ w21s per rlifesrc,[8] formerly 19 with gfind[11]
    w23s partial (with rlifesrc also; 17498s):
    ..oo.oooo...
    .ooo.oooooo..
    oooo.o.ooo..o.
    ooo.o.ooooo.o..
    ...o.ooo.oooo...
    ooo.o.o.ooo.o....
    oo.ooo.oooo.......
    ooooo.oo...o...o...
    oooo.oo..oo.oo.oo...
    .oooooo.ooo..oooo....
    .o.oooo.oo.oo.........
    ....o..o..o.oo.ooo.....
     .oooo..o.oooooo.o......
      ......oo.oooo...o......
       ......o..oooo..........
        ...ooo.oo.o..ooo.oo....
         ...oo.o....o....oo.....
          .....oo..o.ooo..ooo....
           ......o.o.o.o.oo.o.....
            .......o.ooo.oo.ooo....
             .............o..oo.....
              .....oo.oo..o....ooooo.
               ....ooooooo..o..ooo.o..
                .....o......ooo.o.ooo..
                 ....ooo..oo...o.oo.oo..
                  .....oo..o..o.oo..ooo..
                   ....oo..o.o..oo........
                    .....oo.o..oo.o.oo.o...
                     ....ooo.ooooo.oo.oo....
                      ...oo.ooo.oooo..oo.....
                       ..o.oo..o.oooo.ooooo...
                        .ooo....oooo..o.oooo...
                         ..ooo.oo.o..o..ooo.o...
                          ..oo.o....o.oooo..o..o.
                           ..o..oooo.o.o.o....ooo.
                            ...oooo..ooo....o.ooo..
                             .....oooo..o.o..oo..oo.
                              ....ooooo..oo..o....o??
                               ...ooo...ooo..oo.oo.??
                                ...o.......oo..o..o??
                                 ...oo.o...o.ooo..o??
                                  ......ooo.oo.o..o??
                                   ...ooo.o.o....????
                                    .ooo...ooo.o.????
                                     .oo..o.....?????
                                      ..o.o...???????
                                       .oo.ooo???????
                                        .????????????
                                         ????????????
  24. ↑ longest partials were this thing and this thing, both 59 cells long
  25. ↑ 1013 cells, note there is a 676-cell w25o from [12]
    there is also a wickstretcher (with a spatial-period-3 wick) at w23o, from [8]
  26. ↑ 584 cells, found in [13]; meanwhile, shortest w22e is 316 cells, the smallest known of any symmetry
  27. ↑ 190 cells, found in [14]; first found was a 980-cell much longer w14e from [6] two days earlier
  28. ↑ proven with rlifesrc in 7 hours; longest partial:
    4ob2o$3o2bo$obo$2bo4bo$4bobob2o$5bobobo$5b2obobobo$10b3o$10b4o$11b2o$10bo$10b3o$11bo2bobo$13b2o2b2o$14bo2bo$18bobo$2
    0bo$18b4o$19bob2o$19b2obo$20bo3b3o$21b5o$21bobo3bo$21b3o3bo$25bob4o$26b5o$25bo2b4o$26b2o2b2o$27b2obo$27b4o$30bo$29bo!    ;
    before this, the entry said 6, which is slightly strengthened by ikpx2 to exclude logical width 6 in its floating rows metric
  29. ↑ w13s disproof took 1459s; see 288-cell largest partial
    none at w15s in 40 × 40, per 177785s search
    41 × 41; see also w15s in 43 × 43 which has the same front- and backend but phaseshifted
  30. ↑ 146 cellls; unique smallest that fits in 33 × 33 during one logical period (two phase-shifts were the only ones found in 56364s in rlifesrc)
    the first (841 cells; also at w14glide) was found by LuveelVoom in [15]; this one was very easy for Luveel to have found were he not to have delved so greedily and used a longer length to increase the plausibility of terminating
  31. ↑ has a small p8 tagalong
    is 340 cells, at w14e there is a 292-cell spaceship[16]
  32. ↑ minpop 224 cells, w11o is 150
  33. ↑ there is a shorter one at w14e that is full of antispace and so is higher-population, found in [17]
  34. ↑ LuveelVoom found that it supports this p4 tagalong
  35. ↑ 164 cells, at w11o the smallest is 97 cells with the same p10 backend
  36. ↑ at w10, there is this thing fitting in 10 × 30; none in 10 × 25 per 288564s exhaustive search
  37. ↑ unique!
    13 disproven in 1147s in rlifesrc, 14 in 4994s, 15 in 37555s, 16's only result found in 206687s and exhausted at 259656s
  38. ↑ it is easy to verify thinnestness; see longest partial at w14 (LLSSS, 378s), longest at w15 (LLSSS, 7901s)
  39. ↑ see largest (103-cell) partial at w8 (from LuveelVoom with rlifesrc), largest (221-cell) partial at w9 (determined by me with rlifesrc, in 353676s)
  40. ↑ at h=8, w>14
  41. ↑ widest partial
    oooo.......o.......................ooo.....oo.....oo...?
    .oo.ooo..oo.oo.....................oo.....oooo....ooooo?
    .o.ooo.o..oo.o.oo.oooo.......ooo..ooo.ooo..o.oo.ooooo..?
    ....o.oooo..oooo..o..o..ooooooo.o.oo.ooo....o...ooooo..?
    .....oo...oo.ooo.......oo.ooo..oo.....ooo.o...o....oo...
    .............o............o.o.o.......o.....o.....o..o..
    ........oo...........................................oo.
    the odd one is the only h=8 with w≤20
  42. ↑ rlifesrc search took 440158s; see largest partial
  43. ↑ first discovered was a w23a which is also height-11, found in [21]
  44. ↑ 618 cells; the other two w25s's within a 62 × 62 bounding box are internal variations (622 and 636 cells respectively)
    for w27s, a 413-cell 41 × 41 is the only one in a 42 × 42 bounding box

    the first two known were a 669-cell w25s and a 761-cell w27s from [22]
  45. ↑ none at w25s in 44 × 44; there are wickstretchers (ie. tunnel-borers) so a spaceship is probable
    back-to-front w25s search finds nothing in 68401s

References

  1. ↑ Saka (November 20, 2015). Re: Day & Night (B3678/S34678) , in which the first(?) known asymmetrical c/3d was found
  2. ↑ 2.0 2.1 Saka (February 10, 2017). Re: Day & Night (B3678/S34678) , in which the thinnest even c/4 and c/5 (longer variant of totem pole) were found
  3. ↑ Sphenocorona (February 26, 2014). Re: Day & Night (B3678/S34678) , in which the first c/5 was discovered at w13o
  4. ↑ C_R_116 (February 12, 2023). Re: Day & Night (B3678/S34678) , in which the former smallest known symmetric c/5d was found
  5. ↑ AforAmpere (February 20, 2020). Re: Day & Night (B3678/S34678) , in which the shortest 2c/5 at the thinnest width (w15a) was found
  6. ↑ 6.0 6.1 AforAmpere (December 12, 2017). Re: Day & Night (B3678/S34678) , in which the shortest w24e 2c/5 was found as well as the first c/8 (which was decidedly not shortest)
  7. ↑ 2718281828 (March 27, 2019). Re: Day & Night (B3678/S34678) , in which the shortest 2c/5 (at w26e and 164 cells) was found
  8. ↑ 8.0 8.1 8.2 DroneBetter (August 26, 2024). Re: Day & Night (B3678/S34678) , in which the existence of a 2c/7d at w21s and c/6d at w11a were disproven with rlifesrc, and Darcy Li's 3c/7 w23o search's wickstretcher and complete spaceship were exhibited
  9. ↑ velcrorex (November 12, 2016). Re: Day & Night (B3678/S34678) , in which the first and smallest w12e c/7 were respectively found
  10. ↑ velcrorex (June 16, 2015). Re: Day & Night (B3678/S34678) , in which the first c/7d was found at w15s
  11. ↑ praosylen (March 26, 2019). Re: Day & Night (B3678/S34678) , in which the existence of a 2c/7d at w19s was disproven with gfind
  12. ↑ May13 (February 10, 2023). Re: Day & Night (B3678/S34678) , in which various w25o 3c/7s were found (minimal minpop 676 cells)
  13. ↑ velcrorex (November 23, 2015). Re: Day & Night (B3678/S34678) , in which the first 3c/7 was found at w20e
  14. ↑ Sokwe (December 14, 2017). Re: Day & Night (B3678/S34678) , in which the shortest w14e c/8 (also the smallest known in general) was found
  15. ↑ LuveelVoom (May 31, 2025). Message in #naturalistic on the Conwaylife Lounge Discord server , which found the first c/8d (but laughably far from the minimal... yes indeed)
  16. ↑ velcrorex (July 2, 2015). Re: Day & Night (B3678/S34678) , in which a 292-cell w14e 2c/8 was discovered
  17. ↑ velcrorex (December 1, 2016). Re: Day & Night (B3678/S34678) , in which the first(?) 4c/8 was found
  18. ↑ AforAmpere (January 22, 2020). Re: Day & Night (B3678/S34678) , in which the first (2,1)c/6 was found at the minimum orthogonal width of 12
  19. ↑ AforAmpere (April 2, 2018). Re: Day & Night (B3678/S34678) , in which a height-8 even-symmetric c/4 was found (not sure of minimality)
  20. ↑ 20.0 20.1 LaundryPizza03 (March 11, 2025). Re: Day & Night (B3678/S34678) , in which the thinnest c and c/2 chequercrawlers at each symmetry were found
  21. ↑ LaundryPizza03 (March 10, 2025). Re: Day & Night (B3678/S34678) , in which the first (and shortest) c/2 chequercrawler was found
  22. ↑ wildmyron (June 14, 2018). Re: Day & Night (B3678/S34678) , in which the first c/3d chequercrawlers were found
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