User:AforAmpere/Day&Night

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< User:AforAmpere
Revision as of 13:03, 3 September 2024 by DroneBetter (talk | contribs) (various improvements to various bounds (and a few new positiive results!), fill in entries for missing speed-period combinations, add glide-symmetric columns, move the existing orthogonally-measured knightship results into table (to make first one's width metric consistently lateral), add tables of results by height as well as chequercrawlers, many notes and citations for existing results)
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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 13 12[2]
(1,1)c/4 8 11 19 8
(2,0)c/4 7 7 8 7 8
(1,0)c/5 9 13[3] 12[n 2]
(1,1)c/5 9[n 3] 11 21
(2,0)c/5 15 19 24
(2,1)c/5 w ≤ 45
(1,0)c/6 9 13 14
(1,1)c/6 11[4] 15 17 14
(2,0)c/6 8[n 4] 9[n 5] 10[n 6] 9[n 7] 10
(2,1)c/6 w ≤ 45
(2,2)c/6 9 13 21
(3,0)c/6 9 9[n 8] 10[n 9]
(1,0)c/7 9 13 12[5]
(1,1)c/7 9 15[6] 15
(2,0)c/7 10 17 16
(2,2)c/7 11 21[n 10] 21
(3,0)c/7 12 23[n 11] 20[9]
(1,0)c/8 7 11 14
(1,1)c/8 9[n 12] 11 13 12
(2,0)c/8 7 11 12[n 13] 11 10
(3,0)c/8 10 19 20
(4,0)c/8 8 9[n 14] 12 9 10
(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 15] 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 5 < w ≤ 10[n 16] 6
(1,1)c/4 8 11 8
(1,1)c/5 9 12
(2,1)c/5 16 11
(1,1)c/6 6 10 9
(2,1)c/6 12
(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 6[n 17] 7 7
(1,0)c/4 7[n 18] 8 8[11]
(1,1)c/4 7 7 7 < w ≤ 9
(1,0)c/5 6 7 6
(2,0)c/5 9 9 9
(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/2 10 19 20
(1,0)c/3 10 19 20
(1,1)c/3 19 25[n 19]
(1,0)c/4 10 19 20
(2,0)c/4 10 19 20 15 16
(1,1)c/4 17 23[n 20] 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. ↑ also known as the totem pole; first known was longer variant found in [2]
  3. ↑ 83 cells, per gfind it is the unique w9a; none at w11a in 21 × 21, a 104-cell one in 21 × 22
  4. ↑ 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
  5. ↑ 147 cells, shortest w11o is 115, shortest w13o is 149
  6. ↑ 110 cells, shortest w12e is 92, at w14e there are (in increasing order of height) 114, 108, 86
  7. ↑ 130 cells, shortest w11glide is 136
  8. ↑ 170 cells, shortest w11o is 64, shortest w13o is 92
  9. ↑ 56 cells, also shortest w12e, shortest w14e is 52
    see also this more interesting w10e
  10. ↑ per rlifesrc,[4] formerly 19 with gfind[7]
  11. ↑ 1013 cells, note there is a 676-cell w25o from [8]
    there is also a wickstretcher (with a spatial-period-3 wick) at w23o, from [4]
  12. ↑ 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
  13. ↑ has a small p8 tagalong
    is 340 cells, at w14e there is a 292-cell spaceship[10]
  14. ↑ minpop 224 cells, w11o is 150
  15. ↑ 164 cells, at w11o the smallest is 97 cells with the same p10 backend
  16. ↑ this is the only one (besides the butterfly) in 10 × 15, shortest w11 is 11 × 13, there are none in a 9 × 16 or 12 × 12 bounding box
  17. ↑ if h=7, w>44; if h=8, w>14
  18. ↑ 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
  19. ↑ 618 cells; the other two 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 [12]
  20. ↑ none at w25s in 44 × 44; there are wickstretchers so a spaceship is probable

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. ↑ 4.0 4.1 4.2 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
  5. ↑ velcrorex (November 12, 2016). Re: Day & Night (B3678/S34678), in which the first and smallest w12e c/7 were respectively found
  6. ↑ velcrorex (June 16, 2015). Re: Day & Night (B3678/S34678), in which the first c/7d was found at w15s
  7. ↑ praosylen (March 26, 2019). Re: Day & Night (B3678/S34678), in which the existence of a 2c/7d at w19s was disproven with gfind
  8. ↑ May13 (February 10, 2023). Re: Day & Night (B3678/S34678), in which various w25o 3c/7s were found (minimal minpop 676 cells)
  9. ↑ velcrorex (November 23, 2015). Re: Day & Night (B3678/S34678), in which the first 3c/7 was found at w20e
  10. ↑ velcrorex (July 2, 2015). Re: Day & Night (B3678/S34678), in which a 292-cell w14e 2c/8 was discovered
  11. ↑ AforAmpere (April 2, 2018). Re: Day & Night (B3678/S34678), in which a height-8 even-symmetric c/4 was found (not sure of minimality)
  12. ↑ wildmyron (June 14, 2018). Re: Day & Night (B3678/S34678), in which the first c/3d chequercrawlers were found
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