User:AforAmpere/HighLife

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Revision as of 16:52, 3 August 2024 by DroneBetter (talk | contribs) (strengthen results, confirm minimality (both width and length) of 2c/6 w16e ("need confirmation"), 2c/6 to w10a (with positive result!), 2c/7 w10a and w16e, fill in missing multiplied periods (with positive results for 3c/6 w17o, 4c/8 w15o, w13glide (two LWSS pair tagalongs, much smaller than Life's w17glide) and w18glide) and diagonal speeds and add glide-symmetric columns (finding a 65-cell 2c/6 at w15glide), height table (which inadvertently led to finding a 32-cell c/4))
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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[1] 15 12
(1,0)c/4 10[n 2] 15 16
(2,0)c/4 5 11 12 5[n 3] 12
10 15 uy0ub3c44kz0evgge968869eggvezxdt3fa44af3tdzy0ev5sws5ve/b36s23 18 14[n 4]
(1,1)c/4 4 11 4[n 5]
10 13
(1,0)c/5 10[3] 17[3] 16
(2,0)c/5 12[5] 19 22[6]
(1,1)c/5 10 17 < w ≤ 27
(1,0)c/6 9 17[7] 18[8]
(2,0)c/6 10 13[4] 16[5] 15[n 6] 12[n 7]
(3,0)c/6 9 17 18
(1,1)c/6 10[9] 19[9] 22[9][10]
(1,0)c/7 9 15 16
(2,0)c/7 10[n 8] 19[11] 18[n 9]
(3,0)c/7 11 21 22
(1,0)c/8 7 13 16[12]
(2,0)c/8 7 13 14 13 12
(3,0)c/8 10[13] 19[13] 20[13]
(4,0)c/8 8 15 18 13[n 10] 18
(1,0)c/9 7 13 14
(2,0)c/9 8[n 11] 15[n 12] 16[n 13]
(3,0)c/9 8 13 14
(4,0)c/9 10 19 20
(4,0)c/10 9 15 16 13 14
(5,0)c/10 8 15 14
(6,0)c/12 8 13 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 14] 7 7
(1,0)c/4 6[n 15] 7[14] 6[n 16] < w ≤ 9
(1,0)c/5 6 6 6
(2,0)c/5 7 7 7
(2,0)c/6 6 6 6 6 6
(3,0)c/6 7 7 7
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. ↑ 84 cells, shortest/smallest w11a is 47 cells, both were first found in [2]
  3. ↑ unique second-thinnest nontrivial (after xWSS's) is a width 11
  4. ↑ 74 cells
    second-shortest w14 is 98 cells
  5. ↑ unique second-thinnest nontrivial is a width 14
  6. ↑ 65 cells, next two shortest w15's are tagalongs of the w15o c/3, both at 287 cells despite considerable variation
  7. ↑ 94 cells, only other at w12 is a 102-cell variant with a longer and thinner backend
  8. ↑ 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!
  9. ↑ 18*58 partial
    3b3o6b3o$3bobo6bobo$3b3o6b3o$4b2o6b2o2$5b2o4b2o3$2b3o8b3o$2bo2bo6bo2bo$b2o3bo4bo3b2o$2bob2o6b2obo$bob2o8b2obo$2b3o8b3o$5bo6bo$5bo6bo$2bo3b2o2b2o3bo$4
    b2o6b2o$5bobo2bobo$4bo3b2o3bo$2bobo8bobo$2bobo8bobo$2bobo8bobo$5b2o4b2o$6bo4bo$3bo2bo4bo2bo$3bo2bo4bo2bo$4b2o6b2o$4bo8bo$2bo3bo4bo3bo$2o4b6o4b2o$b2o4
    bo2bo4b2o$2bo12bo$2b3obo4bob3o$2b2obo6bob2o$3bobob4obobo$7bo2bo$bo5b4o5bo$2bo3bo4bo3bo$2b2ob2o4b2ob2o$4b10o$4b2o6b2o$7bo2bo$3bo3bo2bo3bo$3b2obo4bob2o
    $4b2o6b2o$2bo12bo$bo14bo$bob2o8b2obo$bob3o6b3obo$4b3o4b3o$4bob2o2b2obo$5o2bo2bo2b5o$3bo3bo2bo3bo$2ob4o4b4ob2o$3bo10bo$bobo2bo4bo2bobo$o3bobo4bobo3bo!
  10. ↑ 32 cells, only other one found by gfind at w13glide is this 40-cell variation
  11. ↑ 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!
  12. ↑ 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!
  13. ↑ 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!
  14. ↑ is 7 cells high in all phases, whereas this one is 6 cells high in two
  15. ↑ if h=7, w>42; if h=8, w>14
  16. ↑ if h=7, w>74; if h=8, w>20

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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